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This ebook was issued to Diane Massey, order #11560922926
...
Sh
Show graduate programs a more
d
complete picture of your potential for success
The ETS® Personal Potential Index (ETS® PPI) is a convenient, web-based tool that
collects feedback from evaluators you select to provide information about you on
personal qualities that graduate deans and faculty have told us are important for
success, including:
institutions of your choice
...
help graduate and business schools know you’re up to the challenge
...
ets
...
Unlawful distribution of this ebook is prohibited
...
This book is uniquely suited to help you
do your best on this challenging test
...
Use actual tests to sharpen your skills
and build your confidence
...
Experience test prep that
is as close to the actual test as you can get with the the POWERPREP®II,
Version 2
...
Download the free software at www
...
org/gre/
powerprep2/download
...
Practice with real
test questions created by the test makers
...
Learn valuable hints and tips that can help
you get your best score
...
Get the facts about the
test content and structure—straight from ETS
...
ETS serves individuals, educational institutions, and government agencies by providing customized solutions for teacher certification, English language learning, and elementary, secondary, and post-secondary
education, as well as conducting education research, analysis, and policy studies
...
For more information, visit www
...
org
...
Unlawful distribution of this ebook is prohibited
...
Unlawful distribution of this ebook is prohibited
...
POWERPREP II software is available for individuals planning to take
the computer-based GRE revised General Test, and the Practice Book for the Paper-based
GRE revised General Test is available for individuals planning to take the paper-based test
...
, that is included in the free test preparation is also included in
this Guide
...
For more information about the GRE revised General Test, free and low-cost
GRE test preparation materials, and other GRE products and services,
please visit the GRE website at
www
...
org/gre
Inquiries concerning the practice test questions in this book
should be sent to the GRE testing program at
GRETestQuestionInquiries@ets
...
Unlawful distribution of this ebook is prohibited
...
Unlawful distribution of this ebook is prohibited
...
Unlawful distribution of this ebook is prohibited
...
All rights reserved
...
ISBN: 978-0-07-179121-2
MHID: 0-07-179121-3
The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-179123-6,
MHID: 0-07-179123-X
...
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fashion only, and to the bene t of the trademark owner, with no intention of infringement of the trademark
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McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs
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com
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THE PRAXIS SERIES and
SCORESELECT are trademarks of ETS
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(“McGraw-Hill”) and its licensors reserve all rights in and to the work
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Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the
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Under no circumstances
shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to
use the work, even if any of them has been advised of the possibility of such damages
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This ebook was issued to Diane Massey, order #11560922926
...
Contents
1
How to Use This Book / Software Package
...
1
Structure and Content of the Test
...
4
Test-taking Strategies for the Computer-based Test
...
6
Understanding GRE Scoring
...
11
Preparing for the Analytical Writing Measure
...
12
Analyze an Issue Task
...
25
GRE Scoring Guide: Analyze an Issue
...
39
Score Level Descriptions
...
43
Verbal Reasoning Question Types
...
Unlawful distribution of this ebook is prohibited
...
Discrete Questions: Easy
...
Reading Comprehension Questions: Easy
...
Discrete Questions: Medium
...
Reading Comprehension Questions: Medium
...
Discrete Questions: Hard
...
Reading Comprehension Questions: Hard
...
75
Answers and Explanations
...
107
Quantitative Reasoning Question Types
...
129
Mathematical Conventions for the Quantitative Reasoning Measure
of the GRE revised General Test
...
Discrete Questions: Easy
...
Discrete Questions: Medium
...
Discrete Questions: Hard
...
Data Interpretation Sets
...
164
Answers and Explanations
...
Unlawful distribution of this ebook is prohibited
...
Arithmetic
...
Algebra
...
Geometry
...
Data Analysis
...
304
Section 2: Analytical Writing
...
309
Section 4: Verbal Reasoning
...
329
Section 6: Quantitative Reasoning
...
345
Answer Key
...
351
Analytical Writing Sample Responses and Reader Commentaries
...
353
Section 2: Analyze an Argument
...
367
Section 3: Verbal Reasoning
...
381
Section 5: Quantitative Reasoning
...
413
This ebook was issued to Diane Massey, order #11560922926
...
9
GRE ® Practice Test 2
431
Section 1: Analytical Writing
...
434
Section 3: Verbal Reasoning
...
446
Section 5: Quantitative Reasoning
...
464
Evaluating Your Performance
...
475
Score Conversion Table
...
481
Section 1: Analyze an Issue
...
489
Answers and Explanations
...
496
Section 4: Verbal Reasoning
...
527
Section 6: Quantitative Reasoning
...
Unlawful distribution of this ebook is prohibited
...
The book and software will help you:
b
b
b
b
b
Familiarize yourself with the test format and the test question types
Identify the test-taking skills you most need to focus on
Review the math topics you need to know for the test
Check your progress with Verbal Reasoning and Quantitative Reasoning
practice questions
Practice your test-taking skills using actual GRE tests
The following six-step program has been designed to help you make the best use of this
book and software
...
Read this chapter to learn about the different test sections, the
number of questions in each section, and the section time limits
...
STEP 2 Study the Different GRE Question Types
Chapters 2, 3, and 5 of this book describe the types of questions you’ll encounter in
the three sections of the GRE revised General Test
...
Chapter 3 describes the Verbal Reasoning question types
...
In each case, you will learn what
the questions are designed to measure, and you will get tips for answering each question type
...
STEP 3 Practice Answering GRE Verbal and Quantitative Reasoning
Questions
Chapters 4 and 6 offer sets of practice Verbal Reasoning and Quantitative Reasoning
questions in the format of the GRE revised General Test
...
Answer
the questions in each set, then read through the explanations to see which test topics
you found most challenging
...
Did specific question formats give you
trouble? When did you need to guess at the answer? Use your results to identify your
weaknesses and to sharpen your test-taking skills
...
Unlawful distribution of this ebook is prohibited
...
The Tool also contains the Help screens,
the Review screen, the word-processing software for the Analytical Writing section, and
the on-screen calculator, so that you can become familiar with all of the features of the
computer-based GRE revised General Test
...
You do not necessarily need to tackle every topic in
the review, or to work through the review in the order in which it is presented
...
Each section of the review ends with practice problems that you can use to see how
well you have mastered the material
...
STEP 6 Take the Practice Tests
Once you have completed your review, get ready for the real exam by taking the
authentic GRE Practice Tests in Chapters 8 and 9 of this book and in the POWERPREP®II software
...
If
you are taking one of the tests in Chapters 8 and 9, sit in a quiet space, time yourself,
and work through as much of the test as time allows
...
You’ll gain experience
with the test format, and you’ll learn to pace yourself so that you can earn your highest
score in the time allowed
...
ets
...
This ebook was issued to Diane Massey, order #11560922926
...
1
About the GRE ®
revised General Test
Your goal
for this
chapter
g Review basic information on the structure of the
test, test preparation, and scoring
Introduction
T
he GRE® revised General Test—the most widely accepted graduate admissions
test worldwide—measures verbal reasoning, quantitative reasoning, critical
thinking, and analytical writing skills that are necessary for success in graduate
and business school
...
Applicants come from varying educational and cultural backgrounds, and the GRE revised General Test provides a common measure for
comparing candidates’ qualifications
...
The GRE revised General Test is available at about 700 test centers in more than
160 countries
...
In Mainland China, Hong Kong, Taiwan, and
Korea, the computer-based test is available one to three times per month
...
For the most up-to-date information about the GRE revised General Test, visit the
GRE website at www
...
org/gre
...
Unlawful distribution of this ebook is prohibited
...
b
The Analytical Writing section measures the ability to articulate and support
complex ideas, examine claims and accompanying evidence, sustain a focused
and coherent discussion, and control the elements of standard written English
...
b
The Verbal Reasoning section measures your ability to analyze and evaluate
written material and synthesize information obtained from it; understand the
meanings of words, sentences, and entire texts; and understand relationships
among words and among concepts
...
b
The Quantitative Reasoning section measures your basic mathematical skills
and your understanding of the elementary mathematical concepts of arithmetic, algebra, geometry, and data analysis
...
The Computer-based GRE revised General Test
Typical Test Structure
Measure
Number of Questions
Allotted Time
Analytical Writing
One “Analyze an Issue” task and
one “Analyze an Argument” task
30 minutes per
task
20 questions per section
30 minutes per
section
20 questions per section
35 minutes per
section
Unscored* (Position varies)
Varies
Varies
Research** (At the end
of the test)
Varies
Varies
(One section with two
separately timed tasks)
Verbal Reasoning
(Two sections)
Quantitative Reasoning
(Two sections)
* An unidentified, unscored section that does not count toward a score may be included and may
appear in any order after the Analytical Writing section
...
** An identified research section may be included in place of the unscored section
...
Questions in this section are included for ETS
research purposes and will not count toward your score
...
Unlawful distribution of this ebook is prohibited
...
The Verbal Reasoning, Quantitative Reasoning, and unidentified/unscored sections may appear in any
order; therefore, you should treat each section as if it counts toward your score
...
The
directions at the beginning of each Verbal Reasoning and Quantitative Reasoning section specify the total number of questions in the section and the time allowed for the
section
...
Test Design Features
The Verbal Reasoning and Quantitative Reasoning measures of the computer-based
GRE revised General Test are section-level adaptive
...
Additionally, the design of the revised test features advanced technology that allows
you to freely move forward and backward throughout an entire section
...
Total testing time is approximately 3 hours and 30 minutes
...
Test Design Features
b
b
Answers are entered into the test book, rather than a separate answer sheet
...
Information about
using the calculator to help you answer questions appears in the free Practice
Book for the Paper-based GRE revised General Test, which is available at
www
...
org/gre/prepare
...
Unlawful distribution of this ebook is prohibited
...
At a minimum, before you take the
GRE® revised General Test, you should know what to expect from the test, including
the administrative procedures, types of questions and directions, approximate number
of questions, and amount of time for each section
...
You can find out about the administrative procedures for
the revised General Test in the GRE® Information and Registration Bulletin, which is
available at www
...
org/gre/bulletinandforms
...
In this publication, you’ll find information specific to
each measure of the test
...
It is also important to spend some time preparing for the Analytical Writing section
by reviewing the skills measured, scoring guides and score level descriptions, sample
topics, scored sample essay responses, and reader commentary
...
This
software contains the following functionality: insert text, delete text, cut and paste, and
undo the previous action
...
It is important to budget your time
...
Although GRE readers understand the time constraints under which
you write and will consider your response a first draft, you will still want to produce
the best possible example of your writing
...
Although an occasional typographical, spelling, or grammatical error will not affect
your score, severe or persistent errors will detract from the overall effectiveness of your
writing and lower your score
...
Some require you to select a single answer choice; others
require you to select one or more answer choices, and yet others require you to enter
a numeric answer
...
Unlawful distribution of this ebook is prohibited
...
An on-screen calculator will be provided at the test center for use
during the Quantitative Reasoning sections
...
The testing software has a “mark and review” feature that enables you to mark questions you would
like to revisit during the time provided to work on that section
...
Additionally, you can review questions you’ve already
answered and change your answers, provided you still have time remaining to work on
that section
...
The review screen is
intended to help you keep track of your progress on the test
...
Your Verbal Reasoning and Quantitative Reasoning scores will be determined by
the number of questions you answer correctly
...
Therefore, to maximize your scores on the Verbal
Reasoning and Quantitative Reasoning measures, it is best to answer every question
...
Since no question carries
greater weight than any other, do not waste time pondering individual questions you
find extremely difficult or unfamiliar
...
Then go back and answer the questions that require greater thought,
concluding with the difficult questions if you have time
...
Once you have completed a
section, you may not go back to it
...
Unlawful distribution of this ebook is prohibited
...
You can replenish
your supply of scratch paper as necessary throughout the test by asking the test
administrator
...
You might want to replenish your supply of scratch paper during a scheduled break
...
Test-taking Strategies for the Paper-based Test
Analytical Writing Sections
In the paper-based revised General Test, the topics in the Analytical Writing measure
will be presented in the test book, and you will handwrite your essay responses in the
test book in the space provided
...
Within the 30-minute time limit for each section, you’ll need to allow sufficient time to think about the topic, plan a response, and
compose your essay
...
Save a few minutes at the end of each timed section to check for obvious errors
...
During the actual administration of the revised General Test, you may work only on
the particular writing section the test center supervisor designates and only for the
time allowed
...
The supervisor is authorized to dismiss
you from the center for doing so
...
Some require you to select a single answer choice; others require
you to select one or more answer choices, and yet others require you to enter a
numeric answer
...
A calculator will be provided at the test center for use during the
Quantitative Reasoning sections
...
Also during
that time you may change the answer to any question in that section by erasing it completely and filling in an alternative answer
...
Unlawful distribution of this ebook is prohibited
...
You can, however,
safely make notes or perform calculations on other parts of the page
...
Your Verbal Reasoning and Quantitative Reasoning scores will be determined by
the number of questions you answer correctly
...
Therefore, to maximize your scores on the Verbal
Reasoning and Quantitative Reasoning measures, it is best to answer every question
...
Since no question carries
greater weight than any other, do not waste time pondering individual questions you
find extremely difficult or unfamiliar
...
Then go back and answer the questions that require greater thought, concluding with the difficult questions if you have time
...
You
may not go back to an earlier section of the test after the supervisor announces, “Please
stop work” for that section
...
All answers must be recorded in the test book
...
Understanding GRE Scoring
Analytical Writing Measure
For the Analytical Writing measure, each essay receives a score from two readers using
a six-point holistic scale
...
If the two scores differ by more than one point on the scale, the discrepancy is adjudicated by a third
GRE reader
...
The final scores on the two essays are then averaged and rounded to the nearest
half-point interval on the 0–6 score scale
...
The primary emphasis in scoring the Analytical Writing section is on
your critical thinking and analytical writing skills
...
ets
...
The GRE Program plans to implement e-rater® scoring technology in the scoring
process for the Analytical Writing measure of the computer-based GRE® revised
General Test
...
When e-rater scoring is implemented, information about it
will be available on the GRE website at www
...
org/gre/scores/how
...
Unlawful distribution of this ebook is prohibited
...
In light of the high value placed on independent intellectual
activity within graduate schools and universities, ETS reserves the right to cancel test
scores of any test taker when an essay response includes any of the following:
b
Text that is unusually similar to that found in one or more other GRE essay
responses
b
Quoting or paraphrasing, without attribution, language that appears in published or unpublished sources
b
Unacknowledged use of work that has been produced through collaboration
with others without citation of the contribution of others
b
Essays submitted as work of the test taker that appear to have been borrowed
in whole or in part from elsewhere or prepared by another person
When one or more of the above discrepancies occurs, ETS may conclude, in its
professional judgment, that the essay response does not reflect the independent writing
skills that this test seeks to measure
...
Verbal Reasoning and Quantitative Reasoning Measures
of the Computer-based Test
For the Verbal Reasoning and Quantitative Reasoning measures of the computer-based
GRE revised General Test, the reported scores are based on the number of correct
responses to the questions included in the operational sections of the measure
...
This means the computer selects the second section of a measure based on your
performance on the first section
...
For each of the two measures, a raw score is computed
...
The raw score is then converted to a scaled score through a process known as
equating
...
Thus a given
scaled score for a particular measure reflects the same level of performance regardless
of which second section was selected and when the test was taken
...
First a raw score is computed for each measure
...
The Verbal Reasoning and Quantitative Reasoning raw scores are then converted to
scaled scores through a process known as equating
...
Unlawful distribution of this ebook is prohibited
...
Thus, a given scaled
score for a particular measure reflects the same level of performance regardless of
which edition of the test was taken
...
Descriptions of the analytical writing abilities characteristic of particular score
levels are available in this publication on page 41, and on the GRE website at www
...
org/gre/awscoredescriptions
...
This option lets you decide which test scores to send to
the institutions you designate
...
After test day, you can send scores from your Most Recent, All, or Any
specific test administration(s) for a fee when ordering Additional Score Reports
...
For more
information, visit www
...
org/gre/scoreselect
...
Scores from paper-based administrations are reported within six weeks after the test date
...
For more information on score reporting, visit the GRE website at www
...
org/gre
/scores/get
...
Unlawful distribution of this ebook is prohibited
...
Unlawful distribution of this ebook is prohibited
...
It assesses your ability to articulate and support complex ideas,
construct and evaluate arguments, and sustain a focused and coherent discussion
...
The Analytical Writing measure consists of two separately timed analytical writing
tasks:
b
a 30-minute “Analyze an Issue” task
b
a 30-minute “Analyze an Argument” task
The Issue task presents an opinion on an issue of broad interest followed by specific instructions on how to respond to that issue
...
The Argument task presents a different challenge from that of the Issue task: it
requires you to evaluate a given argument according to specific instructions
...
The two tasks are complementary in that one requires you to construct your own
argument by taking a position and providing evidence supporting your views on the
issue, whereas the other requires you to evaluate someone else’s argument by assessing
its claims and evaluating the evidence it provides
...
Unlawful distribution of this ebook is prohibited
...
It
is important to review the skills measured and how the section is scored
...
The tasks in the Analytical Writing measure relate to a broad range of subjects —
from the fine arts and humanities to the social and physical sciences — but no task
requires specific content knowledge
...
b
The task elicited the kinds of complex thinking and persuasive writing that university faculty consider important for success at the graduate level
...
To help you prepare for the Analytical Writing measure, the GRE Program has published the entire pool of tasks from which your test tasks will be selected
...
You can view the published
pools at www
...
org/gre/awtopics
...
Within the 30-minute time limit for the
Issue task, you will need to allow sufficient time to consider the issue and
the specific instructions, plan a response, and compose your essay
...
Although GRE readers understand the time constraints under which you write and will consider your response a first draft,
you still want it to be the best possible example of your writing that you can
produce under the testing conditions
...
Although an occasional spelling or grammatical error will not affect your score,
severe and persistent errors will detract from the overall effectiveness of your
writing and thus lower your score
...
Unlawful distribution of this ebook is prohibited
...
Each issue topic makes a claim that test takers can discuss from
various perspectives and apply to many different situations or conditions
...
Your task is to present a compelling case
for your own position on the issue according to the specific instructions
...
Then, make notes about the position you want to develop
and list the main reasons and examples that you could use to support that position
...
Each task is accompanied by one of the following sets of instructions
...
In developing and supporting your position, you should consider ways in which
the statement might or might not hold true and explain how these considerations shape your position
...
In developing and supporting your position, describe specific circumstances in which adopting the recommendation would or would not be
advantageous and explain how these examples shape your position
...
In developing and supporting your position, be sure to
address the most compelling reasons and/or examples that could be used to
challenge your position
...
In
developing and supporting your position, you should address both of the views
presented
...
b
Write a response in which you discuss your views on the policy and explain
your reasoning for the position you take
...
The GRE readers scoring your response are not looking for a “right” answer — in
fact, there is no correct position to take
...
13
This ebook was issued to Diane Massey, order #11560922926
...
GRE Analytical Writing
Understanding the Context for Writing: Purpose and Audience
The Issue task is an exercise in critical thinking and persuasive writing
...
Your audience consists of GRE readers who are carefully
trained to apply the scoring criteria identified in the scoring guide for the Analyze an
Issue task (see pages 37–38)
...
The sample responses, particularly at the 5 and 6 score levels, will show you a
variety of successful strategies for organizing, developing, and communicating a persuasive argument
...
For each response, the reader commentary points out aspects
that are particularly persuasive as well as any that detract from the overall effectiveness
of the essay
...
Many college textbooks on composition offer advice on persuasive writing and
argumentation that you might find useful, but even this advice might be more technical and specialized than you need for the Issue task
...
Suppose, for instance, that an Issue topic asks you to consider a policy that would require government financial support for art museums and
the implications of implementing the policy
...
On the other hand, if your position is that government should not
support museums, you might point out that, given limited governmental funds, art
museums are not as deserving of governmental funding as are other, more socially
important, institutions, which would suffer if the policy were implemented
...
It
is not your position that matters so much as the critical thinking skills you display in
developing your position
...
There is no “best” approach: some people prefer to start practicing
without regard to the 30-minute time limit; others prefer to take a “timed test” first and
practice within the time limit
...
Unlawful distribution of this ebook is prohibited
...
The most
successful responses will explore the complexity of the claim and instructions
...
Ask yourself:
b
What reasons might someone use to refute or undermine my position?
b
How should I acknowledge or defend against those views in my essay?
To plan your response, you might want to summarize your position and make brief
notes about how you will support the position you’re going to take
...
Then write
a response developing your position on the issue
...
After you have practiced with some of the topics,
try writing responses to some of the topics within the 30-minute time limit so that you
have a good idea of how to use your time in the actual test
...
Try to determine how each paper meets or misses the criteria for each score
point in the guide
...
15
This ebook was issued to Diane Massey, order #11560922926
...
GRE Analytical Writing
The Form of Your Response
You are free to organize and develop your response in any way that you think will effectively communicate your ideas about the issue and the instructions
...
GRE readers will not be looking for a particular developmental strategy or mode of writing; in fact, when GRE readers are
trained, they review hundreds of Issue responses that, although highly diverse in content and form, display similar levels of critical thinking and persuasive writing
...
They will see others that lead into the writer’s position by making
a prediction, asking a series of questions, describing a scenario, or defining critical
terms in the quotation
...
Look at the sample
Issue responses, particularly at the 5 and 6 score levels, to see how other writers have
successfully developed and organized their arguments
...
What matters is not the number of
examples, the number of paragraphs, or the form your argument takes but, rather, the
cogency of your ideas about the issue and the clarity and skill with which you communicate those ideas to academic readers
...
Discuss the extent to which you agree or disagree with the statement and explain
your reasoning for the position you take
...
Strategies for This Topic
In this task, you are asked to discuss the extent to which you agree or disagree with the
statement
...
You are also instructed to explain
your reasoning and consider ways in which the statement might or might not hold
true
...
Although this topic is accessible to respondents of all levels of ability, for any
response to receive a top score, it is particularly important that you remain focused on
the task and provide clearly relevant examples and/or reasons to support the point of
view you are expressing
...
For example, a respondent who strongly disagrees with the statement may choose
16
This ebook was issued to Diane Massey, order #11560922926
...
GRE Analytical Writing
to use computer technology as proof that thinking ability is not deteriorating
...
To receive a higher-level
score, the respondent should explain in what ways computer technology may call for or
require thinking ability
...
” Although most respondents may take it to mean problem solving, others, with
equal effectiveness, could interpret it as emotional and social intelligence (i
...
, the ability to communicate/connect with others)
...
You may agree with the prompt and argue that:
b
reliance on technology leads to dependency; we come to rely on problemsolving technologies to such a degree that when they fail, we are in worse shape
than if we didn’t have them in the first place
b
everyday technologies such as calculators and cash registers have decreased
our ability to perform simple calculations, a “use it or lose it” approach to
thinking ability
Or you may take issue with the prompt and argue that technology facilitates and
improves our thinking skills, arguing that:
b
developing, implementing, and using technology requires problem solving
b
technology frees us from mundane problem solving (e
...
, calculations) and
allows us to engage in more complex thinking
b
technology provides access to information otherwise unavailable
b
technology connects people at a distance and allows them to share ideas
b
technology is dependent on the human ability to think and make choices (every
implementation of and advance in technology is driven by human intelligence
and decision making)
On the other hand, you could decide to explore the middle ground in the debate
and point out that while technology may diminish some mental skill sets, it enables
other (perhaps more important) types of thinking to thrive
...
e
...
Other approaches could include
taking a historical, philosophical, or sociological stance, or, with equal effectiveness,
using personal examples to illustrate a position
...
e
...
Again, it is important for you to avoid overly general examples, or lists of examples
without expansion
...
Please
keep in mind that what counts is the ability to clearly express a particular point of view
in relation to the issue and specific task instructions and to support that position with
relevant reasons and/or examples
...
Unlawful distribution of this ebook is prohibited
...
Surely there has been no time in history where the
lived lives of people have changed more dramatically
...
Most people commute to
work in an automobile that runs on an internal combustion engine
...
09 microns wide
...
Each of these common occurences would have been inconceivable
at the turn of the 19th century
...
The assumption is that an increased reliance
on technology negates the need for people to think creatively to solve previous
quandaries
...
Technology short
circuits this thinking by making the problems obsolete
...
The prior examples reveal that technology allows for
convenience
...
This efficiency does not preclude the need for humans to think for
themselves
...
For example, the
proliferation of automobiles has introduced a need for fuel conservation on a global
scale
...
Likewise
dependence on oil has created nation-states that are not dependent on taxation,
allowing ruling parties to oppress minority groups such as women
...
In contrast to the statement, we can even see how technology frees the human
imagination
...
WebMD, a popular internet portal for
medical information, permits patients to self research symptoms for a more informed
doctor visit
...
With increased interdisciplinary interactions, inspiration can
arrive from the most surprising corners
...
The unlikely marriage of economics and medicine has healed tense, hyperinflation
environments from South America to Eastern Europe
...
By increasing our reliance on technology, impossible goals
can now be achieved
...
This disease had ravaged the human race since prehistorical
days, and yet with the technology of vaccines, free thinking humans dared to imagine a
*All responses in this publication are reproduced exactly as written, including errors, misspellings, etc
...
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GRE Analytical Writing
world free of smallpox
...
Technology will always mark the human experience, from the discovery of fire to the
implementation of nanotechnology
...
There is no
need to retreat to a Luddite attitude to new things, but rather embrace a hopeful
posture to the possibilities that technology provides for new avenues of human
imagination
...
The
essay cogently argues that technology does not decrease our ability to think for ourselves
...
” In fact,
the problems that have developed alongside the growth of technology (pollution, political unrest in oil-producing nations) actually call for more creative thinking, not less
...
Examples are persuasive and fully developed; reasoning is logically sound and well supported
...
Sentence structure is varied and complex, and the essay clearly demonstrates
facility with the “conventions of standard written English (i
...
, grammar, usage, and
mechanics)” (see Issue Scoring Guide, pages 37–38), with only minor errors appearing
...
Score 5 Response
Surely many of us have expressed the following sentiment, or some variation on it,
during our daily commutes to work: “People are getting so stupid these days!”
Surrounded as we are by striding and strident automatons with cell phones glued to
their ears, PDA’s gripped in their palms, and omniscient, omnipresent CNN gleaming
in their eyeballs, it’s tempting to believe that technology has isolated and infantilized
us, essentally transforming us into dependent, conformist morons best equipped to
sideswip one another in our SUV’s
...
With “Teen
People” style trends shooting through the air from tiger-striped PDA to zebra-striped
PDA, and with the latest starlet gossip zipping from juicy Blackberry to teeny, turbocharged cell phone, technology seems to support young people’s worst tendencies to
follow the crowd
...
After all, today’s tech-aided teens are, courtesy of authentic, hands-on video
games, literally trained to kill; courtesy of chat and instant text messaging, they have
their own language; they even have tiny cameras to efficiently photodocument your
fashion blunders! Is this adolescence, or paparazzi terrorist training camp?
With all this evidence, it’s easy to believe that tech trends and the incorporation
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GRE Analytical Writing
of technological wizardry into our everyday lives have served mostly to enforce
conformity, promote dependence, heighten comsumerism and materialism, and
generally create a culture that values self-absorption and personal entitlement over
cooperation and collaboration
...
After all, even
given the examples provided earlier in this essay, it seems clear that technology hasn’t
impaired our thinking and problem-solving capacities
...
However, we are
inarguably more efficient in our badness these days
...
Harnessed correctly, technology can improve our ability to think and act for ourselves
...
Reader Commentary
The language of this essay clearly illustrates both its strengths and weaknesses
...
See, for example, the problems of parallelism in the second to last sentence of paragraph 2 (“After
all, today’s tech-aided teens
...
Such lucid prose, however, is often countered
with an over-reliance upon abstractions and tangential reasoning (what does the fact
that video games “literally train [teens] to kill” have to do with the use or deterioration
of thinking abilities, for example?)
...
Score 4 Response
In all actuality, I think it is more probable that our bodies will surely deteriorate long
before our minds do in any significant amount
...
The ever increasing amount of
technology that we incorporate into our daily lives makes people think and learn every
day, possibly more than ever before
...
may
even reach limits never dreamed of before by average people
...
If you think about it, using technology to solve more complicating problems gives
humans a chance to expand their thinking and learning, opening up whole new worlds
for many people
...
If it wasn’t for
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GRE Analytical Writing
the invention of new technological devices, I wouldn’t be sitting at this computer trying
to philosophize about technology
...
Think what an impact the printing press, a technologically superior mackine at
the time, had on the ability of the human race to learn and think
...
When we get up there’s instant coffee and the microwave and all these
great things that help us get ready for our day
...
Going off to school or work in our cars
instead of a horse and buggy
...
Using technology to solve our continually more complicated problems as a human
race is definately a good thing
...
The ability to use what technology we have is an example
Reader Commentary
This essay meets all the criteria of a 4-level essay
...
The position is then developed with relevant reasons (“using technology
to solve more complicat[ed] problems gives humans a chance to expand their thinking
and learning
...
Point 1, “Using technology,” is supported with the simple, but relevant notions that technology allows us
access to information and abilities to which we would not normally have access
...
Though the development and organization of the essay
does suffer from an occasional misstep (see paragraph 3’s abrupt progression from
coffeepots to the benefits of technology to cars), the essay as a whole flows smoothly
and logically from one idea to the next
...
Though they
both utilize some very superficial discussion and often fail to probe deeply into the
issue, this writer does, however, take the analysis a step further
...
To support the notion that advances in technology actually help increase thinking
ability, the writer draws a clever parallel between the promise of modern, sophisticated
technology (computer) and the equally substantial/pervasive technology of the past
(printing press)
...
The writer displays sufficient control of language and the conventions of
standard written English
...
There is a sentence fragment (“Going off
...
isn’t deteriorating,
it’s continuing to grow
...
These errors, though, are minor and do
not interfere with the clarity of the ideas being presented
...
Unlawful distribution of this ebook is prohibited
...
On the contrary, advancements in technology had advanced our vast
knowledge in many fields, opening opportunities for further understanding and
achievement
...
The future ability of growing new brain cells and the possibility to reverse
the onset of alzheimer’s is now becoming a reality
...
One aspect where the ability of humans may initially be seen as an example of
deteriorating minds is the use of internet and cell phones
...
Now humans
can sit in a chair and type anything into a computer and get an answer
...
I
think if humans understand that we should not have such a reliance on computer
technology, that we as a species will advance further by utilizing the opportunity of
computer technology as well as the other sources of information outside of a
computer
...
Reader Commentary
This essay never moves beyond a superficial discussion of the issue
...
” Each point, then, is developed with relevant but insufficient evidence
...
Development of the second point is hindered by a lack of specificity and organization
...
The writer cites
a need for regulation/supplementation and warns of the detriment of over-reliance
upon technology
...
can be detrimental
...
we will advance further”)
...
”
This second paragraph is a series of generalizations, which are loosely connected and
lack a much needed grounding
...
g
...
Despite the
accumulation of such flaws, though, meaning is generally clear
...
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GRE Analytical Writing
Score 2 Response
In recent centuries, humans have developed the technology very rapidly, and you may
accept some merit of it, and you may see a distortion in society occured by it
...
There are
many symptoms and resons of it
...
Of course, you can see the phenomena of human laziness along with developed
technology in some place
...
What makes human to be laze of thinking is not merely technology, but the
the tendency of human that they treat them as a magic stick and a black box
...
The most important thing to use the thechnology, regardless the new or old, is to
comprehend the fundamental idea of them, and to adapt suit tech to tasks in need
...
In this procedure, humans have to consider
as long as possible to acquire adequate functions
...
In addition, the technology as it is do not vain automatically, the is created by
humans
...
Consequently, if you are not passive to the new tech, but offensive to it, you would
not lose your ability to think deeply
...
Reader Commentary
The language of this essay is what most clearly links it to the score point of 2
...
It is unclear what the writer means
when he/she states, “To be lazy for human in some meaning is one of the fashion issues
in thesedays,” or “
...
” Despite such severe flaws, the
writer has made an obvious attempt to respond to the prompt (“I can not agree with
the statement that the technology make humans to be reluctant to thinking thoroughly”) as well as an unclear attempt to support such an assertion (“Not understanding the aims and theory of them [technology] couses the disapproval problems” and
“The most important thing to use the thechnology
...
Holistically, the essay displays a seriously flawed but not fundamentally deficient attempt to develop and support its claims
...
As the
language falters, so too does the analysis
...
Unlawful distribution of this ebook is prohibited
...
Reader Commentary
The essay is clearly on topic, as evidenced by the writer’s usage of the more significant
terms from the prompt: “technically” (technologically), “humans”, “thinking” (think)
and “deterioating” (deteriorate)
...
Meaning aside, the brevity of the essay (one sentence) clearly indicates the writer’s
inability to develop a response that addresses the specific instructions given (“Discuss
the extent to which you agree or disagree with the statement above and explain your
reasoning for the position you take”)
...
The coherent phrases in this one-sentence response are those tied to the prompt:
“Humans have invented machines” and “their thinking process is deterioating
...
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GRE Analytical Writing
Analyze an Argument Task
Understanding the Argument Task
The Analyze an Argument task assesses your ability to understand, analyze, and evaluate arguments according to specific instructions and to clearly convey your evaluation
in writing
...
Your task is to discuss the logical soundness of the author’s case
according to the specific instructions by critically examining the line of reasoning
...
You might want
to read them more than once and possibly make brief notes about points you want to
develop more fully in your response
...
In tracing this line,
look for transition words and phrases that suggest that the author is attempting to
make a logical connection (e
...
, however, thus, therefore, evidently, hence, in conclusion)
...
You are not being asked to discuss whether the statements in the argument are true or accurate
...
You are not being asked to express your own views on
the subject being discussed (as you were in the Issue task)
...
It is important that you address the argument according to the specific instructions
...
b
Write a response in which you discuss what specific evidence is needed to evaluate the argument and explain how the evidence would weaken or strengthen
the argument
...
Be sure to explain how the argument depends on these
assumptions and what the implications are for the argument if the assumptions
prove unwarranted
...
Be sure to explain how the answers to these
questions would help to evaluate the recommendation
...
Unlawful distribution of this ebook is prohibited
...
Be sure to explain how the answers to these questions
would help to evaluate the advice
...
Be sure to explain how the answers to these questions would
help to evaluate the recommendation
...
Be sure to explain how the answers to these questions would help to evaluate the prediction
...
b
Write a response in which you discuss what questions would need to be
addressed in order to decide whether the conclusion and the argument on
which it is based are reasonable
...
“Analyze an Argument” is primarily a critical thinking task requiring a written
response
...
Understanding the Context for Writing: Purpose and Audience
The purpose of the task is to see how well equipped you are to insightfully evaluate an
argument written by someone else and to effectively communicate your evaluation in
writing to an academic audience
...
To get a clearer idea of how GRE readers apply the Argument scoring criteria to
actual essays, you should review scored sample Argument essay responses and reader
commentary
...
The reader commentary discusses specific aspects of analytical writing, such as
cogency of ideas, development and support, organization, syntactic variety, and facility
with language
...
Preparing for the Argument Task
Because the Argument task is meant to assess analytical writing and informal reasoning skills that you have developed throughout your education, it has been designed so
as not to require any specific course of study or to advantage students with a particular
type of training
...
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...
You will not be expected to know
methods of analysis or technical terms
...
You will not
need to see that the principal has committed the post hoc, ergo propter hoc fallacy; you
will simply need to see that there are other possible explanations for the improved
attendance, to offer some commonsense examples, and perhaps to suggest what would
be necessary to verify the conclusion
...
This would have to be ruled out in order for the
principal’s conclusion to be valid
...
g
...
There is no one way to practice that is best
for everyone
...
If you follow this approach, take all the time you need to evaluate the argument
...
Unlawful distribution of this ebook is prohibited
...
When you’ve gone as far as you
can with your evaluation, look over the notes and put them in a good order for discussion (perhaps by numbering them)
...
Even
if you choose not to write a full essay response, you should find it very helpful to practice evaluating a few of the arguments and sketching out your responses
...
For example, you will not want to discuss one point so
exhaustively or to provide so many equivalent examples that you run out of time to
make your other main points
...
It can also be very informative to trade papers on the same topic with fellow students
and discuss one another’s responses in terms of the scoring guide
...
How to Interpret Numbers, Percentages, and Statistics in Argument Topics
Some arguments contain numbers, percentages, or statistics that are offered as evidence in support of the argument’s conclusion
...
It is important to remember that you are not being asked to do a
mathematical task with the numbers, percentages, or statistics
...
In the example above,
the conclusion is that a community event has become less popular
...
Each of these could
explain the difference in attendance, and thus would weaken the conclusion that the
event was “less popular
...
Consider the claim that
the drama club at a school deserves more funding because its membership has
increased by 100 percent
...
Remember
that any numbers, percentages, or statistics in Argument tasks are used only as evidence in support of a conclusion, and you should always consider whether they actually support the conclusion
...
Your response may, but need not,
incorporate particular writing strategies learned in English composition or writingintensive college courses
...
Unlawful distribution of this ebook is prohibited
...
In fact, when GRE readers are trained, they review
hundreds of Argument responses that, although highly diverse in content and form,
display similar levels of critical thinking and analytical writing
...
The
readers know that a writer can earn a high score by developing several points in an
evaluation or by identifying a central feature in the argument and developing that evaluation extensively
...
You should make choices about format and organization that you think support
and enhance the overall effectiveness of your evaluation
...
You
might want to organize your evaluation around the structure of the argument itself,
discussing the argument line by line
...
Similarly, you might want to use examples if they help illustrate an important
point in your evaluation or move your discussion forward (remember, however, that, in
terms of your ability to perform the Argument task effectively, it is your critical thinking and analytical writing, not your ability to come up with examples, that is being
assessed)
...
Sample Argument Task
In surveys Mason City residents rank water sports (swimming, boating, and fishing) among their favorite recreational activities
...
For years
there have been complaints from residents about the quality of the river’s water
and the river’s smell
...
Use of the river for water sports is, therefore, sure to increase
...
Write a response in which you examine the stated and/or unstated assumptions of
the argument
...
Strategies for This Topic
This argument cites a survey to support the prediction that the use of the Mason River
is sure to increase and thus recommends that the city government should devote more
money in this year’s budget to the riverside recreational facilities
...
Unlawful distribution of this ebook is prohibited
...
A successful response, then, must discuss both the argument’s
assumptions AND the implications of these assumptions for the argument
...
Though responses may well raise other points not mentioned here and need not
mention all of these points, some assumptions of the argument, and some ways in
which the argument depends on those assumptions, include:
b
The assumption that people who rank water sports “among their favorite recreational activities” are actually likely to participate in them
...
) This assumption underlies the claim that use of
the river for water sports is sure to increase after the state cleans up the Mason
River and that the city should for that reason devote more money to riverside
recreational facilities
...
(It is possible that survey results exaggerate the interest in water sports
...
b
The assumption that Mason City residents would actually want to do water
sports in the Mason River
...
)
This assumption underlies the claim that use of the river for water sports is
sure to increase after the state cleans up the Mason River and that the city
should for that reason devote more money to riverside recreational facilities
...
This assumption underlies the claim that the city should
devote more money in this year’s budget to riverside recreational facilities
...
b
The assumption that the riverside recreational facilities are facilities designed
for people who participate in water sports and not some other recreational pursuit
...
b
The assumption that the dirtiness of the river is the cause of its being little used
and that cleaning up the river will be sufficient to increase recreational use of
the river
...
) This assumption
underlies the claim that the state’s plan to clean up the river will result in
increased use of the river for water sports
...
This assumption motivates the state’s plan to clean up the river and
underlies the claim that use of the river for water sports is sure to increase
...
)
b
The assumption that the state’s cleanup will occur soon enough to require
adjustments to this year’s budget
...
Unlawful distribution of this ebook is prohibited
...
b
The assumption that the cleanup, when it happens, will benefit those parts of
the river accessible from the city’s facilities
...
b
The assumption that the city government ought to devote more attention to
maintaining a recreational facility if demand for that facility increases
...
Should any of the above assumptions prove unwarranted, the implications are:
b
That the logic of the argument falls apart/ is invalid/ is unsound
...
Essay Responses and Reader Commentary
Score 6 Response *
While it may be true that the Mason City government ought to devote more money to
riverside recreational facilities, this author’s argument does not make a cogent case
for increased resources based on river use
...
Citing surveys of city residents, the author reports city resident’s love of water
sports
...
For example, the
survey could have asked residents if they prefer using the river for water sports or
would like to see a hydroelectric dam built, which may have swayed residents toward
river sports
...
The survey may have been 10 pages long,
with 2 questions dedicated to river sports
...
Unless the survey is
fully representative, valid, and reliable, it can not be used to effectively back the
author’s argument
...
While a polluted, smelly river would likely cut down on river sports, a concrete
connection between the resident’s lack of river use and the river’s current state is not
effectively made
...
To strengthen his/her argument, the
author would benefit from implementing a normed survey asking a wide range of
residents why they do not currently use the river
...
If the river’s water quality and smell result from problems
which can be cleaned, this may be true
...
, if any
...
Unlawful distribution of this ebook is prohibited
...
But if the quality and aroma results from the natural mineral deposits in the
water or surrounding rock, this may not be true
...
This is not something
likely to be afffected by a clean-up
...
Regardless of whether the river’s quality is able to be improved or
not, the author does not effectively show a connection between water quality and river
usage
...
For these reasons, city government may decide to
invest in improving riverside recreational facilities
...
Reader Commentary
This insightful response identifies important assumptions and thoroughly examines
their implications
...
By showing that each assumption is highly suspect, this essay demonstrates the
weakness of the entire argument
...
Paragraph 3 examines the
tenuous connection between complaints and limited use of the river for recreation
...
Finally, paragraph 4 explains that certain geologic features may prevent effective river cleanup
...
In addition, careful organization insures that each new point builds upon the previous ones
...
Although this essay does contain minor errors, it still conveys ideas fluently
...
g
...
assumptions” and “may have swayed residents”)
...
Note, for example, the sustained parallelism in the first
sentence of the concluding paragraph
...
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...
GRE Analytical Writing
Score 5 Response
The author of this proposal to increase the budget for Mason City riverside recreational
facilities offers an interesting argument but to move forward on the proposal would
definitely require more information and thought
...
For example, consider the survey rankings among Mason City residents
...
But, survey
responses can hardly be used as indicators of actual behavior
...
Yet every profession does not equal a new gym membership
...
While water sports may
be among the residents’ favorite activities, this allows for many other favorites
...
Do they favor these water
sports above a softball field or soccer field? Are they willing to sacrifice the municipal
golf course for better riverside facilities? Indeed the survey hardly provides enough
information to discern future use of improved facilities
...
While it is not illogical to expect some increase, at what level will
people begin to use the river? The answer to this question requires a survey to find out
the reasons our residents use or do not use the river
...
Likewise, the author is optimistic regarding the state promise to clean the river
...
Is this a
campaign year and the plans a campaign promise from the state representative? What
is the timeline for the clean-up effort? Will the state fully fund this project? We can
imagine the misuse of funds in renovating the riverside facilities only to watch the
new buildings fall into dilapidation while the state drags the river clean-up
...
The current budget situation must be assessed to determine if this increase can
be afforded
...
The author naively
assumes that the money can simply appear without forethought on where it will come
from
...
While the
proposal does highlight a possibility, more information is required to warrant any
action
...
The major assumptions discussed are:
b
b
b
b
That a survey can accurately predict behavior,
That cleaning the river will, in itself, increase recreational usage,
That state plans to clean the river will actually be realized,
That Mason City can afford to spend more on riverside recreational facilities
...
Unlawful distribution of this ebook is prohibited
...
Paragraph 2, for
example, points out vagueness in the wording of the survey: Even if water sports rank
among the favorite recreational activities of Mason City residents, other sports may still
be much more popular
...
Paragraph 4 considers several reasons why river cleanup plans may not be successful (the plans may be nothing more than campaign promises, or funding may not be
adequate)
...
Instead of dismissing each assumption in isolation, this response places them in a
logical order and considers their connections
...
g
...
” or “The answer to this question requires
...
Minor errors in punctuation are present, but word choices are apt and sentences suitably varied in pattern and length
...
Thus, the response satisfies all requirements for a score of 5, but its development is
not thorough or compelling enough for a 6
...
This is not
necessarily true, as people may rank water sports among their favorite recreational
activities, but that does not mean that those same people have the financial ability,
time or equipment to pursue those interests
...
If recreational facilities already exist along the
Mason River, why should the city allot more money to fund them? If the recreational
facilities already in existence will be used more in the coming years, then they will be
making more money for themselves, eliminating the need for the city government to
devote more money to them
...
If the city government alloted more money to the recreational facilities, then the
budget is being cut from some other important city project
...
Reader Commentary
This competent response identifies some important unstated assumptions:
b
b
That cleaning up the Mason River will lead to increased recreational use,
That existing facilities along the river need more funding
...
Unlawful distribution of this ebook is prohibited
...
g
...
Similarly, paragraphs 2
and 3 explain that riverside recreational facilities may already be adequate and may, in
fact, produce additional income if usage increases
...
This essay does not, however, rise to a score of 5 because it fails to consider several
other unstated assumptions (e
...
, that the survey is reliable or that the efforts to clean
the river will be successful)
...
Mason City may actually have a budget surplus so
that cuts to other projects will not be necessary, and cleaning the river may provide
other real benefits even if it is not used more for water sports
...
Score 3 Response
Surveys are created to speak for the people; however, surveys do not always speak
for the whole community
...
If that is so evident, why has
the river not been used? The blame can not be soley be placed on the city park
department
...
The real
issue is not the residents use of the river, but their desire for a more pleasant smell and
a more pleasant sight
...
If the budget is changed to accomodate the clean up of the Mason
River, other problems will arise
...
If more money is taken out of the budget to clean the river an assumption
can be made
...
In addition, to the budget being used to clean up
Mason River, it will also be allocated in increasing riverside recreational facilites
...
There are many assumptions being made;
however, the government can not make the assumption that people want the river to
be cleaned so that they can use it for recreational water activities
...
Reader Commentary
Even though much of this essay is tangential, it offers some relevant examination of the
argument’s assumptions
...
Then the response drifts to irrelevant matters — a defense of the city park department, a prediction of budget problems, and the problem of pleasing city residents
...
g
...
Near the end, the response does correctly note that city government
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...
GRE Analytical Writing
should not assume that residents want to use the river for recreation
...
In summary, the language in this response is reasonably clear, but its examination
of unstated assumptions remains limited, and therefore the essay earns a score of 3
...
First, this statement mentions raking water sports as their favorite recreational
activities at the first sentence
...
This is a wrong cause and result to solve the problem
...
As a result, the state expects that water sports will increase
...
Third, the last statement is the conclusion
...
This
statement is also a wrong cause and result
...
The
supporting setences are not strong enough to support this issue
...
In his/her vague references to causal fallacies, the writer attempts
logical analysis but never refers explicitly or implicitly to any unusual assumptions
...
g
...
Because this response “does not follow the directions for the assigned task” (see the
Argument Scoring Guide, pages 39–40) and contains errors in sentence structure and
logical development, it earns a score of 2
...
They statement also assumes that if the
state cleans up the river, the use of the river for water sports will definitely increase
...
Sentence
one states an assumption that is actually not present in the argument, and sentence
two correctly states an assumption but provides no discussion of its implications
...
As such, it clearly “provides little evidence of the ability to develop an organized
response (i
...
, is disorganized and/or extremely brief)” (see Argument Scoring Guide,
pages 39–40) and should earn a score of 1
...
Unlawful distribution of this ebook is prohibited
...
A typical response in this category
b articulates a clear and insightful position on the issue in accordance with the
assigned task
b develops the position fully with compelling reasons and/or persuasive examples
b sustains a well-focused, well-organized analysis, connecting ideas logically
b conveys ideas fluently and precisely, using effective vocabulary and sentence
variety
b demonstrates superior facility with the conventions of standard written English
(i
...
, grammar, usage, and mechanics) but may have minor errors
Score 5
In addressing the specific task directions, a 5 response presents a generally thoughtful,
well-developed analysis of the issue and conveys meaning clearly
...
A typical response in this category
b presents a clear position on the issue in accordance with the assigned task
b develops the position with relevant reasons and/or examples
b is adequately focused and organized
b demonstrates sufficient control of language to express ideas with acceptable
clarity
b generally demonstrates control of the conventions of standard written English
but may have some errors
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GRE Analytical Writing
Score 3
A 3 response demonstrates some competence in addressing the specific task directions,
in analyzing the issue, and in conveying meaning but is obviously flawed
...
A typical response in this category exhibits ONE OR MORE of the following characteristics:
b is unclear or seriously limited in addressing the specific task directions and/or
in presenting or developing a position on the issue
b provides few, if any, relevant reasons or examples in support of its claims
b is poorly focused and/or poorly organized
b has serious problems in language and sentence structure that frequently interfere with meaning
b contains serious errors in grammar, usage, or mechanics that frequently obscure
meaning
Score 1
A 1 response demonstrates fundamental deficiencies in analytical writing
...
g
...
e
...
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GRE Analytical Writing
GRE Scoring Guide: Analyze an Argument
Score 6
In addressing the specific task directions, a 6 response presents a cogent, well-articulated examination of the argument and conveys meaning skillfully
...
e
...
A typical response in this category
b clearly identifies aspects of the argument relevant to the assigned task and
examines them in a generally perceptive way
b develops ideas clearly, organizes them logically, and connects them with appropriate transitions
b offers generally thoughtful and thorough support for its main points
b conveys ideas clearly and well, using appropriate vocabulary and sentence
variety
b demonstrates facility with the conventions of standard written English but may
have minor errors
Score 4
In addressing the specific task directions, a 4 response presents a competent examination of the argument and conveys meaning with acceptable clarity
...
Unlawful distribution of this ebook is prohibited
...
A typical response in this category exhibits ONE OR MORE of the following characteristics:
b does not identify or examine most of the aspects of the argument relevant to the
assigned task, although some relevant examination of the argument is present
b mainly discusses tangential or irrelevant matters, or reasons poorly
b is limited in the logical development and organization of ideas
b offers support of little relevance and value for its main points
b has problems in language and sentence structure that result in a lack of clarity
b contains occasional major errors or frequent minor errors in grammar, usage,
or mechanics that can interfere with meaning
Score 2
A 2 response largely disregards the specific task directions and/or demonstrates serious
weaknesses in analytical writing
...
A typical response in this category exhibits ONE OR MORE of the following characteristics:
b provides little or no evidence of understanding the argument
b provides little evidence of the ability to develop an organized response (e
...
, is
disorganized and/or extremely brief)
b has severe problems in language and sentence structure that persistently interfere with meaning
b contains pervasive errors in grammar, usage, or mechanics that result in incoherence
Score 0
Off topic (i
...
, provides no evidence of an attempt to respond to the assigned topic), is
in a foreign language, merely copies the topic, consists of only keystroke characters, or
is illegible, or nonverbal
...
Unlawful distribution of this ebook is prohibited
...
The reported score, the average of the scores for the two tasks, ranges
from 0 to 6, in half-point increments
...
The Analytical Writing section is designed to assess both critical thinking skills
and writing ability
...
For a full description of
how these criteria are used to assess essay responses, please refer to the scoring guides
for the Issue and Argument tasks, which are available on the GRE website at
www
...
org/gre/revised/scoreguides
...
5: Sustains insightful, in-depth analysis of complex ideas; develops and
supports main points with logically compelling reasons and/or highly persuasive examples; is well focused and well organized; skillfully uses sentence variety and precise
vocabulary to convey meaning effectively; demonstrates superior facility with sentence
structure and language usage but may have minor errors that do not interfere with
meaning
...
5: Provides generally thoughtful analysis of complex ideas; develops and
supports main points with logically sound reasons and/or well-chosen examples; is generally focused and well organized; uses sentence variety and vocabulary to convey
meaning clearly; demonstrates good control of sentence structure and language usage
but may have minor errors that do not interfere with meaning
...
5: Provides competent analysis of ideas; develops and supports main
points with relevant reasons and/or examples; is adequately organized; conveys meaning with reasonable clarity; demonstrates satisfactory control of sentence structure and
language usage but may have some errors that affect clarity
...
5: Displays some competence in analytical writing, although the writing
is flawed in at least one of the following ways: limited analysis or development; weak
organization; weak control of sentence structure or language usage, with errors that
often result in vagueness or lack of clarity
...
5: Displays serious weaknesses in analytical writing
...
Scores 1 and 0
...
The writing is
fundamentally flawed in at least one of the following ways: content that is extremely
confusing or mostly irrelevant to the assigned tasks; little or no development; severe
and pervasive errors that result in incoherence
...
Unlawful distribution of this ebook is prohibited
...
Score NS: The examinee produced no text whatsoever
...
Unlawful distribution of this ebook is prohibited
...
Verbal Reasoning questions appear in several formats, each of which is discussed
in detail below
...
The other half requires you to read, interpret, and complete existing sentences, groups of sentences, or paragraphs
...
The number of choices varies depending
on the type of question
...
Turn the page to begin
...
Unlawful distribution of this ebook is prohibited
...
Those abilities include
b
b
b
b
b
b
b
b
b
b
b
b
b
understanding the meaning of individual words
understanding the meaning of individual sentences
understanding the meaning of paragraphs and larger bodies of text
distinguishing between minor and major points
summarizing a passage
drawing conclusions from the information provided
reasoning from incomplete data, inferring missing information
understanding the structure of a text, how the parts relate to one another
identifying the author’s perspective
identifying the author’s assumptions
analyzing a text and reaching conclusions about it
identifying strengths and weaknesses
developing and considering alternative explanations
As this list implies, reading and understanding a piece of text requires far more
than a passive understanding of the words and sentences it contains — it requires active
engagement with the text, asking questions, formulating and evaluating hypotheses,
and reflecting on the relationship of the particular text to other texts and information
...
The test contains approximately ten
passages; the majority of the passages in the test are one paragraph in length, and only
one or two are several paragraphs long
...
Typically, about half of the questions on the test will be based on passages, and the
number of questions based on a given passage can range from one to six
...
Many,
but not all, of the questions are standard multiple-choice questions, in which you are
required to select a single correct answer; others ask you to select multiple correct
answers, and still others ask you to select a sentence from the passage
...
General Advice
Reading passages are drawn from many different disciplines and sources, so you may
encounter material with which you are not familiar
...
If, however,
you encounter a passage that seems particularly hard or unfamiliar, you may want to
save it for last
...
Unlawful distribution of this ebook is prohibited
...
b Try to distinguish main ideas from supporting ideas or evidence
...
b Similarly, try to distinguish ideas that the author is strongly committed to
from those he or she advances as hypothetical or speculative
...
b Try to identify the relationship between different ideas
...
b
Answer each question on the basis of the information provided in the passage
and do not rely on outside knowledge
...
You should not expect
to agree with everything you encounter in the reading passages
...
Tips for Answering
b Read all the answer choices before making your selection, even if you think
you know what the answer is in advance
...
The correct answer is the one that most accurately and
most completely answers the question posed
...
b Pay attention to context
...
Many words have
quite different meanings in different contexts
...
Unlawful distribution of this ebook is prohibited
...
To gain credit for these questions,
you must select all the correct answers, and only those; there is no credit for partially
correct answers
...
Tips for Answering
b Evaluate each answer choice separately on its own merits
...
Make sure the answer choice you pick accurately and completely answers the
b
question posed
...
Be careful also not to pick
an answer choice simply because it is a true statement
...
Questions of this type can have three correct answer choices
...
To answer the question, choose one of the sentences and click on it; clicking anywhere on a sentence will highlight it
...
Note
...
Similar multiple-choice questions are used in its place
...
Do not evaluate any sentences that
are outside the paragraphs under consideration
...
A correct answer choice must accurately match the description in the
question
...
46
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GRE Verbal Reasoning
Sample Question Set
Questions 1 to 3 are based on the following reading passage
...
Glass based two symphonies on music by rock musicians David Bowie and Brian Eno,
but the symphonies’ sound is distinctively his
...
Yet this use of popular elements has not made Glass a
composer of popular music
...
Select only one answer choice
...
The passage addresses which of the following issues related to Glass’s use of
popular elements in his classical compositions?
A
ɕ
B
ɕ
C
ɕ
How it is regarded by listeners who prefer rock to the classics
How it has affected the commercial success of Glass’s music
Whether it has contributed to a revival of interest among other composers
in using popular elements in their compositions
D Whether it has had a detrimental effect on Glass’s reputation as a
ɕ
composer of classical music
E Whether it has caused certain of Glass’s works to be derivative in quality
ɕ
Consider each of the three choices separately and select all that apply
...
The passage suggests that Glass’s work displays which of the following qualities?
A
Ȟ A return to the use of popular music in classical compositions
B
Ȟ An attempt to elevate rock music to an artistic status more closely
C
Ȟ
3
...
Explanation
The passage describes in general terms how Philip Glass uses popular music in his
classical compositions and explores how Glass can do this without being imitative
...
Question 1: One of the important points that the passage makes is that when Glass
uses popular elements in his music, the result is very much his own creation (it is “distinctively his”)
...
Thus one issue
47
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...
GRE Verbal Reasoning
that the passage addresses is the one referred to in answer Choice E—it answers it in
the negative
...
The correct answer is Choice E
...
Since the passage says that Glass revived the use of popular music in
classical compositions, answer Choice A is clearly correct
...
Finally, since Glass’s style has always mixed
elements of rock with classical elements, Choice C is correct
...
Question 3: Almost every sentence in the passage refers to incorporating rock
music in classical compositions, but only the last sentence distinguishes two ways of
doing so
...
Thus the correct answer is the last sentence of the passage
...
Text Completion questions test this ability by omitting crucial
words from short passages and asking the test taker to use the remaining information
in the passage as a basis for selecting words or short phrases to fill the blanks and create a coherent, meaningful whole
...
Unlawful distribution of this ebook is prohibited
...
Instead, try to analyze the passage in the
following way:
b Read through the passage to get an overall sense of it
...
b Think up your own words for the blanks
...
b Do not assume that the first blank is the one that should be filled first
...
Select your choice for that
blank, and then see whether you can complete another blank
...
b Double-check your answers
...
Sample Questions
For each blank select one entry from the corresponding column of choices
...
1
...
He emphasizes the enormous gaps in our knowledge, the
sparseness of our observations, and the (iii)__________, calling attention to the
many aspects of planetary evolution that must be better understood before we
can accurately diagnose the condition of our planet
...
To understand what the
author of the book is being complimented on, it is useful to focus on the second blank
...
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...
The only answer choice that fits the case is “obscure,” since
enhancing and underscoring are generally good things to do, not things one should
refrain from doing
...
” Notice that trying to fill blank
(i) without filling blank (ii) first is very hard—each choice has at least some initial plausibility
...
”
Thus the correct answer is overshadowed (Choice A), obscure (Choice E), and
superficiality of our theories (Choice I)
...
Vain and prone to violence, Caravaggio could not handle success: the more his
(i)__________ as an artist increased, the more (ii)__________ his life became
...
So
roughly what the second part must say is that as Caravaggio became more successful,
his life got more out of control
...
And for blank (i), the best choice is “eminence,” since
to increase in eminence is a consequence of becoming more successful
...
Thus the correct answer is eminence (Choice C) and tumultuous (Choice D)
...
In parts of the Arctic, the land grades into the landfast ice so _______ that you
can walk off the coast and not know you are over the hidden sea
...
The word that does that is “imperceptibly”; if the land grades imperceptibly into the
ice, you might well not know that you had left the land
...
Thus the correct answer is imperceptibly (Choice B)
...
Unlawful distribution of this ebook is prohibited
...
Sentence Equivalence questions consist of a single sentence with just one blank, and
they ask you to find two choices that both lead to a complete, coherent sentence and
that produce sentences that mean the same thing
...
These questions are marked with square boxes beside the answer choices, not circles or
ovals
...
This can be misleading for two reasons
...
Second, the pair
of words that do constitute the correct answer may not mean exactly the same
thing, since all that matters is that the resultant sentences mean the same thing
...
b Identify words or phrases that seem particularly significant, either because
they emphasize the structure of the sentence (words like although or
moreover) or because they are central to understanding what the sentence
is about
...
Try to fill in the blank with a word
that seems to you to fit and then see if two similar words are offered among
the answer choices
...
b Double-check your answers
...
51
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GRE Verbal Reasoning
Sample Questions
Select the two answer choices that, when used to complete the sentence, fit the
meaning of the sentence as a whole and produce completed sentences that are alike
in meaning
...
Although it does contain some pioneering ideas, one would hardly characterize
the work as __________
...
The work contains some pioneering
ideas, but apparently it is not overall a pioneering work
...
” Note that “orthodox” and
“conventional” are two words that are very similar in meaning, but neither one completes the sentence sensibly
...
2
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
ameliorated
ascertained
diagnosed
exacerbated
overlooked
worsened
Explanation
The sentence relates a piece of reasoning, as indicated by the presence of “so that”:
asking for the assistance of foreign technocrats would be counterproductive because of
the effects such technocrats have had already
...
Thus the correct answer is exacerbated (Choice D) and worsened (Choice F)
...
Unlawful distribution of this ebook is prohibited
...
Three
of the practice sets consist of examples of the discrete question types, Text Completion and Sentence Equivalence; and the other three sets consist of Reading
Comprehension questions
...
The
first two are easy, the next two are medium, and the final two are hard
...
Then, at the end of the
chapter, you will find complete explanations for every question
...
Sharpen your GRE Verbal Reasoning skills by working your way through these
question sets
...
Review the answer explanations carefully, paying particular attention to the
explanations for questions that you answered incorrectly
...
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GRE Verbal Reasoning Practice Questions
SET 1
...
Fill all blanks in the way that best completes the text
...
Dominant interests often benefit most from _________ of governmental
interference in business, since they are able to take care of themselves if left
alone
...
centralization
improvisation
elimination
prophetic
normal
monotonous
virtual
typical
An investigation that is _________ can occasionally yield new facts, even notable
ones, but typically the appearance of such facts is the result of a search in a
definite direction
...
authorization
Kagan maintains that an infant’s reactions to its first stressful experiences are
part of a natural process of development, not harbingers of childhood
unhappiness or _________ signs of adolescent anxiety
...
intensification
timely
unguided
consistent
uncomplicated
subjective
It is (i)_________ that so many portrait paintings hang in art museums, since the
subject matter seems to dictate a status closer to pictures in the family photograph album than to high art
...
Blank (i)
A
ɕ
B
ɕ
C
ɕ
surprising
understandable
irrelevant
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
challenges
justifies
changes
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GRE Verbal Reasoning Practice Questions
5
...
Blank (i)
A
ɕ
B
ɕ
C
ɕ
activism
apathy
affability
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
devoted to
indifferent to
shaped by
For Questions 6 to 8, select the two answer choices that, when used to complete
the sentence, fit the meaning of the sentence as a whole and produce completed
sentences that are alike in meaning
...
As my eyesight began to _________, I spent a lot of time writing about it — both
poems and “eye journals” — describing what I saw as I looked out through
damaged eyes
...
The judge’s standing in the legal community, though shaken by phony allegations
of wrongdoing, emerged, at long last, _________
...
deteriorate
sharpen
improve
decline
recover
adjust
unqualified
undiminished
undecided
undamaged
unresolved
unprincipled
Modern agricultural practices have been extremely successful in increasing the
productivity of major food crops, yet despite heavy use of pesticides, _________
losses to diseases and insect pests are sustained each year
...
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...
Reading Comprehension Questions: Easy
For each of Questions 1 to 9, select one answer choice unless otherwise instructed
...
A person who agrees to serve as mediator between two warring factions at the
request of both abandons by so agreeing the right to take sides later
...
The passage above emphasizes which of the following points about mediators?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
They should try to form no opinions of their own about any issue that is
related to the dispute
...
They should not agree to serve unless they are equally acceptable to all
parties to a dispute
...
They should reserve the right to abandon their impartiality so as not to be
open to the charge of having been deceitful
...
Unlawful distribution of this ebook is prohibited
...
Was Felix Mendelssohn (1809–1847) a great composer? On its face, the question seems
absurd
...
From then on, he was recognized as an artist of preternatural
abilities, not only as a composer but also as a pianist and conductor
...
Despite general acknowledgment of his genius, there has been a
noticeable reluctance to rank him with, say, Schumann or Brahms
...
working on a small scale of emotion and texture
...
Select a sentence in the passage whose function is to indicate the range of
Mendelssohn’s musical talents
...
The passage suggests that anyone attempting to evaluate Mendelssohn’s career
must confront which of the following dichotomies?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
4
...
The tension between Mendelssohn’s career as a composer and his career
as a pianist and conductor
The contrast between Mendelssohn’s popularity and that of Schumann
and Brahms
The discrepancy between Mendelssohn’s popularity and his standing
among critics
The inconsistency between Mendelssohn’s reputation during his lifetime
and his reputation since his death
The gap between Mendelssohn’s prodigious musical beginnings and his
decline in later years
most composers since Mendelssohn
Schumann and Brahms
the music-listening public
music critics generally
Haggin exclusively
The author mentions Schumann and Brahms primarily in order to
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
provide examples of composers who are often compared with
Mendelssohn
identify certain composers who are more popular than Mendelssohn
identify composers whom Mendelssohn influenced
establish the milieu in which Mendelssohn worked
establish a standard of comparison for Mendelssohn as a composer
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GRE Verbal Reasoning Practice Questions
Questions 6 and 7 are based on the following reading passage
...
But in agriculture, unlike other industries where
women were viewed as temporary workers, women’s employment did not end with the
war
...
Consequently, the 1950s saw a growing number of women engaged in farm labor, even
though rhetoric in the popular media called for the return of women to domestic life
...
It can be inferred from the passage that the manufacturing and agricultural
sectors in the United States following the Second World War differed in which of
the following respects?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
The rate of expansion in each sector
The percentage of employees in each sector who were men
The trend in the wages of men employed in each sector
The attitude of the popular media toward the employment of women in
each sector
E
ɕ The extent to which women in each sector were satisfied with their jobs
7
...
The great majority of women who joined the workforce during the Second
World War were employed in manufacturing jobs
...
The increase in women’s employment that accompanied the Second World
War was longer lasting in agriculture than it was in manufacturing
...
58
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GRE Verbal Reasoning Practice Questions
Questions 8 and 9 are based on the following reading passage
...
There is some dispute about the method of transport involved
...
Yet the results of flotation experiments and the low temperatures of air currents cast doubt on these hypotheses
...
While it is likely that fewer varieties of
plant seeds have reached Hawaii externally than internally, more varieties are known
to be adapted to external than to internal transport
...
The author of the passage is primarily concerned with
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
9
...
Unlawful distribution of this ebook is prohibited
...
Discrete Questions: Medium
For Questions 1 to 5, select one entry for each blank from the corresponding column
of choices
...
1
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
2
...
This was
clear in her agonizing over how far to try to represent the minute details of a
performance in a written text, and this (ii)_________ makes her work a landmark
in ethnomusicology
...
reverence for
detachment from
curiosity about
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
fastidiousness
didacticism
iconoclasm
Political advertising may well be the most (i)_________ kind of advertising:
political candidates are usually quite (ii)_________, yet their campaign
advertisements often hide important differences behind smoke screens of smiles
and empty slogans
...
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...
Richard M
...
He said, (ii)_________ research, the government’s
greatest role in assuring continuing innovation is promoting a strong, modern
patent office
...
Russell said
...
Blank (i)
Blank (ii)
Blank (iii)
A
ɕ
D
ɕ in addition to
G
ɕ evaluate
B
ɕ
no bearing on
E
ɕ aside from
H
ɕ protect
C
ɕ
5
...
The invention has only to be deemed “more likely
than not” to work in order to receive initial approval
...
For this reason
the endless stream of (iii)_________ devices will continue to yield occasional
patents
...
Unlawful distribution of this ebook is prohibited
...
6
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
7
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
8
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
complicated
engaged
essential
fanciful
inconsequential
involved
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GRE Verbal Reasoning Practice Questions
SET 4
...
Questions 1 and 2 are based on the following reading passage
...
A Dream offers a rich read, varied in both the lives and texts of the women portrayed, and the perspectives and styles of the sixteen essayists
...
In these critical senses, A Dream is
inadequate
...
1
...
B
Ȟ It seems to focus on stylistic variety at the expense of accuracy of detail
...
2
...
essayists”) in the context of the passage as a whole?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
To give examples of how A Dream presents fascinating portraits that
display awareness of the tenuous nature of representations of reality
To elaborate on how A Dream fulfills the author’s childhood criteria for a
pleasurable book
To suggest that the author enjoyed A Dream for reasons more
sophisticated than the reasons she enjoyed certain books as a child
To illustrate ways in which the author finds A Dream to be inadequate in
certain critical senses
To imply that A Dream is too varied in focus to provide a proper
contextualization of the biographical details it offers
63
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...
GRE Verbal Reasoning Practice Questions
3
...
hyalina departs for the
depths where food is scarce and the water cold
...
galeata remains near the
warm surface where food is abundant
...
galeata grows and
reproduces much faster, its population is often outnumbered by D
...
Which of the following, if true, would help resolve the apparent paradox
presented above?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The number of species of zooplankton living at the bottom of the lake is
twice that of species living at the surface
...
In order to make the most of scarce food resources, D
...
galeata
...
galeata clusters under vegetation during the hottest part of the day to
avoid the Sun’s rays
...
galeata produces twice as many offspring per individual in any given
period of time as does D
...
64
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GRE Verbal Reasoning Practice Questions
Questions 4 and 5 are based on the following reading passage
...
Jacksonian America was not a fluid, egalitarian
society where individual wealth and poverty were ephemeral conditions
...
Pessen in his iconoclastic study of the very rich in the United States between
1825 and 1850
...
Though
active in commerce or the professions, most of the wealthy were not self-made but had
inherited family fortunes
...
Indeed, in several cities the wealthiest one
percent constantly increased its share until by 1850 it owned half of the community’s
wealth
...
4
...
They formed a distinct upper class
...
Some of them worked as professionals or in business
...
Many of them retained their wealth in spite of financial upheavals
...
Tocqueville’s analysis of the United States in the Jacksonian era remains
the definitive account of this period
...
The social patterns and political power of the extremely wealthy in the
United States between 1825 and 1850 are well documented
...
65
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GRE Verbal Reasoning Practice Questions
Questions 6 to 9 are based on the following reading passage
...
The interaction resulting from the differences between predator and prey led to a general
improvement in brain functions; however, certain components of intelligence were
improved far more than others
...
It ranges from a passive, freefloating awareness to a highly focused, active fixation
...
From the more relaxed to the more vigorous
levels, sensitivity to novelty is increased
...
The processes of arousal and
concentration give attention its direction
...
Thus begins
concentration, the holding of consistent images
...
Consciousness links past attention to the present and permits the
integration of details with perceived ends and purposes
...
Herbivores and carnivores develop different
kinds of attention related to escaping or chasing
...
For both, arousal attunes the animal to what is ahead
...
The predator is searchingly aggressive, inner-directed, tuned by the
nervous system and the adrenal hormones, but aware in a sense closer to human consciousness than, say, a hungry lizard’s instinctive snap at a passing beetle
...
The herbivore prey is of a different mind
...
6
...
Unlawful distribution of this ebook is prohibited
...
It can be inferred from the passage that in animals less intelligent than the
mammals discussed in the passage
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
8
...
past experience is less helpful in ensuring survival
attention is more highly focused
muscular coordination is less highly developed
there is less need for competition among species
environment is more important in establishing the proper ratio of prey
to predator
Interplay of predator and prey
Persistence of free-floating awareness in animals of the grasslands
Gradual dominance of warm-blooded mammals over cold-blooded reptiles
Interaction of early large mammals with less intelligent species
Improvement of the capacity for memory among herbivores and
carnivores
According to the passage, as the process of arousal in an organism continues,
all of the following may occur EXCEPT
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
the production of adrenaline
the production of norepinephrine
a heightening of sensitivity to stimuli
an increase in selectivity with respect to stimuli
an expansion of the range of states mediated by the brain stem
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GRE Verbal Reasoning Practice Questions
SET 5
...
Fill all blanks in the way that best completes the text
...
For some time now, _________ has been presumed not to exist: the cynical
conviction that everybody has an angle is considered wisdom
...
rationality
flexibility
diffidence
disinterestedness
insincerity
Human nature and long distances have made exceeding the speed limit a
(i)_________ in the state, so the legislators surprised no one when, acceding to
public demand, they (ii)_________ increased penalties for speeding
...
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
endorsed
considered
rejected
Serling’s account of his employer’s reckless decision making (i)_________ that
company’s image as (ii)_________ bureaucracy full of wary managers
...
Unlawful distribution of this ebook is prohibited
...
No other contemporary poet’s work has such a well-earned reputation for
(i)_________, and there are few whose moral vision is so imperiously unsparing
...
This new collection is the
poet’s fourth book in six years — an ample output even for poets of sunny
disposition, let alone for one of such (ii)_________ over the previous 50 years
...
Blank (i)
Blank (ii)
Blank (iii)
A
ɕ
D
ɕ penitential
G
ɕ taciturnity
B
ɕ
intrinsic frivolity
E
ɕ intractable
H
ɕ volubility
C
ɕ
5
...
By
contrast, managers who perceive environmental performance to be (iii)_________
to financial success may view an environmental management system as
extraneous
...
Blank (i)
A
ɕ
Blank (ii)
Blank (iii)
eclipse
D
ɕ uncritically
G
ɕ complementary
ɕ
bolster
ɕ
H
ɕ intrinsic
C
ɕ
degrade
B
6
...
Instead it tries to deepen our
understanding through (i)_________ what is already closest to us — the
experiences, thoughts, concepts, and activities that make up our lives but that
ordinarily escape our notice precisely because they are so familiar
...
Blank (i)
A
ɕ
attainment of
B
ɕ
rumination on
C
ɕ
detachment from
Blank (ii)
Blank (iii)
D
ɕ essentially
G
ɕ most prosaic
E
ɕ utterly
H
ɕ somewhat
F
ɕ thoroughly
I
ɕ refreshingly
irrelevant
mysterious
commonplace
hackneyed
novel
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GRE Verbal Reasoning Practice Questions
For Questions 7 to 9, select the two answer choices that, when used to complete
the sentence, fit the meaning of the sentence as a whole and produce completed
sentences that are alike in meaning
...
The government’s implementation of a new code of ethics appeared intended to
shore up the ruling party’s standing with an increasingly _________ electorate at a
time when the party is besieged by charges that it trades favors for campaign
money
...
Overlarge, uneven, and ultimately disappointing, the retrospective exhibition
seems too much like special pleading for a forgotten painter of real but _________
talents
...
aloof
placid
restive
skittish
tranquil
vociferous
limited
partial
undiscovered
circumscribed
prosaic
hidden
Newspapers report that the former executive has been trying to keep a low profile
since his _________ exit from the company
...
Unlawful distribution of this ebook is prohibited
...
Reading Comprehension Questions: Hard
For each of Questions 1 to 8, select one answer choice unless otherwise instructed
...
In the United States between 1850 and 1880, the number of farmers continued to
increase, but at a rate lower than that of the general population
...
The number of farmers in the general population increased slightly in the
30 years between 1850 and 1880
...
The proportion of farmers in the United States labor force remained
constant in the 30 years between 1850 and 1880
...
The proportion of farmers in the general population increased from 68
percent in 1850 to 72 percent in 1880
...
When total
agricultural acreage (planted acreage plus fallow acreage) is compared, however,
Soviet yield was 114 percent of United States yield
...
B
ɕ
C
ɕ
The United States had more fallow acreage than planted acreage
...
D
ɕ The Soviet Union had more planted acreage than fallow acreage
...
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GRE Verbal Reasoning Practice Questions
Questions 3 and 4 are based on the following reading passage
...
Oriented to the prevailing wind, the front wall of perforated
cardboard, moistened and cooled by a trickle of seawater pumped in, cools and moistens hot air blowing in
...
Though greenhouses normally capture the heat of sunlight,
a double-layered roof, the inner layer coated to reflect infrared light outward, allows
visible sunlight in but traps solar heat between the two layers
...
There the air
absorbs more moisture, which then condenses on a metal wall cooled by seawater, and
thus distilled water for irrigating the plants collects
...
3
...
4
...
Unlawful distribution of this ebook is prohibited
...
Many critics of Emily Brontë’s novel Wuthering Heights see its second part as a counterpoint that comments on, if it does not reverse, the first part, where a romantic reading receives more confirmation
...
Granted that the presence of these elements need not argue for an authorial awareness
of novelistic construction comparable to that of Henry James, their presence does
encourage attempts to unify the novel’s heterogeneous parts
...
This is not because such an interpretation necessarily stiffens into a thesis (although rigidity in any interpretation of this or of any novel is always a danger),
but because Wuthering Heights has recalcitrant elements of undeniable power that, ultimately, resist inclusion in an all-encompassing interpretation
...
5
...
Which of the following inferences about Henry James’s awareness of novelistic
construction is best supported by the passage?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
7
...
The second part has little relation to the first part
...
The second part provides less substantiation for a romantic reading
...
James, more than any other novelist, was aware of the difficulties of
novelistic construction
...
James’s awareness of novelistic construction derived from his reading of
Brontë
...
James’s awareness of novelistic construction precluded him from violating
the unity of his novels
...
Unlawful distribution of this ebook is prohibited
...
8
...
Hamlet has elements that are not amenable to an all-encompassing critical
interpretation
...
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GRE Verbal Reasoning Practice Questions
ANSWER KEY
SET 1
...
2
...
4
...
6
...
8
...
Reading Comprehension Questions: Easy
1
...
3
...
5
...
7
...
9
...
Sentence 4: From then on, he was recognized as an artist of preternatural
abilities, not only as a composer but also as a pianist and conductor
...
Choice B: discussing different theories about the transport of plant seeds to
Hawaii
Choice D: challenge the claim that ocean currents are responsible for the
transport of plant seeds to Hawaii
SET 3
...
2
...
4
...
6
...
8
...
Unlawful distribution of this ebook is prohibited
...
Reading Comprehension Questions: Medium
1
...
3
...
5
...
7
...
9
...
Choice B: To elaborate on how A Dream fulfills the author’s childhood criteria for
a pleasurable book
Choice B: Predators of zooplankton, such as whitefish and perch, live and feed
near the surface of the lake during the day
...
Choice E: Pessen challenges a view of the social and economic systems in the
United States from 1825 to 1850, but he draws conclusions that are incorrect
...
Discrete Questions: Hard
1
...
3
...
5
...
7
...
9
...
Reading Comprehension Questions: Hard
1
...
3
...
5
...
7
...
Choice E: The proportion of farmers in the general population increased from
68 percent in 1850 to 72 percent in 1880
...
Choice B: The directional movement of wind; AND Choice C: The temperature
differential between the sea and the desert
...
Choice D: The second part provides less substantiation for a romantic reading
...
Choice B: not be inflexible in its treatment of the elements in the novel
Choice B: Hamlet has elements that are not amenable to an all-encompassing
critical interpretation
...
Unlawful distribution of this ebook is prohibited
...
Discrete Questions: Easy
For Questions 1 to 5, select one entry for each blank from the corresponding column
of choices
...
1
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
intensification
authorization
centralization
improvisation
elimination
Explanation
The sentence explains why dominant interests often benefit from a certain condition
...
Thus the best answer
is “elimination
...
Thus the correct answer is elimination (Choice E)
...
Kagan maintains that an infant’s reactions to its first stressful experiences are
part of a natural process of development, not harbingers of childhood
unhappiness or _________ signs of adolescent anxiety
...
The missing word describes signs of adolescent
anxiety as they relate to the infant
...
Since an infant cannot literally display signs of adolescent anxiety, “normal,” “monotonous,” and “typical” are all incorrect
...
Thus the correct answer is prophetic (Choice A)
...
Unlawful distribution of this ebook is prohibited
...
An investigation that is _________ can occasionally yield new facts, even notable
ones, but typically the appearance of such facts is the result of a search in a
definite direction
...
” Among
the answer choices, only “unguided” provides a contrasting description; none of the
other choices suggests an appropriate contrast
...
4
...
But perhaps it is the artistic skill with which the
portraits are painted that (ii)_________ their presence in art museums
...
” So the suggestion is that the presence of portrait paintings in art museums is in that sense odd or
unfitting
...
The second sentence, in contrast to the first, offers a point in favor of portraits — “artistic skill
...
Of the choices for Blank (ii), “justifies” is the one that completes
that thought
...
5
...
Blank (i)
A
ɕ
B
ɕ
C
ɕ
activism
apathy
affability
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
devoted to
indifferent to
shaped by
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GRE Verbal Reasoning Practice Questions
Explanation
The sentence tells us that there is a contrast between the way Simpson related to politics in his college years and how he related to politics later in life
...
The part of the sentence beginning
with “despite” indicates that Simpson’s relation to politics in his college years did not
involve engagement in the political activity that was “rife
...
And of the choices for Blank (i), only
“activism” supplies the required contrast with “indifferent to
...
For Questions 6 to 8, select the two answer choices that, when used to complete
the sentence, fit the meaning of the sentence as a whole and produce completed
sentences that are alike in meaning
...
As my eyesight began to _________, I spent a lot of time writing about it — both
poems and “eye journals” — describing what I saw as I looked out through
damaged eyes
...
The words that best do so are “deteriorate” and “decline” (Choices A and D), which generate sentences alike in meaning
...
Though “adjust”
makes some sense when inserted into the blank, no other option produces a sentence
similar in meaning
...
7
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
unqualified
undiminished
undecided
undamaged
unresolved
unprincipled
Explanation
The use of the word “though” establishes a contrast between the blank, which requires
a description of the judge’s standing, and “phony allegations of wrongdoing
...
Unlawful distribution of this ebook is prohibited
...
The only words that do so are “undiminished”
and “undamaged” (Choices B and D), which produce sentences alike in meaning
...
Thus the correct answer is undiminished (Choice B) and undamaged (Choice D)
...
Modern agricultural practices have been extremely successful in increasing the
productivity of major food crops, yet despite heavy use of pesticides, _________
losses to diseases and insect pests are sustained each year
...
The only words that describe an appropriate level of losses are “significant” and “considerable” (Choices C and D), which produce sentences alike in
meaning
...
Thus the correct answer is significant (Choice C) and considerable (Choice D)
...
Reading Comprehension Questions: Easy
For each of Questions 1 to 9, select one answer choice unless otherwise instructed
...
A person who agrees to serve as mediator between two warring factions at the
request of both abandons by so agreeing the right to take sides later
...
The passage above emphasizes which of the following points about mediators?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
They should try to form no opinions of their own about any issue that is
related to the dispute
...
They should not agree to serve unless they are equally acceptable to all
parties to a dispute
...
They should reserve the right to abandon their impartiality so as not to be
open to the charge of having been deceitful
...
Unlawful distribution of this ebook is prohibited
...
This is the point
made in Choice B, which is therefore the correct answer
...
The passage does not
rule out the possibility that one can have an opinion about issues related to a dispute
without taking sides in the actual dispute
...
Choices D and E are both inconsistent with the main point of the
passage, the importance of impartiality at all times, so both are incorrect
...
Was Felix Mendelssohn (1809–1847) a great composer? On its face, the question seems
absurd
...
From then on, he was recognized as an artist of preternatural
abilities, not only as a composer but also as a pianist and conductor
...
Despite general acknowledgment of his genius, there has been a
noticeable reluctance to rank him with, say, Schumann or Brahms
...
working on a small scale of emotion and texture
...
2
...
Explanation
This question asks which sentence in the passage serves to indicate the range of
Mendelssohn’s musical talents
...
conductor”), the only sentence in the passage that mentions Mendelssohn’s achievements across three different realms: composing, piano performance, and conducting
...
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...
GRE Verbal Reasoning Practice Questions
3
...
Therefore, Choice C is correct
...
4
...
The “reluctance” is mentioned in the context of a discussion about
Mendelssohn’s critical standing and thus is being ascribed to music critics generally
...
Choice C is incorrect because the word “reluctance” is
mentioned only after the passage turns from discussing the popular view of
Mendelssohn to the critical view
...
5
...
Unlawful distribution of this ebook is prohibited
...
Therefore, Choice E is correct
...
However, careful consideration reveals that the
point the author is making when Schumann and Brahms are mentioned is not the frequency of that comparison but the results of it
...
Choices B, C, and D are incorrect because the passage does not discuss Schumann’s
and Brahms’s popularity, Mendelssohn’s influence on other composers, or the milieu in
which Mendelssohn worked
...
While most scholarship on women’s employment in the United States recognizes that
the Second World War (1939–1945) dramatically changed the role of women in the
workforce, these studies also acknowledge that few women remained in manufacturing
jobs once men returned from the war
...
Instead, the expansion of agriculture and a steady decrease in the number of male
farmworkers combined to cause the industry to hire more women in the postwar years
...
Description
The first sentence states that the Second World War led to significant changes in
women’s employment, but that these changes were largely reversed in manufacturing
after the war
...
6
...
We are told that few women remained
in the manufacturing sector once men returned from the war, while the number of
women who worked in agriculture increased after the war as the number of men in
agriculture decreased
...
Choices A, C, and E are incorrect
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GRE Verbal Reasoning Practice Questions
because the passage provides no information about rates of expansion, wage trends, or
women’s job satisfaction
...
7
...
The great majority of women who joined the workforce during the Second
World War were employed in manufacturing jobs
...
The increase in women’s employment that accompanied the Second World
War was longer lasting in agriculture than it was in manufacturing
...
Explanation
The correct choice for this question is Choice D
...
However, not only did women’s employment in agriculture not decline after the end of
the war, it actually increased
...
Questions 8 and 9 are based on the following reading passage
...
There is some dispute about the method of transport involved
...
Yet the results of flotation experiments and the low temperatures of air currents cast doubt on these hypotheses
...
While it is likely that fewer varieties of
plant seeds have reached Hawaii externally than internally, more varieties are known
to be adapted to external than to internal transport
...
It introduces one possible method — ocean and air currents — but refers to evidence that casts
doubt on that method
...
84
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GRE Verbal Reasoning Practice Questions
8
...
”
Choice A can be eliminated: while the passage does refer to flotation experiments, it
does not elaborate on experimental methods
...
Choices D and E
are incorrect because the passage does not resolve any disputes
...
The author mentions the results of flotation experiments on plant seeds (lines
7–8) most probably in order to
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
support the claim that the distribution of plants in Hawaii is the result of
the long-distance dispersal of seeds
lend credibility to the thesis that air currents provide a method of
transport for plant seeds to Hawaii
suggest that the long-distance dispersal of seeds is a process that requires
long periods of time
challenge the claim that ocean currents are responsible for the transport
of plant seeds to Hawaii
refute the claim that Hawaiian flora evolved independently from flora in
other parts of the world
Explanation
This question asks why the author mentions flotation experiments
...
Thus, Choice D is correct
...
Choice B is eliminable
since the flotation experiments are introduced at a point where the author is challenging, rather than lending credibility to, the air current hypothesis and because flotation
experiments would more likely reflect on ocean currents than air currents
...
Finally, Choice E is eliminable since it too describes an idea
that is not discussed in the passage
...
Unlawful distribution of this ebook is prohibited
...
Discrete Questions: Medium
For Questions 1 to 5, select one entry for each blank from the corresponding column
of choices
...
1
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
predictable
unexpected
admirable
explicit
confusing
Explanation
The words “on the other hand” indicate that while the existence of societal codes of
behavior is no surprise, their character may be quite surprising
...
“Predictable” is
the very opposite of surprising, and none of the other answer choices means “surprising
...
2
...
This was
clear in her agonizing over how far to try to represent the minute details of a
performance in a written text, and this (ii)_________ makes her work a landmark
in ethnomusicology
...
The only
choice for blank (ii) that matches this description is “fastidiousness”; neither “didacticism” nor “iconoclasm” reflects the notion of agonizing over details
...
Thus the correct answer is reverence for (Choice A) and fastidiousness (Choice D)
...
Unlawful distribution of this ebook is prohibited
...
Political advertising may well be the most (i)_________ kind of advertising:
political candidates are usually quite (ii)_________, yet their campaign
advertisements often hide important differences behind smoke screens of smiles
and empty slogans
...
Looking to the second part of the sentence, however, we
can see such expressions as “hide” and “smoke screens,” both of which suggest that the
correct answer for Blank (i) is “deceptive
...
Reading the sentence again
with “deceptive” and “dissimilar” in place confirms those choices
...
4
...
Russell said 52 percent of the nation’s growth since the Second World
War had (i)_________ invention
...
“Unless we can (iii)_________ original ideas, we will not have
invention,” Mr
...
Speculating on the state of innovation over the next
century, several inventors agreed that the future lay in giving children the tools to
think creatively and the motivation to invent
...
This implies that Blank (i) should be filled with “come through,”
which emphasizes the importance of invention; the other choices suggest that invention is irrelevant or somehow harmed by growth
...
” Finally, the second sentence emphasizes the importance for innovation of a strong
patent office, and this thought is reaffirmed in the following quotation from Mr
...
Thus the correct answer is come through (Choice C), aside from supporting
(Choice E), and protect (Choice H)
...
Unlawful distribution of this ebook is prohibited
...
Statements presented as fact in a patent application are (i)_________ unless a
good reason for doubt is found
...
And, although thousands of
patents are challenged in court for other reasons, no incentive exists for anyone
to expend effort (ii)_________ the science of an erroneous patent
...
Blank (i)
Blank (ii)
Blank (iii)
A
ɕ presumed
D
ɕ corroborating
G
ɕ novel
B
ɕ carefully
E
ɕ advancing
H
ɕ bogus
C
ɕ considered
F
ɕ debunking
I
ɕ obsolete
verifiable
scrutinized
capricious
Explanation
The paragraph appears to be explaining some odd or unexpected aspect of the patent
process
...
The only choice for Blank (ii) that is concerned with challenging a patent is
“debunking,” since “corroborating” and “advancing” suggest support instead
...
And we can also now better understand the first sentence — it too must help explain how bogus devices get patents,
which it can do only if the blank is filled with “presumed verifiable,” suggesting that
patent applications are taken at face value and not dismissed out of hand nor subjected
to careful scrutiny
...
For Questions 6 to 8, select the two answer choices that, when used to complete
the sentence, fit the meaning of the sentence as a whole and produce completed
sentences that are alike in meaning
...
Ever a demanding reader of the fiction of others, the novelist Chase was likewise
often the object of _________ analyses by his contemporaries
...
Since he is described as a
“demanding reader,” the words that best fit the blank will be similar in meaning to
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...
GRE Verbal Reasoning Practice Questions
“demanding
...
Although “acerbic analyses” means close to the same thing as “scathing analyses,” both
“acerbic” and “scathing” have meanings that are quite different from “demanding,” so
neither fits well in the blank
...
7
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
stinginess
diffidence
frugality
illiberality
intolerance
thrift
Explanation
The sentence explains that the person spoken of is not miserly, since she is quite prepared to be generous
...
The words “frugality”
and “thrift” fulfill this requirement and yield two sentences that are alike in meaning,
so that pair forms the correct answer
...
Other choices, such as “diffidence,” might perhaps make a sensible
sentence if placed in the blank but do not form part of the correct answer since they
have no companion word that would make a sentence of similar meaning
...
8
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
complicated
engaged
essential
fanciful
inconsequential
involved
Explanation
Because the second half of the sentence illustrates the idea that “structure mirrors
thought,” any word that fills the blank must be similar in meaning to “convoluted
...
“Fanciful,” while somewhat similar in meaning to “convoluted,” is not as similar to either “complicated” or “involved”
as those words are to each other
...
Thus the correct answer is complicated (Choice A) and involved (Choice F)
...
Unlawful distribution of this ebook is prohibited
...
Reading Comprehension Questions: Medium
For each of Questions 1 to 9, select one answer choice unless otherwise instructed
...
I enjoyed A Dream of Light & Shadow: Portraits of Latin American Women Writers for
the same reasons that, as a child, I avidly consumed women’s biographies: the fascination with how the biographical details of another female’s life are represented and
interpreted
...
Yet, as an adult, I have
come to demand of any really “great” book a self-consciousness about the tenuous
nature of representations of reality, a critical contextualization of florid detail, and a
self-awareness of the role of ideology in our lives
...
Description
The passage follows the following structure: the first sentence discusses a collection of
biographical sketches and what the author found particularly appealing about similar
works as a child; the second sentence describes several positive aspects of this particular collection and how it satisfies the author’s early interests; the third sentence
describes a demanding set of criteria that the author now applies when assessing such
work; and in the fourth sentence the author says the collection being discussed does
not meet those criteria
...
1
...
It seems to focus on stylistic variety at the expense of accuracy of detail
...
Explanation
Choices A and C are correct
...
Choice A is correct: the book does not demonstrate sufficient awareness of the
“tenuous nature of representations of reality
...
Choice C is correct: the book does not offer an adequate “critical contextualization
of florid detail
...
Unlawful distribution of this ebook is prohibited
...
Which of the following best describes the function of the second sentence
(“A Dream
...
The correct choice is
Choice B
...
Choice
A is incorrect both because the sentence does not provide examples and because the collection does not display an awareness of the tenuous nature of representations of reality
...
Choice D is incorrect because the sentence describes the virtues of the collection
...
Choice E is incorrect because, according to the passage, the fact that the collection is varied makes it a “rich”
read
...
3
...
hyalina departs for the
depths where food is scarce and the water cold
...
galeata remains near the
warm surface where food is abundant
...
galeata grows and
reproduces much faster, its population is often outnumbered by D
...
Which of the following, if true, would help resolve the apparent paradox
presented above?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The number of species of zooplankton living at the bottom of the lake is
twice that of species living at the surface
...
In order to make the most of scarce food resources, D
...
galeata
...
galeata clusters under vegetation during the hottest part of the day to
avoid the Sun’s rays
...
galeata produces twice as many offspring per individual in any given
period of time as does D
...
Description
The paragraph presents an apparent paradox: the zooplankton that spends the day in
less hospitable conditions often outnumbers the one that stays in more hospitable conditions
...
Unlawful distribution of this ebook is prohibited
...
galeata is consumed at a higher rate than D
...
hyalina is often more numerous, so Choice B is correct
...
Choices A and
D are incorrect because nothing is said in the paragraph to show the relevance of the
presence of other species of zooplankton, nor of the habit of clustering under vegetation, to the relative population size of the two species
...
Tocqueville, apparently, was wrong
...
At least so
argues E
...
Pessen does present a quantity of examples, together with some refreshingly intelligible statistics, to establish the existence of an inordinately wealthy class
...
In no sense mercurial, these great fortunes survived the
financial panics that destroyed lesser ones
...
Although these observations are true, Pessen overestimates their importance by
concluding from them that the undoubted progress toward inequality in the late eighteenth century continued in the Jacksonian period and that the United States was a
class-ridden, plutocratic society even before industrialization
...
4
...
Many of them were able to increase their holdings
...
Most of them accumulated their own fortunes
...
Explanation
For this question, you are to identify the one statement that CANNOT be correctly
attributed to Pessen
...
According to the passage, Pessen maintains all of the following: there was a class of “inordinately wealthy” Americans (Choice A); in some
places that class “constantly increased its share” (Choice B); its members were “active
in commerce or the professions” (Choice C); and “these great fortunes survived the
financial panics that destroyed lesser ones” (Choice E)
...
” Therefore, Choice D is correct
...
Unlawful distribution of this ebook is prohibited
...
Which of the following best states the author’s main point?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
Pessen’s study has overturned the previously established view of the social
and economic structure of early-nineteenth-century America
...
Pessen’s study is valuable primarily because it shows the continuity of the
social system in the United States throughout the nineteenth century
...
Pessen challenges a view of the social and economic systems in the United
States from 1825 to 1850, but he draws conclusions that are incorrect
...
Choices A, C, and D omit any reference to the author’s critical evaluation of Pessen’s
study, and hence are not statements of the author’s main point
...
Because Pessen criticizes Tocqueville and the author criticizes Pessen, it might
seem that the author’s main point is to defend Tocqueville’s analysis
...
Choice E is correct
...
Questions 6 to 9 are based on the following reading passage
...
The interaction resulting from the differences between predator and prey led to a general
improvement in brain functions; however, certain components of intelligence were
improved far more than others
...
It ranges from a passive, freefloating awareness to a highly focused, active fixation
...
From the more relaxed to the more vigorous
levels, sensitivity to novelty is increased
...
The processes of arousal and
concentration give attention its direction
...
Thus begins
concentration, the holding of consistent images
...
Consciousness links past attention to the present and permits the
integration of details with perceived ends and purposes
...
Herbivores and carnivores develop different
kinds of attention related to escaping or chasing
...
Unlawful distribution of this ebook is prohibited
...
For both, arousal attunes the animal to what is ahead
...
The predator is searchingly aggressive, inner-directed, tuned by the
nervous system and the adrenal hormones, but aware in a sense closer to human consciousness than, say, a hungry lizard’s instinctive snap at a passing beetle
...
The herbivore prey is of a different mind
...
Description
The passage describes improvements in certain components of intelligence among
early large mammals of the grasslands
...
6
...
The “hungry lizard’s instinctive snap” is contrasted with the mammal’s higher level of awareness
...
The example of the hungry lizard provides a contrast; it does not demonstrate a similarity or extend the
author’s argument
...
Brutality is not mentioned in the
passage as a characteristic of predators, and there is no suggestion that all animals lack
consciousness
...
It can be inferred from the passage that in animals less intelligent than the
mammals discussed in the passage
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
past experience is less helpful in ensuring survival
attention is more highly focused
muscular coordination is less highly developed
there is less need for competition among species
environment is more important in establishing the proper ratio of prey
to predator
Explanation
Choice A is correct
...
In the context of the entire passage, it can be inferred that
94
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...
GRE Verbal Reasoning Practice Questions
more intelligent animals, such as the grassland mammals discussed, are better able to
use past experience to help them survive than less intelligent animals are
...
The second paragraph of the passage indicates that attention is more highly
focused in animals of greater, rather than less, intelligence
...
The author does not discuss muscular coordination as an element in intelligence, gives no indication that in less intelligent species there is less need for competition, and does not discuss how a proper ratio of prey to predator is established
...
According to the passage, improvement in brain function among early large
mammals resulted primarily from which of the following?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
Interplay of predator and prey
Persistence of free-floating awareness in animals of the grasslands
Gradual dominance of warm-blooded mammals over cold-blooded reptiles
Interaction of early large mammals with less intelligent species
Improvement of the capacity for memory among herbivores and
carnivores
Explanation
Choice A is correct
...
Choice B is incorrect
...
Choices C and D are incorrect: the passage does not discuss the relationship between mammals and reptiles or the interaction between large
mammals and less intelligent species
...
Improved capacity for
memory is an improvement in brain function, rather than a reason for improved brain
function
...
According to the passage, as the process of arousal in an organism continues,
all of the following may occur EXCEPT
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
the production of adrenaline
the production of norepinephrine
a heightening of sensitivity to stimuli
an increase in selectivity with respect to stimuli
an expansion of the range of states mediated by the brain stem
Explanation
This question asks you what does NOT occur during arousal
...
According to the passage, arousal does stimulate the production of adrenaline and norepinephrine (lines 24–26); does increase sensitivity to stimuli (lines 12–13); and does increase concentration on specific stimuli
(lines 16–18)
...
Only
Choice E is correct
...
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GRE Verbal Reasoning Practice Questions
SET 5
...
Fill all blanks in the way that best completes the text
...
For some time now, _________ has been presumed not to exist: the cynical
conviction that everybody has an angle is considered wisdom
...
The
missing word will describe the opposite of the cynical conviction that “everybody has
an angle,” that is, that each person is concerned primarily with his or her own interests
...
None of
the other answer choices means something that is contrasted with or opposed to being
primarily concerned with one’s own interests
...
2
...
Blank (i)
A
ɕ controversial habit
B
ɕ cherished tradition
C
ɕ disquieting ritual
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
endorsed
considered
rejected
Explanation
The reference to human nature and long distances suggest that it is rather routine for
drivers to exceed the speed limit in this state
...
” In Blank (ii) we need to consider what the legislature
would do that would surprise no one with regard to increased penalties for speeding
...
Thus the correct answer is cherished tradition (Choice B) and rejected (Choice F)
...
Unlawful distribution of this ebook is prohibited
...
Serling’s account of his employer’s reckless decision making (i)_________ that
company’s image as (ii)_________ bureaucracy full of wary managers
...
For Blank (i), “belies” is the best choice since Serling’s account would certainly
belie or contradict the company’s image
...
As for Blank (ii), “a cautious” is the most logical choice
...
Thus the correct answer is belies (Choice A) and a cautious (Choice F)
...
No other contemporary poet’s work has such a well-earned reputation for
(i)_________, and there are few whose moral vision is so imperiously unsparing
...
This new collection is the
poet’s fourth book in six years — an ample output even for poets of sunny
disposition, let alone for one of such (ii)_________ over the previous 50 years
...
Blank (i)
Blank (ii)
Blank (iii)
A
ɕ patent
D
ɕ penitential
G
ɕ taciturnity
B
ɕ intrinsic frivolity
E
ɕ intractable
H
ɕ volubility
C
ɕ near
F
ɕ impetuous
I
ɕ pellucidity
accessibility
impenetrability
austerity
prolixity
prodigality
Explanation
Since the author of the paragraph has described the poet’s reputation as “well-earned,”
the correct completion for Blank (i) must be something that is consistent with what the
rest of the passage says about the poet’s work
...
The Blank (ii) completion must contrast with “ample output,” and of the available options, only “penitential austerity” does so
...
The change
the paragraph has described is an increase in output, so “volubility” is the correct
choice
...
Unlawful distribution of this ebook is prohibited
...
5
...
By
contrast, managers who perceive environmental performance to be (iii)_________
to financial success may view an environmental management system as
extraneous
...
Blank (i)
Blank (ii)
Blank (iii)
A
ɕ eclipse
D
ɕ uncritically
G
ɕ complementary
B
ɕ bolster
E
ɕ appropriately
H
ɕ intrinsic
C
ɕ degrade
F
ɕ hotly
I
ɕ peripheral
accept
acknowledge
dispute
Explanation
The first two sentences introduce two contrasting sets of managers
...
The other options for Blank (iii)
— “complementary” and “intrinsic” — are not consistent with the idea that environmental management systems are extraneous
...
Blank (ii) is not straightforward —
clearly these managers would not “hotly dispute” this claim, but “appropriately
acknowledge” is less easily ruled out
...
In fact, a system is not even necessary
...
”
Thus the correct answer is bolster (Choice B), uncritically accept (Choice D), and
peripheral (Choice I)
...
Unlawful distribution of this ebook is prohibited
...
Philosophy, unlike most other subjects, does not try to extend our knowledge by
discovering new information about the world
...
Philosophy
begins by finding (ii)_________ the things that are (iii) _________
...
” The first blank asks us to identify that activity, and although “attainment” makes
little sense in context, both “rumination on” and “detachment from” have some appeal
...
Blank (ii) requires something that suggests the importance of familiar things as subjects of philosophical rumination, and “utterly mysterious” does just that
...
Similarly, Blank (iii) needs to be consistent with the description of those
things as familiar and close
...
“Somewhat hackneyed” has some plausibility but is too
negative given the overall tone of the sentence; there is no indication that those things
are in any way trite
...
For Questions 7 to 9, select the two answer choices that, when used to complete
the sentence, fit the meaning of the sentence as a whole and produce completed
sentences that are alike in meaning
...
The government’s implementation of a new code of ethics appeared intended to
shore up the ruling party’s standing with an increasingly _________ electorate at a
time when the party is besieged by charges that it trades favors for campaign
money
...
Unlawful distribution of this ebook is prohibited
...
In their own way, Choices A,
C, D, and F are consistent with that idea, but only two of these when taken
together — “restive” and “skittish” — produce sentences that are alike in meaning
...
The same holds for “vociferous
...
Thus the correct answer is restive (Choice C) and skittish (Choice D)
...
Overlarge, uneven, and ultimately disappointing, the retrospective exhibition
seems too much like special pleading for a forgotten painter of real but
_________ talents
...
The words “limited” and “circumscribed” do so and also produce sentences that are alike in meaning, so this pair forms the correct answer
...
Other choices, such as “partial” and “prosaic” might
make sense in context, but none of the other choices that meets that criterion also
has a companion choice that would produce another sentence alike in meaning
...
9
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
celebrated
mysterious
long-awaited
fortuitous
indecorous
unseemly
Explanation
The sentence needs to be completed with a word that suggests a reason for the
executive to wish to keep a low profile
...
Unlawful distribution of this ebook is prohibited
...
Therefore, that pair forms the correct answer
...
Thus the correct answer is indecorous (Choice E) and unseemly (Choice F)
...
Reading Comprehension Questions: Hard
For each of Questions 1 to 8, select one answer choice unless otherwise instructed
...
In the United States between 1850 and 1880, the number of farmers continued to
increase, but at a rate lower than that of the general population
...
The rate of growth of the United States labor force and the rate of growth
of the general population rose simultaneously in the 30 years between
1850 and 1880
...
The proportion of farmers in the United States labor force decreased from
64 percent in 1850 to 49 percent in 1880
...
Explanation
The given sentence indicates that the proportion of farmers in the general population
decreased from 1850 to 1880
...
Choice
A is incorrect because it agrees with the given sentence, and Choices B, C, and D are all
incorrect because they refer to the labor force, about which the given sentence says
nothing
...
Unlawful distribution of this ebook is prohibited
...
A ten-year comparison between the United States and the Soviet Union in terms
of crop yields per acre revealed that when only planted acreage is compared,
Soviet yields were equal to 68 percent of United States yields
...
From the information above, which of the following can be most reliably inferred
about United States and Soviet agriculture during the ten-year period?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
A higher percentage of total agricultural acreage was fallow in the United
States than in the Soviet Union
...
Fewer total acres of available agricultural land were fallow in the Soviet
Union than in the United States
...
The Soviet Union produced a greater volume of crops than the United
States produced
...
Therefore, Choice A is the correct answer
...
Similarly, it is impossible to determine the total volume of crops produced in the Soviet Union, so Choice E is incorrect
...
For hot desert locations with access to seawater, a new greenhouse design generates
freshwater and cool air
...
This cool, humidified air accelerates plant growth; little water
evaporates from leaves
...
This heated air, drawn
down from the roof, then mixes with the greenhouse air as it reaches a second
seawater-moistened cardboard wall at the back of the greenhouse
...
Description
The passage describes a greenhouse design and the process by which the design generates freshwater and cool air in a desert environment lacking in these things
...
Unlawful distribution of this ebook is prohibited
...
3
...
This question asks the reader which of the three phenomena listed in the answer choices is used in the process described in the passage
...
Choice B is correct: the second sentence describes the orientation of a perforated
cardboard wall toward the prevailing wind so that hot air blows in and is moistened
...
For the following question, consider each of the choices separately and select all that
apply
...
It can be inferred that the greenhouse roof is designed to allow for which of the
following?
A
Ȟ The avoidance of intense solar heat inside the greenhouse
B
Ȟ The entry of sunlight into the greenhouse to make the plants grow
C
Ȟ The mixture of heated air with greenhouse air to enhance the collection of
moisture
Explanation
All three choices are correct
...
Choice A is correct: the purpose of the double-layered roof is to trap solar heat
before it gets inside the greenhouse proper
...
Choice C is correct: the last two sentences of the passage describe how heated air
from the roof is drawn down to mix with greenhouse air, resulting in the collection of
distilled water for irrigation purposes
...
Unlawful distribution of this ebook is prohibited
...
Many critics of Emily Brontë’s novel Wuthering Heights see its second part as a counterpoint that comments on, if it does not reverse, the first part, where a romantic reading receives more confirmation
...
Granted that the presence of these elements need not argue for an authorial awareness
of novelistic construction comparable to that of Henry James, their presence does
encourage attempts to unify the novel’s heterogeneous parts
...
This is not because such an interpretation necessarily stiffens into a thesis (although rigidity in any interpretation of this or of any novel is always a danger),
but because Wuthering Heights has recalcitrant elements of undeniable power that, ultimately, resist inclusion in an all-encompassing interpretation
...
Description
The passage discusses a critical view concerning the unity of structure of Wuthering
Heights, then, following the use of “However,” expresses a reservation about that view
...
According to the passage, which of the following is a true statement about the
first and second parts of Wuthering Heights?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The second part has received more attention from critics
...
The second part annuls the force of the first part
...
The second part is better because it is more realistic
...
According to
the first sentence, the first part of the novel tends to confirm the “romantic” reading
more strongly than the second
...
Nothing in the passage
suggests that critics have paid more attention to the second part, that the two parts
have little relation, or that the second part is better
...
Choice C is a more extreme statement than any found in the passage, and
therefore it is incorrect
...
Which of the following inferences about Henry James’s awareness of novelistic
construction is best supported by the passage?
A
ɕ
James, more than any other novelist, was aware of the difficulties of
novelistic construction
...
James’s awareness of novelistic construction derived from his reading of
Brontë
...
E
ɕ James’s awareness of novelistic construction precluded him from violating
the unity of his novels
...
Unlawful distribution of this ebook is prohibited
...
The third sentence implies that James represents a very high degree of
authorial awareness of novelistic construction and that no such claim is necessarily
being made for Brontë
...
Choice A is incorrect,
since the passage does not imply that there are particular difficulties that James understood uniquely among novelists
...
The passage also does not say anything about
commentators’ opinions of the unity of James’s works; therefore Choice D is incorrect
...
7
...
Choice A may seem attractive
because in the passage the author says that Wuthering Heights has heterogeneous elements that resist inclusion in a unifying interpretive scheme
...
By contrast, the author’s parenthetical
statement about rigidity does present a general warning against inflexibility of interpretation, and it is this that supports Choice B as the correct answer
...
Although the author mentions recalcitrant elements of Wuthering Heights,
there is no suggestion by the author that such elements deserve a special focus in interpretation
...
The author of the passage does not indicate
which elements, if any, of novelistic construction are most worthy of consideration
...
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...
GRE Verbal Reasoning Practice Questions
For the following question, consider each of the choices separately and select all that
apply
...
The author of the passage suggests which of the following about Hamlet?
A
Ȟ Hamlet has usually attracted critical interpretations that tend to stiffen
B
Ȟ
C
Ȟ
into theses
...
Hamlet is less open to an all-encompassing critical interpretation than is
Wuthering Heights
...
This question asks the reader which of the three statements about
Hamlet listed in the answer choices are suggested by the author of the passage
...
Choice B is correct: Hamlet is mentioned only in the final sentence of the passage,
which refers to “this respect” in which Hamlet and Wuthering Heights are similar
...
Choice C is incorrect: the passage mentions only a feature shared between Hamlet
and Wuthering Heights
...
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5
GRE ®
Quantitative Reasoning
Your goals
for this
chapter
g Learn the four types of GRE® Quantitative
Reasoning questions
g Get tips for answering each question type
g Study sample Quantitative Reasoning questions
with solutions
g Learn how to use the on-screen calculator
Overview of the Quantitative Reasoning Measure
The Quantitative Reasoning measure of the GRE revised General Test assesses your:
b
b
b
basic mathematical skills
understanding of elementary mathematical concepts
ability to reason quantitatively and to model and solve problems with quantitative methods
Some of the questions in the measure are posed in real-life settings, while others
are posed in purely mathematical settings
...
Arithmetic topics include properties and types of integers, such as divisibility,
factorization, prime numbers, remainders, and odd and even integers; arithmetic
operations, exponents, and roots; and concepts such as estimation, percent, ratio,
rate, absolute value, the number line, decimal representation, and sequences of
numbers
...
Geometry topics include parallel and perpendicular lines, circles, triangles—
including isosceles, equilateral, and 30°-60°-90° triangles—quadrilaterals, other
polygons, congruent and similar figures, three-dimensional figures, area, perimeter,
volume, the Pythagorean theorem, and angle measurement in degrees
...
Data analysis topics include basic descriptive statistics, such as mean, median,
mode, range, standard deviation, interquartile range, quartiles, and percentiles; interpretation of data in tables and graphs, such as line graphs, bar graphs, circle graphs,
boxplots, scatterplots, and frequency distributions; elementary probability, such as
probabilities of compound events and independent events; random variables and
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...
GRE Quantitative Reasoning
probability distributions, including normal distributions; and counting methods,
such as combinations, permutations, and Venn diagrams
...
Inferential
statistics is not tested
...
The publication Math Review for the GRE revised General Test, which is available at www
...
org/gre/prepare,
provides detailed information about the content of the Quantitative Reasoning measure
...
The mathematical symbols, terminology, and conventions used in the Quantitative Reasoning measure are those that are standard at the high school level
...
Whenever nonstandard notation is
used in a question, it is explicitly introduced in the question
...
Two of these assumptions are (i) all numbers used are real numbers and (ii) geometric figures are
not necessarily drawn to scale
...
ets
...
Quantitative Reasoning Question Types
The Quantitative Reasoning measure has four types of questions:
¼
¼
¼
¼
Quantitative Comparison questions
Multiple-choice questions—Select One Answer Choice
Multiple-choice questions—Select One or More Answer Choices
Numeric Entry questions
Each question appears either independently as a discrete question or as part of a
set of questions called a Data Interpretation set
...
In the computer-based test, you are allowed to use a basic calculator—provided
on-screen—on the Quantitative Reasoning measure
...
For those taking the paper-based test, handheld calculators will be provided at
the test center for use during the test
...
ets
...
Quantitative Comparison Questions
Description
Questions of this type ask you to compare two quantities—Quantity A and Quantity
B—and then determine which of the following statements describes the comparison
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Unlawful distribution of this ebook is prohibited
...
Quantitative Comparison questions
always have the same answer choices, so get to know them, especially the last
choice, “The relationship cannot be determined from the information given
...
Also, if you determine that one quantity is
greater than the other, make sure you carefully select the corresponding choice
so as not to reverse the first two choices
...
Don’t waste time performing needless
computations in order to compare the two quantities
...
¼ Remember that geometric figures are not necessarily drawn to scale
...
Examine the results
...
If one or both of the quantities are algebraic expressions, you
can substitute easy numbers for the variables and compare the resulting
quantities in your analysis
...
g
...
If you see that Quantity A is greater than
Quantity B in one case and Quantity B is greater than Quantity A in another
case, choose “The relationship cannot be determined from the information
given
...
If both quantities are algebraic or arithmetic
expressions and you cannot easily see a relationship between them, you can try
to simplify the comparison
...
Begin by setting up a comparison involving the
two quantities, as follows:
||
Quantity A ? Quantity B
||
where ? is a “placeholder” that could represent the relationship greater than
(>), less than (<), or equal to (=) or could represent the fact that the
relationship cannot be determined from the information given
...
For example, you may conclude after the last step
that ? represents equal to (=)
...
To understand this strategy more fully, see sample
questions 6 to 9
...
Unlawful distribution of this ebook is prohibited
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity A
1
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Thus, 29 is the least prime number greater than 24, and Quantity A is 29
...
Thus, 23 is
the greatest prime number less than 28, and Quantity B is 23
...
Lionel is younger than Maria
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity B
Maria’s age
Quantity A is greater
...
The two quantities are equal
...
Explanation
If Lionel’s age is 6 years and Maria’s age is 10 years, then Quantity A is greater,
but if Lionel’s age is 4 years and Maria’s age is 10 years, then Quantity B is
greater
...
The correct answer is Choice D, the relationship cannot be determined
from the information given
...
Unlawful distribution of this ebook is prohibited
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity B
150
Quantity A is greater
...
The two quantities are equal
...
Explanation
Without doing the exact computation, you can see that 54 percent of 360 is
1
greater than of 360, which is 180, and 180 is greater than Quantity B, 150
...
Figure 1
Q
P
S
PQ = PR
R
Quantity A
PS
4
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
You are also given that PQ = PR
...
Furthermore,
because the figure is not necessarily drawn to scale, you cannot determine the
relative sizes of PS and SR visually from the figure, though they may appear to
be equal
...
Following are two possible variations of Figure 1, each of which is drawn to be
consistent with the information PQ = PR
...
Unlawful distribution of this ebook is prohibited
...
Thus, the correct answer is Choice D, the relationship cannot be
determined from the information given
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity B
y
Quantity A is greater
...
The two quantities are equal
...
Explanation
If x = 0, then y = 2(02) + 7(0) − 3 = −3, so in this case, x > y; but if x = 1, then
y = 2(12) + 7(1) − 3 = 6, so in that case, y > x
...
Note that plugging numbers into expressions may not be conclusive
...
It is
also conclusive if there are only a small number of possible numbers to plug in and
all of them yield the same result, say, that Quantity B is greater
...
If
you plug many of them in and each time the result is, for example, that Quantity A
is greater, you still cannot conclude that Quantity A is greater for every possible
number that could be plugged in
...
112
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...
GRE Quantitative Reasoning
The following sample questions focus on simplifying the comparison
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity B
y
Quantity A is greater
...
The two quantities are equal
...
Explanation
Set up the initial comparison:
3y + 2
?y
5
||
Then simplify:
Step 1: Multiply both sides by 5 to get
||
3y + 2 ? 5y
Step 2: Subtract 3y from both sides to get
||
2 ? 2y
Step 3: Divide both sides by 2 to get
||
1?y
The comparison is now simplified as much as possible
...
It follows from y > 4 that y > 1, or 1 < y, so that in the comparison 1 ? y, the
||
||
placeholder ? represents less than (<): 1 < y
...
To go from the comparison
between 1 and y to a comparison between Quantities A and B, start with the last
comparison, 1 < y, and carefully consider each simplification step in reverse
order to determine what each comparison implies about the preceding
comparison, all the way back to the comparison between Quantities A and B if
possible
...
Each simplification step can be reversed as follows:
¼
¼
¼
Reverse step 3: multiply both sides by 2
...
Reverse step 1: divide both sides by 5
...
Thus, the correct answer is Choice B, Quantity B is greater
...
Unlawful distribution of this ebook is prohibited
...
Also, note that when you simplify an inequality, the steps of multiplying or dividing both sides by a negative number change the direction of the inequality; for example, if x < y, then −x > −y
...
This is another
reason to consider the impact of each step carefully
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity B
228
Quantity A is greater
...
The two quantities are equal
...
Explanation
Set up the initial comparison:
230 − 229
? 228
2
||
Then simplify:
Step 1: Multiply both sides by 2 to get
||
230 − 229 ? 229
Step 2: Add 229 to both sides to get
||
230 ? 229 + 229
Step 3: Simplify the right-hand side using the fact that (2)(229) = 230 to get
||
230 ? 230
The resulting relationship is equal to (=)
...
So Quantities A and B are
also equal
...
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GRE Quantitative Reasoning
Quantity A
x2 + 1
8
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Since the square
of a number is always greater than or equal to 0, and 0 is greater than −1, the
simplified comparison is the inequality (x − 1)2 > −1 and the resulting
relationship is greater than (>)
...
Therefore, Quantity
A is greater than Quantity B
...
w>1
Quantity A
7w − 4
9
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Unlawful distribution of this ebook is prohibited
...
Although you are given that
9
w > 1, you still don’t know how w compares to , or 1
...
For example, if w = 1
...
8, but if w = 2, then w > 1
...
In other words, the relationship between
9
w and cannot be determined
...
Thus, the
relationship between Quantities A and B cannot be determined
...
The strategy of simplifying the comparison works most efficiently when you note
that a simplification step is reversible while actually taking the step
...
Be
aware that some common operations like squaring both sides are generally not reversible and may require further analysis using other information given in the question in order to justify reversing such steps
...
Unlawful distribution of this ebook is prohibited
...
Tips for Answering
¼ Use the fact that the answer is there
...
¼ Check your computations—you may have made a mistake, such as mis-keying
a number on the calculator
...
¼ Examine the answer choices
...
You may have to consider each choice
separately, or you may be able to see a relationship between the choices that
will help you find the answer more quickly
...
However, be careful, as that
method may take more time than using reasoning
...
In other questions, too, it may be helpful to
scan the choices briefly before solving the problem to get a better sense of
what the question is asking
...
In other questions, you
may find that estimation is sufficient and will help you avoid spending time on
long computations
...
1
...
The correct
answer is Choice A, −4
...
Unlawful distribution of this ebook is prohibited
...
Which of the following numbers is farthest from the number 1 on the
number line?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
−10
−5
0
5
10
Explanation
Circling each of the answer choices in a sketch of the number line (Figure 4)
shows that of the given numbers, −10 is the greatest distance from 1
...
For example, the distance between −10 and 1 is
⎪−10 − 1⎪ = 11, and the distance between 10 and 1 is ⎪10 − 1⎪ = ⎪9⎪ = 9
...
y
y = f(x)
1
O
1
x
Figure 5
3
...
For which of the following functions g,
defined for all numbers x, does the graph of g intersect the graph of f ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
g(x) = x − 2
g(x) = x + 3
g(x) = 2x − 2
g(x) = 2x + 3
g(x) = 3x − 2
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GRE Quantitative Reasoning
Explanation
You can see that all five choices are linear functions whose graphs are lines with
various slopes and y-intercepts
...
y
y = f (x)
1
x
O 1
Figure 6
It is clear that this line will not intersect the graph of f to the left of the y-axis
...
Consequently, as the value of x increases, the value of y increases
faster for f than for g, and therefore the graphs do not intersect to the right of
the y-axis
...
Note that if the y-intercept of either of
the lines in Choices A and B were greater than or equal to 4 instead of less than
4, they would intersect the graph of f
...
Hence,
they are parallel to the graph of f (to the right of the y-axis) and therefore will
not intersect it
...
The correct answer is Choice E, g(x) = 3x − 2
...
A car got 33 miles per gallon using gasoline that cost $2
...
Approximately what was the cost, in dollars, of the gasoline used in driving
the car 350 miles?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
$10
$20
$30
$40
$50
Explanation
Scanning the answer choices indicates that you can do at least some estimation
350
and still answer confidently
...
95) dollars
...
95) by estimating
33
33
33
a little low, 10, and estimating 2
...
You can also use the calculator to compute a more exact
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GRE Quantitative Reasoning
answer and then round the answer to the nearest 10 dollars, as suggested by the
answer choices
...
287
...
Thus, the correct answer is Choice C, $30
...
A certain jar contains 60 jelly beans—22 white, 18 green, 11 yellow, 5 red,
and 4 purple
...
09
0
...
54
0
...
91
Explanation
Since there are 5 red and 4 purple jelly beans in the jar, there are 51 that are
51
neither red nor purple, and the probability of selecting one of these is
...
85
...
85
...
A question may or may not specify the number
of choices to select
...
Tips for Answering
¼ Note whether you are asked to indicate a specific number of answer choices or
all choices that apply
...
Note that there may be only one correct choice
...
Knowing the least and/or greatest possible value may
enable you to quickly determine all of the choices that are correct
...
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GRE Quantitative Reasoning
Sample Questions
Select one or more answer choices according to the specific question directions
...
¼
¼
The correct answer may be just one of the choices or as many as all of the
choices, depending on the question
...
If the question specifies how many answer choices to select, select exactly that
number of choices
...
Which two of the following numbers have a product that is between −1 and
0?
Indicate both of the numbers
...
The product of the
pair must be negative, so the possible products are (−20)(2−4), (−20)(3−2),
(−10)(2−4), and (−10)(3−2)
...
The first
−20
20
−20
20
product is 4 = − Ͻ −1, the second product is 2 = − Ͻ −1, and third
2
16
3
9
−10
10
product is 4 = − Ͼ −1, so you can stop there
...
2
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
F
Ǣ
8
9
12
18
21
36
Explanation
You can first identify the multiples of 2, which are 8, 12, 18, and 36, and then
among the multiples of 2 identify the multiples of 3, which are 12, 18, and 36
...
The correct answer consists of Choices C (12), D (18), and F (36)
...
Unlawful distribution of this ebook is prohibited
...
Each employee of a certain company is in either Department X or
Department Y, and there are more than twice as many employees in
Department X as in Department Y
...
Which of the following amounts could be
the average salary for all of the employees of the company?
Indicate all such amounts
...
Clearly the average salary is between $25,000 and
$35,000, and all of the answer choices are in this interval
...
If there were exactly twice as many employees in Department X as in
Department Y, then the average salary for all employees would be, to the nearest
dollar, the following weighted mean,
(2)(25,000) + (1)(35,000)
Ϸ 28,333 dollars
2+1
where the weight for $25,000 is 2 and the weight for $35,000 is 1
...
This means that $28,333 is the greatest possible
average
...
Thus, the correct answer consists of Choices A ($26,000) and B
($28,000)
...
To see that $26,000 is possible, in the
weighted mean above, use the respective weights 9 and 1 instead of 2 and 1
...
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GRE Quantitative Reasoning
4
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
F
Ǣ
G
Ǣ
H
Ǣ
I
Ǣ
J
Ǣ
0
1
2
3
4
5
6
7
8
9
Explanation
The units digit of 57n is the same as the units digit of 7n for all positive integers
n
...
Because this is true for every
positive integer n, you need to consider only powers of 7
...
In this sequence, the first digit, 7, appears again, and the
pattern of four digits, 7, 9, 3, 1, repeats without end
...
The correct answer consists of Choices B (1), D (3), H (7), and J (9)
...
In the computer-based test, use the computer mouse and keyboard to enter your answer
...
Since there are no answer
choices to guide you, read the question carefully and make sure you provide
the type of answer required
...
Pay special attention to
units such as feet or miles, to orders of magnitude such as millions or billions,
and to percents as compared with decimals
...
For example, if an answer of 46
...
If your solution strategy
involves intermediate computations, you should carry out all computations
exactly and round only your final answer in order to get the required degree of
accuracy
...
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GRE Quantitative Reasoning
¼ Examine your answer to see if it is reasonable with respect to the information
given
...
Sample Questions
Enter your answer as an integer or a decimal if there is a single answer box OR as a
fraction if there are two separate boxes—one for the numerator and one for the
denominator
...
¼
¼
¼
¼
¼
¼
¼
First, click on the answer box—a cursor will appear in the box—and then type the
number
...
For a negative sign, type a hyphen
...
To remove a negative sign, type the hyphen again and it will disappear; the
number will remain
...
Equivalent forms of the correct answer, such as 2
...
50, are all correct
...
To enter a fraction, type the numerator and the denominator in the respective boxes
using the keyboard
...
A decimal
point cannot be used in a fraction
...
Fractions do not need to be reduced to lowest terms, though you may need to
reduce your fraction to fit in the boxes
...
One pen costs $0
...
35
...
25 by 18 yields $4
...
35 by 100 yields $35
...
The
total cost is therefore $4
...
00 = $39
...
Equivalent decimals, such as
$39
...
500, are considered correct
...
50 (or equivalent)
...
In fact, only numbers, a decimal point,
and a negative sign can be entered in the answer box
...
Unlawful distribution of this ebook is prohibited
...
Rectangle R has length 30 and width 10, and square S has length 5
...
20
Therefore, the perimeter of S is
of the perimeter of R
...
Because the fraction does not need to be reduced to lowest
20
terms, any fraction that is equivalent to
is also considered correct, as long as
80
2
1
it fits in the boxes
...
20
Thus, the correct answer is
(or any equivalent fraction)
...
For the large cars sold at an auction that is summarized in the table above,
what was the average sale price per car?
$
Explanation
From Figure 7, you see that the number of large cars sold was 20 and the sales
total for large cars was $120,000 (not $120)
...
was
20
The correct answer is $6,000 (or equivalent)
...
)
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GRE Quantitative Reasoning
4
...
What is the profit expressed as a percent of the merchant’s
cost?
Give your answer to the nearest whole percent
...
333
...
3 percent, which is 33%, to the
nearest whole percent
...
If you use the calculator and the Transfer Display button, the number that
will be transferred to the answer box is 33
...
You will need to adjust the number in
the answer box by deleting all of the digits to the right of the decimal point
(using the Backspace key)
...
33, is incorrect
...
Entering 0
...
33%
...
Working alone at its constant rate, machine A produces k car parts in 10
minutes
...
How many minutes does it take machines A and B, working
simultaneously at their respective constant rates, to produce k car parts?
minutes
Explanation
k
k
parts per minute, and machine B produces
parts per
10
15
minute
...
To compute the time required to produce k parts at
150
6
k
k
this rate, divide the amount k by the rate to get
= 6
...
One way to check that the answer of 6 minutes is reasonable is to observe
that if the slower rate of machine B were the same as machine A’s faster rate of
k parts in 10 minutes, then the two machines, working simultaneously, would
take half the time, or 5 minutes, to produce the k parts
...
Similarly, if the faster rate of machine A were the same as
machine B’s slower rate of k parts in 15 minutes, then the two machines would
take half the time, or 7
...
So the answer has to
be less than 7
...
Thus, the answer of 6 minutes is reasonable compared
to the lower estimate of 5 minutes and the upper estimate of 7
...
Machine A produces
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GRE Quantitative Reasoning
Data Interpretation Sets
Description
Data Interpretation questions are grouped together and refer to the same table,
graph, or other data presentation
...
The types of questions may be Multiple-choice (both types) or
Numeric Entry
...
Focus on those aspects of the
data that are necessary to answer the questions
...
¼ Bar graphs and circle graphs, as well as other graphical displays of data, are
drawn to scale, so you can read or estimate data visually from such graphs
...
¼ The questions are to be answered only on the basis of the data presented,
everyday facts (such as the number of days in a year), and your knowledge of
mathematics
...
Sample Questions
Questions 1 to 3 are based on the following data
...
If the dollar amount of sales at Store P was $800,000 for 2006, what was
the dollar amount of sales at that store for 2008 ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
$727,200
$792,000
$800,000
$880,000
$968,000
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GRE Quantitative Reasoning
Explanation
According to Figure 8, if the dollar amount of sales at Store P was $800,000 for
2006, then it was 10 percent greater for 2007, which is 110 percent of that
amount, or $880,000
...
The correct answer is Choice B, $792,000
...
2
...
1 percent
...
08A, is the amount of decrease from 2007 to 2008
...
08A = 0
...
Therefore, the desired percent can be obtained by
A
1
=
= 1
...
Expressed as a
dividing A by 0
...
92A 0
...
1 percent, this number is 108
...
Thus, the correct answer is 108
...
3
...
A
Ǣ
B
Ǣ
C
Ǣ
For 2008 the dollar amount of sales at Store R was greater than that at
each of the other four stores
...
The dollar amount of sales at Store R for 2008 was more than 17
percent greater than that for 2006
...
Even though Store R had the greatest
percent increase from 2006 to 2008, its actual dollar amount of sales for 2008
may have been much smaller than that for any of the other four stores, and
therefore Choice A is not necessarily true
...
If B is the
dollar amount of sales at Store S for 2006, then the dollar amount for 2007 is 93
percent of B, or 0
...
85)(0
...
7905B
...
05 = 20
...
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GRE Quantitative Reasoning
For Choice C, if C is the dollar amount of sales at Store R for 2006, then the
dollar amount for 2007 is given by 1
...
12)(1
...
176C
...
6 percent
increase, which is greater than 17 percent, so Choice C must be true
...
Using the Calculator
Sometimes the computations you need to do in order to answer a question in the
Quantitative Reasoning measure are somewhat time-consuming, like long division, or
involve square roots
...
The on-screen calculator is shown in Figure 9
...
You must use your mathematical knowledge
to determine whether the calculator’s results are reasonable and how the results can
be used to answer a question
...
Use it for calculations that you know are tedious, such as long division, square
roots, and addition, subtraction, or multiplication of numbers that have several
digits
...
10
Avoid using it to introduce decimals if you are asked to give an answer as a
fraction
...
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GRE Quantitative Reasoning
¼
If you use the calculator, estimate the answer beforehand so that you can
determine whether the calculator’s answer is “in the ballpark
...
The following guidelines are specific to the on-screen calculator in the computerbased test:
¼
¼
¼
¼
When you use the computer mouse or the keyboard to operate the calculator,
take care not to mis-key a number or operation
...
The Transfer Display button can be used on Numeric Entry questions with a
single answer box
...
You should check that the transferred number has the correct form to
answer the question
...
Take note that the calculator respects order of operations, as explained below
...
The order is as follows: parentheses, exponentiation (including square
roots), multiplications and divisions (from left to right), additions and subtractions
(from left to right)
...
This is how the on-screen calculator in the Quantitative Reasoning measure performs the operations
...
For such calculators, the result of entering
1 + 2 4 ןis 12
...
)
¼
In addition to parentheses, the on-screen calculator has one memory location
and three memory buttons that govern it: memory recall MR , memory clear
|
|
| |
|
|
MC , and memory sum M+
...
Some computations are not defined for real numbers: for example, division by
zero or taking the square root of a negative number
...
Similarly, if you enter 1 עΊ , then Error will be
| |
displayed
...
¼
The calculator displays up to eight digits
...
For example, the
calculation 10,000,000 = 01 ןresults in Error
...
If a computation results in a positive number less than
0
...
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GRE Quantitative Reasoning
Below are some examples of computations using the calculator
...
73
...
Compute 4 +
2
Explanation
| |
| | | |
| | | |
| | | |
Enter 4 + 6
...
365
...
73 = 2 נto get 3
...
365
...
Compute −
8
...
3
...
Here are two
ways to do that
...
4 + 9
...
2528571
...
3
8
...
3 | |ע| |=| 07 |נwould erroneously compute −8
...
70
sign after 9
...
4 + 9
...
In the
8
...
3
is the repeating
70
decimal −0
...
2528571
...
Find the length, to the nearest 0
...
Explanation
| | | | | | | || |
| |
| | | | | | | || |
| |
Enter 21 = 45 ן 45 + 12 ןΊ to get 57
...
Again, pressing the = before
the Ί is essential because 21 45 ן 45 + 12 ןΊ = would erroneously compute
212 + 54Ί54
...
Note that parentheses could be used, as
in ( 21 = ) 45 ן 45 ( + ) 12 ןΊ , but they are not necessary because the
| | | | | || || | | | | || || |
multiplications already take precedence over the addition
...
939624
...
01, so the
correct answer is 57
...
4
...
Explanation
| || | | || | | || |
Enter 15 = ע 51 ן ע 51 ן עto get −3,375
...
Unlawful distribution of this ebook is prohibited
...
Convert 6 miles per hour to feet per second
...
8
...
8 feet per second
...
At a fund-raising event, 43 participants donated $60 each, 21 participants
donated $80 each, and 16 participants donated $100 each
...
You can use the memory buttons and parentheses
43 + 21 + 16
for this computation as follows:
Enter 43 = 06 ןM+ 21 = 08 ןM+ 16 = 001 ןM+ MR נ
| | | || | | | | || | | | | || || || |
| | | | | | | || |
When the |M+| button is first used, the number in the calculator display is
( 43 + 21 + 16 ) = to get 73
...
25 per participant
...
Each subsequent use of the M+ button adds the
| |
number in the current display to the number stored in memory and replaces the
number stored in memory by the sum
...
To clear the
memory, use the MC button, and the M next to the display disappears
...
Unlawful distribution of this ebook is prohibited
...
Whenever nonstandard or special notation or terminology is used in a test question, it is explicitly introduced in the question
...
These assumptions appear in the test at the beginning of
the Quantitative Reasoning sections, and they are elaborated below
...
Such notation and terminology are
clarified below
...
Finally, there are some guidelines for how certain information given in test questions should be interpreted and used in the context of answering the questions—information such as certain words, phrases, quantities, mathematical expressions, and
displays of data
...
Numbers and Quantities
¼
¼
¼
¼
¼
¼
¼
All numbers used in the test questions are real numbers
...
This is the main assumption regarding numbers
...
Numbers are expressed in base 10 unless otherwise noted, using the 10 digits 0
through 9 and a period to the right of the ones digit, or units digit, for the
decimal point
...
When a positive integer is described by the number of its digits, e
...
, a two-digit
integer, the digits that are counted include the ones digit and all the digits
further to the left, where the left-most digit is not 0
...
Some other conventions involving numbers: one billion means 1,000,000,000, or
109 (not 1012, as in some countries); one dozen means 12; the Greek letter p
represents the ratio of the circumference of a circle to its diameter and is
approximately 3
...
When a positive number is to be rounded to a certain decimal place and the
number is halfway between the two nearest possibilities, the number should be
rounded to the greater possibility
...
5 rounded to the nearest
integer is 24, and 123
...
01 is 123
...
When the
number to be rounded is negative, the number should be rounded to the lesser
possibility
...
5 rounded to the nearest integer is −37
...
083 and = 0
...
as in
12
7
If r, s, and t are integers and rs = t, then r and s are factors, or divisors, of t; also,
t is a multiple of r (and of s) and t is divisible by r (and by s)
...
For example, −7 is a factor of
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GRE Quantitative Reasoning
¼
¼
¼
¼
¼
35, 8 is a factor of −40, and the integer 4 has six factors: −4, −2, −1, 1, 2, and
4
...
However, the term multiple can be used with any real numbers s and t
provided r is an integer
...
2 is a multiple of 0
...
The least common multiple of two nonzero integers a and b is the least positive
integer that is a multiple of both a and b
...
If an integer n is divided by a nonzero integer d resulting in a quotient q with
remainder r, then n = qd + r, where 0 ≤ r < ⎪d⎪
...
For example, when 20 is divided by 7, the quotient is 2 and the
remainder is 6; when 21 is divided by 7, the quotient is 3 and the remainder is 0;
and when −17 is divided by 7, the quotient is −3 and the remainder is 4
...
The first five prime numbers are 2, 3, 5, 7, and 11
...
The first five composite
numbers are 4, 6, 8, 9, and 10
...
The integer 0 is neither positive nor negative
...
Letters are also used to label various objects, such as line
ℓ, point P, function f, set S, list T, event E, random variable X, Brand X, City Y,
and Company Z
...
When numbers, constants, or variables are given, their possible values are all real
numbers unless otherwise restricted
...
Here are some examples: n is a nonzero integer; 1 ≤ x < p; and T
is the tens digits of a two-digit positive integer, so T is an integer from 1 to 9
...
These include
the arithmetic operations +,−, ,ןand ,נthough multiplication is usually denoted
by juxtaposition, often with parentheses, e
...
, 2y and (3)(4
...
g
...
These two
8
2
35
21
numbers are equal to
and − , respectively
...
g
...
100
Mathematical expressions are to be interpreted with respect to order of operations,
which establishes which operations are performed before others in an expression
...
For
example, the value of the expression 1 + 2 4 ןis 9, because the expression is
evaluated by first multiplying 2 and 4 and then adding 1 to the result
...
Therefore, −32 = −9, but (−3)2 = 9 because parentheses take precedence
over exponentiation
...
Unlawful distribution of this ebook is prohibited
...
lines ℓ and m are parallel
lines ℓ and m are perpendicular
Because all numbers are assumed to be real, some expressions are not defined
...
Sometimes special symbols or notation are introduced in a question
...
The operation छ is defined for all integers r and s by r छ s =
1+r2
1
The operation ϳ is defined for all nonzero numbers x by ϳx = −
...
” The meaning is
taken from the context
...
For example, “the function g is
defined for all x ≥ 0 by g(x) = 2x + Ίx
...
If f and g are two functions, then the composition of g with f is denoted
by g( f (x))
...
Lines are assumed to be “straight” lines that extend in both directions without
end
...
When a square, circle, polygon, or other closed geometric figure is described in
words but not shown, the figure is assumed to enclose a convex region
...
For example, a quadrilateral cannot be any of the following:
Not closed
Not convex
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GRE Quantitative Reasoning
¼
¼
¼
The phrase area of a rectangle means the area of the region enclosed by the
rectangle
...
The distance between a point and a line is the length of the perpendicular line
segment from the point to the line, which is the shortest distance between the
point and the line
...
In a geometric context, the phrase similar triangles (or other figures) means that
the figures have the same shape
...
Geometric Figures
¼
¼
Geometric figures consist of points, lines, line segments, curves (such as circles),
angles, and regions; also included are labels, and markings or shadings that
identify these objects or their sizes
...
Points, lines, angles, etc
...
All figures are assumed to lie in a plane
unless otherwise indicated
...
Unless otherwise
indicated, angle ABC, also denoted by ∠ ABC or ∠ B, refers to the smaller of the
two angles
...
The meaning can be determined from the
context
...
That is, you should not
assume that quantities such as lengths and angle measures are as they appear in a
figure
...
Also, assume that points on a line or a curve are in the order shown, points shown
to be on opposite sides of a line or curve are so oriented, and more generally,
assume all geometric objects are in the relative positions shown
...
To illustrate some of these conventions, consider the geometric figure below
...
Unlawful distribution of this ebook is prohibited
...
˼ ABD and DBC are triangles, and points R, S, and T lie on the closed curve
...
˼ Point D is a distinct point between points A and C
...
˼ Point E is on BD
...
˼ Angle ABC is a right angle, as indicated by the small square symbol at
point B
...
˼ Line ℓ intersects the closed curve at points S and T, and the curve is
tangent to AB at T
...
The following cannot be determined from the figure
...
˼ The measure of angle DBC is less than x degrees
...
˼ Angle SRT is a right angle
...
Coordinate Systems
¼
¼
¼
¼
Coordinate systems, such as xy-planes and number lines, are drawn to scale
...
The positive direction of a number line is to the right
...
The rectangular coordinate plane, or rectangular coordinate system, commonly
known as the xy-plane, is shown below
...
Each point in the xyplane has coordinates (x, y) that give its location with respect to the axes; for
example, the point P(2,−8) is located 2 units to the right of the y-axis and 8 units
below the x-axis
...
y
10
Quadrant II
5
–10
O
–5
Quadrant III –5
Quadrant I
5
10
x
Quadrant IV
P(2, –8)
–10
137
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...
GRE Quantitative Reasoning
¼
¼
Intermediate grid lines or tick marks in a coordinate system are evenly spaced
unless otherwise noted
...
The term y-intercept is used analogously
...
Sets, Lists, and Sequences
¼
¼
¼
¼
¼
Sets of numbers or other elements appear in some questions
...
When the
elements of a set are given, repetitions are not counted as additional elements and
the order of the elements is not relevant
...
A set
with one or more members is called nonempty; there is a set with no members,
called the empty set and denoted by л
...
If all of the elements in A are also in B, then A is a subset of B
...
If A and B have no elements in
common, they are called disjoint sets or mutually exclusive sets
...
When the elements of
a list are given, repetitions are counted as additional elements and the order of the
elements is relevant
...
The terms data set and set of data are not sets in the mathematical sense given
above
...
Sequences are lists that often have an infinite number of elements, or terms
...
For example, a1, a2, a3,
...
represents an infinite sequence in which the first term is a1, the second term is a2,
and more generally, the nth term is an for every positive integer n
...
Sometimes the
first few terms of a sequence are given explicitly, as in the following sequence of
consecutive even negative integers: −2,−4,−6,−8,−10,
...
” This phrase refers to 10
integers, with or without “inclusive” at the end
...
Data and Statistics
¼
¼
Numerical data are sometimes given in lists and sometimes displayed in other
ways, such as in tables, bar graphs, or circle graphs
...
The term average is used in two ways, with and without the qualification
“(arithmetic mean)
...
Unlawful distribution of this ebook is prohibited
...
The term average does not
refer to either median or mode in the test
...
”
When mean is used in the context of data, it means arithmetic mean
...
For a list of data, the mode of the data is the most frequently occurring number in
the list
...
For data listed in increasing order, the first quartile, second quartile, and third
quartile of the data are three numbers that divide the data into four groups that
are roughly equal in size
...
The second group is from the first quartile up to the second
quartile, which is also the median of the data
...
Note that the four groups themselves are sometimes
referred to as quartiles—first quartile, second quartile, third quartile, and fourth
quartile
...
”
For data listed in increasing order, the percentiles of the data are 99 numbers that
divide the data into 100 groups that are roughly equal in size
...
For a list of data, where the arithmetic mean is denoted by m, the standard
deviation of the data refers to the nonnegative square root of the mean of the
squared differences between m and each of the data
...
For a list of data, the range of the data is the greatest number in the list minus the
least number
...
Data Distributions and Probability Distributions
¼
¼
¼
Some questions display data in frequency distributions, where discrete data values
are repeated with various frequencies, or where preestablished intervals of
possible values are assigned frequencies corresponding to the numbers of data in
the intervals
...
, 951–1,000 hours; consequently, each of the intervals would
have a number, or frequency, of lifetimes, and the sum of the 10 frequencies is
300
...
In the example above, the 10 frequencies of the
10 intervals would each be divided by 300, yielding 10 relative frequencies
...
139
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GRE Quantitative Reasoning
¼
Some questions describe probability experiments, or random experiments, that have
a finite number of possible outcomes
...
If each outcome of an experiment is equally likely, then
the probability of an event E is defined as the following ratio:
P(E) =
¼
¼
¼
¼
¼
¼
¼
¼
¼
¼
¼
the number of outcomes in the event E
the number of possible outcomes in the experiment
If E and F are two events in an experiment, then “E and F ” is an event, which is
the set of outcomes that are in the intersection of events E and F
...
If E and F are two events and E and F are mutually exclusive, then P(E and F) = 0
...
Events
E and F are independent if and only if P(E and F) = P(E)P(F)
...
The values of the random variable may be the actual outcomes of the
experiment if the outcomes are numerical, or the random variable may be related
to the outcomes more indirectly
...
A random variable from an experiment with only a finite number of possible
outcomes also has only a finite number of values and is called a discrete random
variable
...
Every value of a discrete random variable X, say X = a, has a probability denoted
by P(a)
...
The mean of the
random variable X is the sum of the products XP(X) for all values of X
...
For a continuous random variable X, every interval of values, say a ≤ X ≤ b, has a
probability, which is denoted by P(a ≤ X ≤ b)
...
The curve is the graph of a function f whose values are
nonnegative and whose graph is therefore above the x-axis
...
The area of the entire region
under the curve is 1
...
The median of X is the point M on the x-axis at which the line
x = M divides the region under the distribution curve into two regions of equal
area
...
It is
also called the standard deviation of the probability distribution of X
...
A random variable X with this distribution
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...
GRE Quantitative Reasoning
¼
is called normally distributed
...
The right and left tails of the distribution
become ever closer to the x-axis but never touch it
...
The
following figure shows the distribution, including approximate probabilities
corresponding to the six intervals shown
...
34
0
...
34
0
...
02
0
...
Standard conventions apply to graphs of data unless otherwise indicated
...
Scales, grid lines, dots, bars, shadings, solid and dashed lines, legends,
etc
...
Sometimes, scales that do not begin
at 0 are used, and sometimes broken scales are used
...
In some Venn diagrams, all of
the circles are inside a rectangular region that represents a universal set
...
Sometimes a
number is placed above a circle to indicate the number of elements in the entire
circle
...
For example, if a
question states that “30 percent of the company’s profit was from health
products,” then 30 is to be used as an exact number; it is not to be treated as
though it were a nearby number, say 29 or 30
...
An integer that is given as the number of certain objects, whether in a real-life or
pure-math setting, is to be taken as the total number of such objects
...
Fractions and percents are understood in a similar way, so
“one-fifth, or 20 percent, of the 50 marbles in the bag are green” means 10
marbles in the bag are green and 40 marbles are not green
...
Unlawful distribution of this ebook is prohibited
...
Unless otherwise indicated, the phrase “difference between two quantities” is
assumed to mean “positive difference,” that is, the greater quantity minus the
lesser quantity
...
The profit does not involve any other
amounts unless they are explicitly given
...
In questions involving real-life scenarios in which a variable is given to represent
a number of existing objects or another nonnegative amount, the context implies
that the variable is greater than 0
...
Some quantities may involve units, such as inches, pounds, and Celsius degrees,
while other quantities are pure numbers
...
However, if an answer to a question
requires converting one unit of measurement to another, then the relationship
between the units is given in the question, unless the relationship is a common
one, such as the relationships between minutes and hours, dollars and cents, and
metric units like centimeters and meters
...
When reading questions, do not introduce unwarranted assumptions
...
As another example, do not consider sales taxes on
purchases unless explicitly mentioned
...
Also, the display may contain more than one graph or table
...
In a Data Interpretation set of questions, each question should be considered
separately from the others
...
In many questions, mathematical expressions and words appear together in a
phrase
...
For
example, if n is an integer, then the phrase “the sum of the first two consecutive
integers greater than n + 6” means (n + 7) + (n + 8); it does not mean “the sum of
the first two consecutive integers greater than n” plus 6, or
(n + 1) + (n + 2) + 6
...
However, in a phrase like “the function g is defined for
all x ≥ 0,” the phrase “for all x ≥ 0” is a mathematical shorthand for “for all
numbers x such that x ≥ 0
...
Unlawful distribution of this ebook is prohibited
...
Each of the first three practice sets consists of Quantitative Comparison
questions, both types of Multiple-choice questions, and Numeric Entry questions
...
The first is easy,
the second is medium, and the third is hard
...
Following the last set is an answer key for quick reference
...
Each explanation is
presented with the corresponding question, so that you can easily see what was asked
and what the various answer choices or Numeric Entry answer boxes were
...
For the Discrete question sets, begin with the easy sets and then
move on to the medium and hard sets
...
For the practice questions in this chapter, use the directions that begin on the
following page
...
Unlawful distribution of this ebook is prohibited
...
Notes: All numbers used are real numbers
...
Geometric figures, such as lines, circles, triangles, and quadrilaterals, are not
necessarily drawn to scale
...
You
should assume, however, that lines shown as straight are actually straight,
points on a line are in the order shown, and more generally, all geometric
objects are in the relative positions shown
...
Coordinate systems, such as xy-planes and number lines, are drawn to scale;
therefore, you can read, estimate, or compare quantities in such figures by
sight or by measurement
...
Directions for Quantitative Comparison questions
Compare Quantity A and Quantity B, using additional information centered
above the two quantities if such information is given
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
A symbol that appears more than once in a question has the same meaning
throughout the question
...
Unlawful distribution of this ebook is prohibited
...
¼
Your answer may be an integer, a decimal, or a fraction, and it may be
negative
...
Equivalent forms of the correct answer, such as 2
...
50, are all correct
...
Enter the exact answer unless the question asks you to round your answer
...
Discrete Questions: Easy
Quantitative Comparison
For Questions 1 to 6, compare Quantity A and Quantity B, using additional
information centered above the two quantities if such information is given
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
A symbol that appears more than once in a question has the same meaning
throughout the question
...
Then she sold the bicycle for 40 percent
more than the total amount she spent buying and
repairing it
...
The price at which Emma
sold the bicycle
Quantity B
$140
A
B
C
D
145
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GRE Quantitative Reasoning Practice Questions
R
Q
P
V
S
T
In the figure above, squares PQRV and VRST have
sides of length 6
...
The area of the shaded
region
36
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
In 2009 the property tax on each home in Town X
was p percent of the assessed value of the home,
where p is a constant
...
Quantity A
3
...
Quantity B
x
y
r, s, and t are three consecutive odd integers such
that r < s < t
...
Quantity B
r+s+1
s+t−1
146
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GRE Quantitative Reasoning Practice Questions
y
k
ℓ
x
O
P
Quantity A
The slope of line k
6
...
y°
x°
7
...
z°
x+y+z
?
45
2
3
4
5
6
A certain store sells two types of pens: one type for $2 per pen and the
other type for $3 per pen
...
Unlawful distribution of this ebook is prohibited
...
If y = 3x and z = 2y, what is x + y + z in terms of x ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
10
...
75 when shipping
any package with contents worth $25
...
00 when shipping any package with contents worth over $25
...
If Dan
uses the shipping company to ship three packages with contents worth
$18
...
00, and $127
...
10x
$1
...
25
$2
...
75
$3
...
¼
¼
¼
¼
Your answer may be an integer, a decimal, or a fraction, and it may be
negative
...
Equivalent forms of the correct answer, such as 2
...
50, are all correct
...
Enter the exact answer unless the question asks you to round your answer
...
Unlawful distribution of this ebook is prohibited
...
In the rectangular solid above, TU = 3, UV = 4, and VR = 2
...
A list of numbers has a mean of 8 and a standard deviation of 2
...
If x is a
number in the list that is 2 standard deviations above the mean, what is the
value of x ?
x=
Multiple-choice Questions—Select One or More Answer Choices
For Question 14, select all the answer choices that apply
...
Surgery
24%
Internal
Medicine
25%
The circle graph above shows the distribution of 200,000 physicians by
specialty
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
Pediatrics
Internal Medicine
Surgery
Anesthesiology
Psychiatry
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GRE Quantitative Reasoning Practice Questions
SET 2
...
Select one of the following four answer choices and fill in the corresponding
oval to the right of the question
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Machine R, working alone at a constant rate,
produces x units of a product in 30 minutes, and
machine S, working alone at a constant rate,
produces x units of the product in 48 minutes, where
x is a positive integer
...
Quantity B
The number of units of
the product that machine
R, working alone at its
constant rate, produces
in 3 hours
The number of units of
the product that machine
S, working alone at its
constant rate, produces
in 4 hours
A
B
C
D
A
B
C
D
Frequency Distribution for List X
Number
1
2
3
5
Frequency
10
20
18
12
Frequency Distribution for List Y
Number
6
7
8
9
Frequency
24
17
10
9
List X and list Y each contain 60 numbers
...
The
average (arithmetic mean) of the numbers in list X is
2
...
1
...
Quantity A
2
...
Unlawful distribution of this ebook is prohibited
...
Quantity B
Quantity A
3
...
Quantity B
y
Among the 9,000 people attending a football game at
College C, there were x students from College C and y
students who were not from College C
...
Quantity B
The number of people
attending the game who
were not students
9,000 − x − y
Multiple-choice Questions—Select One Answer Choice
For Questions 6 to 10, select a single answer choice
...
If x ≠ 0, which of the following is equivalent to
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
x(x2)3
?
x2
x2
x3
x4
x5
x6
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GRE Quantitative Reasoning Practice Questions
y
1
O
7
...
d is 4 more than n
...
7
d is 2 times n
...
By weight, liquid A makes up 8 percent of solution R and 18 percent of
solution S
...
−2
d − 3n
= 1, which of the following statements describes d in terms of n ?
7n − d
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
9
...
What is
the value of f ( f (−1)) ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
8
...
Two
members of the organization will be selected at random
...
5
0
...
7
0
...
9
152
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...
GRE Quantitative Reasoning Practice Questions
Numeric Entry
For Questions 11 and 12, enter your answer in the answer box(es) below the
question
...
If a question asks for a fraction, there will be two boxes—one for the
numerator and one for the denominator
...
5 and 2
...
Fractions do not need to be reduced to lowest terms
...
Garden
11
...
The garden is 18 feet long and 12 feet wide
...
What is the area of the
walkway?
square feet
12
...
The x-intercept of line k is −4, and line k passes
through the midpoint of the line segment whose endpoints are (2, 9) and
(2, 0)
...
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...
GRE Quantitative Reasoning Practice Questions
Multiple-choice Questions—Select One or More Answer Choices
For Questions 13 and 14, select all the answer choices that apply
...
If the lengths of two sides of a triangle are 5 and 9, respectively, which of
the following could be the length of the third side of the triangle?
Indicate all such lengths
...
0
y
z
On the number line shown above, the tick marks are equally spaced
...
A
Ǣ
B
Ǣ
C
Ǣ
xyz < 0
x+z=y
z( y − x) > 0
154
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GRE Quantitative Reasoning Practice Questions
SET 3
...
Select one of the following four answer choices and fill in the corresponding
oval to the right of the question
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
B
125°
C
6
A
4
D
In the figure above, ABCD is a parallelogram
...
Quantity B
The area of ABCD
24
A
B
C
D
A
B
C
D
Frequency
40
30
20
10
0
1–5
6 –10 11–15 16 –20 21–25 26–30 31–35
Measurement Intervals
In the course of an experiment, 95 measurements
were recorded, and all of the measurements were
integers
...
The graph above
shows the frequency distribution of the 95
measurements by measurement interval
...
Quantity B
The average (arithmetic
mean) of the 95
measurements
The median of the 95
measurements
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GRE Quantitative Reasoning Practice Questions
x is an integer greater than 1
...
Quantity B
3x+1
4x
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A, B, and C are three rectangles
...
The length and width of rectangle B are
20 percent greater and 20 percent less, respectively,
than the length and width of rectangle C
...
Quantity B
The area of rectangle A
The area of rectangle B
The random variable X is normally distributed
...
Quantity A
5
...
Quantity A
6
...
Unlawful distribution of this ebook is prohibited
...
7
...
From
the 11 candidates available for the team, the manager has already chosen 3
to be on the team
...
6
24
56
120
462
Which of the following could be the graph of all values of x that satisfy the
6x − 5
inequality 2 − 5x ≤ −
?
3
A
ɕ
B
ɕ
0
C
ɕ
0
D
ɕ
0
E
ɕ
9
...
Unlawful distribution of this ebook is prohibited
...
Parallelogram OPQR lies in the xy-plane, as shown in the figure above
...
What are the coordinates of point R ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
11
...
What is the value
of k ?
1
A
ɕ 4p
1
B
ɕ 2p
C
ɕ 1
4
D
ɕ
E
ɕ
12
...
What is the sum of the first 20 terms of this sequence?
The sequence of numbers a1, a2, a3,
...
is defined by an =
C
ɕ
1
1 + 1 − 20
2
1
1
1 + 1 − 21 + 22
2
1
1
1− +
20 22
D
ɕ
1−
E
ɕ
1
1
−
20 22
A
ɕ
B
ɕ
1
22
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GRE Quantitative Reasoning Practice Questions
Numeric Entry
For Question 13, enter your answer in the answer box(es) below the question
...
If a question asks for a fraction, there will be two boxes—one for the
numerator and one for the denominator
...
5 and 2
...
Fractions do not need to be reduced to lowest terms
...
Y
1
2
2
3
4
7
5
4
8
3
2
8
7
4
13
...
What is the mean of the distribution?
Give your answer to the nearest 0
...
Multiple-choice Questions—Select One or More Answer Choices
For Questions 14 and 15, select all the answer choices that apply
...
Let S be the set of all positive integers n such that n2 is a multiple of both
24 and 108
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
12
24
36
72
159
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...
GRE Quantitative Reasoning Practice Questions
15
...
2
inches, and the range of the heights of the male students in the class is 15
...
Which of the following statements individually provide(s) sufficient
additional information to determine the range of the heights of all the
students in the class?
Indicate all such statements
...
8 inches taller than the tallest
female student in the class
...
1 inches
greater than the median height of the female students in the class
...
6 inches greater than the average height of the female students in
the class
...
Unlawful distribution of this ebook is prohibited
...
Data Interpretation Sets
For Questions 1 to 7, select a single answer choice unless otherwise directed
...
PERCENT OF FEMALE FACULTY AND PERCENT OF MALE FACULTY
AT UNIVERSITY X, BY FIELD
Total female faculty: 200
Total male faculty: 250
Biological Sciences
Business
Education
Engineering
Female
Male
Field
Fine Arts
Health Sciences
Humanities
Physical Sciences
Social Sciences
Other
0
5
10
15
Percent
20
25
Medium Question
1
...
Approximately what is the ratio of the number of students in engineering to
the number of faculty in engineering?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
8 to 1
10 to 1
12 to 1
14 to 1
20 to 1
Medium Question
2
...
Unlawful distribution of this ebook is prohibited
...
Hard Question
3
...
What
9
fraction of all the faculty members in those two fields combined are tenured
professors?
female and
Questions 4 to 7 are based on the following data
...
Easy Question
4
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
F
Ǣ
G
Ǣ
H
Ǣ
2001
2002
2003
2004
2005
2006
2007
2008
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GRE Quantitative Reasoning Practice Questions
Medium Question
5
...
In 2008 the value of exports was approximately what percent greater than
the value of imports?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
40%
60%
70%
120%
140%
Hard Question
7
...
Unlawful distribution of this ebook is prohibited
...
Discrete Questions: Easy
1
...
3
...
5
...
7
...
9
...
11
...
13
...
Choice
Choice
Choice
Choice
given
...
C: The two quantities are equal
...
D: The relationship cannot be determined from the information
B: Quantity B is greater
...
C: 4
D: 12
A: 10x
C: $2
...
Discrete Questions: Medium
1
...
3
...
5
...
7
...
9
...
11
...
13
...
Choice A: Quantity A is greater
...
Choice D: The relationship cannot be determined from the information
given
...
Choice C: The two quantities are equal
...
Choice C: 15%
Choice C: 0
...
Unlawful distribution of this ebook is prohibited
...
Discrete Questions: Hard
1
...
3
...
5
...
7
...
9
...
11
...
13
...
15
...
Choice
Choice
Choice
Choice
Choice
Choice
Choice
B: Quantity B is greater
...
D: The relationship cannot be determined from the information
A: Quantity A is greater
...
C: The two quantities are equal
...
29
Choice A: 12
AND
Choice C: 36
Choice A: The tallest male student in the class is 5
...
SET 4
...
2
...
4
...
6
...
Choice A: 8 to 1
Choice E: 51%
24
(or any equivalent fraction)
87
Choice
AND
Choice
AND
Choice
AND
Choice
AND
Choice
AND
Choice
Choice
Choice
Choice
A: 2001
B: 2002
C: 2003
F: 2006
G: 2007
H: 2008
E: $640 million
E: 140%
A: $200 million
165
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GRE Quantitative Reasoning Practice Questions
Answers and Explanations
For the practice questions in this chapter, use the following directions
...
Notes: All numbers used are real numbers
...
Geometric figures, such as lines, circles, triangles, and quadrilaterals, are not
necessarily drawn to scale
...
You
should assume, however, that lines shown as straight are actually straight,
points on a line are in the order shown, and more generally, all geometric
objects are in the relative positions shown
...
Coordinate systems, such as xy-planes and number lines, are drawn to scale;
therefore, you can read, estimate, or compare quantities in such figures by
sight or by measurement
...
Directions for Quantitative Comparison questions
Compare Quantity A and Quantity B, using additional information centered
above the two quantities if such information is given
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
A symbol that appears more than once in a question has the same meaning
throughout the question
...
Unlawful distribution of this ebook is prohibited
...
¼
¼
¼
¼
Your answer may be an integer, a decimal, or a fraction, and it may be
negative
...
Equivalent forms of the correct answer, such as 2
...
50, are all correct
...
Enter the exact answer unless the question asks you to round your answer
...
Discrete Questions: Easy
Quantitative Comparison
For Questions 1 to 6, use the directions for Quantitative Comparison questions
...
Then she sold the bicycle for 40 percent
more than the total amount she spent buying and
repairing it
...
The price at which Emma
sold the bicycle
Quantity B
$140
A
B
C
D
Explanation
In this question you are asked to compare the price at which Emma sold the
bicycle with $140
...
If you notice that 140 is 40 percent more than 100, you can conclude that 40
percent more than 102 is greater than 40 percent more than 100, and therefore,
Quantity A is greater than Quantity B
...
(If you
solve the problem in this way, you do not have to calculate the value of Quantity A
...
Since 40 percent of 102
is (0
...
8, it follows that Quantity A, the price at which Emma sold the
bicycle, is 102
...
80 = 142
...
Thus Quantity A, $142
...
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GRE Quantitative Reasoning Practice Questions
Q
P
R
V
S
T
In the figure above, squares PQRV and VRST have
sides of length 6
...
The area of the shaded
region
Quantity B
36
A
B
C
D
Explanation
In this question you are asked to compare the area of the shaded region with 36
...
Therefore, you can conclude that the length of QS is 12, and the area of the
1
shaded right triangle PQS is (12)(6), or 36
...
In 2009 the property tax on each home in Town X
was p percent of the assessed value of the home,
where p is a constant
...
Quantity A
3
...
One way of doing this is to determine the value of the constant p and
then use that value to calculate the tax on the home that had an assessed value
of $160,000
...
Once
property tax of $2,500, you can conclude that p is equal to
125,000
you know that the property tax is 2% of the assessed value, you can determine
that tax on the home that had an assessed value of $160,000 was 2% of 160,000,
or 3,200
...
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GRE Quantitative Reasoning Practice Questions
Another way to calculate the property tax on a home with an assessed value
of $160,000 is by setting up a proportion
...
x
2,500
=
160,000 125,000
125,000x = (160,000)(2,500)
(160,000)(2,500)
x=
125,000
x = 3,200
The correct answer is Choice A
...
Quantity B
y
A
B
C
D
Explanation
One way to approach this question is to plug in values for one of the variables
and determine the corresponding value for the other variable
...
For example, you can plug in x = 0
and find that the corresponding value of y is −1; then you can plug in y = 0 and
find that the corresponding value of x is −1
...
A second way to plug in: If you prefer to always plug in values of x to
determine corresponding values of y, you can begin by writing the equation
x + y = −1 as y = −x − 1
...
You can start by plugging in the value x = 0
...
If you
continue plugging in a variety of values of x, some negative and some positive,
you will see that sometimes x is greater than y and sometimes y is greater than x
...
What about negative values of x? A quick inspection of the equation
y = −x − 1 allows you to conclude that if x < −1, then y > 0, so y is greater
than x
...
Therefore, the relationship between the
two quantities x and y cannot be determined from the information given, and the
correct answer is Choice D
...
Quantity A
5
...
Unlawful distribution of this ebook is prohibited
...
This means that if you express the three consecutive odd integers
in terms of r, they are r, r + 2, and r + 4
...
Simplification 1: Begin simplifying by expressing s and t in terms of r
...
||
||
2r + 3 |?| 2r + 5
3 |?| 5
r+s+1 ? s+t−1
r + (r + 2) + 1 ? (r + 2) + (r + 4) − 1
In the last step of the simplification, you can easily see that 3 < 5
...
Simplification 2: Since the number s appears in both quantities, you can
begin the simplification by subtracting s from both sides of the relationship and
then express t in terms of r
...
||
||
r + 1 |?| (r + 4) − 1
r + 1 |?| r + 3
1 |?| 3
r+s+1 ? s+t−1
r+1 ? t−1
In the last step of the simplification, you can easily see that 1 < 3
...
Note that in this solution, the fact that r is odd is not used; what is used is
the fact that the consecutive odd integers differ by 2
...
Quantity B
The slope of line k
The slope of line ℓ
A
B
C
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D
GRE Quantitative Reasoning Practice Questions
Explanation
Note that the slope of each of the lines is positive, since each line rises as it goes
to the right
...
You can also use the definition of the slope to arrive at the correct answer
...
Because both
lines pass through point P on the y-axis, they have the same rise from P to the
x-axis
...
Thus,
the run of line ℓ from the y-axis to the x-intercept is greater than the run of line
k
...
The greater denominator
results in a lesser fraction and a lesser slope for line ℓ
...
Multiple-choice Questions—Select One Answer Choice
For Questions 7 to 11, select a single answer choice
...
z°
In the figure above, what is the value of
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
x+y+z
?
45
2
3
4
5
6
Explanation
The sum of the measures, in degrees, of the three interior angles of any triangle
is 180Њ
...
Therefore,
=
= 4, and the correct
45
45
answer is Choice C
...
Unlawful distribution of this ebook is prohibited
...
A certain store sells two types of pens: one type for $2 per pen and the
other type for $3 per pen
...
In fact, it is reasonable to begin by
looking at how many of the $2 pens the customer can buy if the customer does
not buy any $3 pens
...
If the customer bought 11 of the $2 pens, there would be $3 left over with
which to buy a $3 pen
...
If the customer bought 10 of the $2 pens, there would be $5 left over
...
As the number of $2 pens decreases, the total number of pens that the
customer can buy with $25 decreases as well
...
The correct answer is Choice D
...
If y = 3x and z = 2y, what is x + y + z in terms of x ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
10x
9x
8x
6x
5x
Explanation
It is not necessary to find the individual values of x, y, and z to answer the
question
...
This means that you need to use the information
provided about y and z to express them in terms of the variable x
...
Using substitution, you can rewrite the expression as follows
...
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GRE Quantitative Reasoning Practice Questions
10
...
75 when shipping
any package with contents worth $25
...
00 when shipping any package with contents worth over $25
...
If Dan
uses the shipping company to ship three packages with contents worth
$18
...
00, and $127
...
75
$2
...
50
$2
...
00
Explanation
Note that two of the packages being shipped have contents that are worth $25
...
Therefore, each of them has an insurance fee of $0
...
50
...
00, and it has an insurance
fee of $1
...
Therefore, the total insurance fee for the three packages is
$1
...
00 = $2
...
11
...
Therefore, the ratio of the number of females who purchase the product
to the number of males who purchase the product is 55 to 45, or 11 to 9, and
the correct answer is Choice A
...
Unlawful distribution of this ebook is prohibited
...
S
T
R
V
12
...
What is the area
of the shaded rectangular region?
Explanation
To find the area of the shaded rectangular region, you need to multiply the
length of the rectangular region by its width
...
Note that VR is the
length of the shaded rectangle
...
Note that VT lies on the front face of the
rectangular solid
...
You know that
UV = 4 and TU = 3, so by the Pythagorean theorem you can conclude that
VT = Ί32 + 42 = Ί9 + 16 = Ί25 = 5
...
The correct answer is 10
...
A list of numbers has a mean of 8 and a standard deviation of 2
...
If x is a
number in the list that is 2 standard deviations above the mean, what is the
value of x ?
x=
Explanation
You are given that x is 2 standard deviations above the mean, 8
...
5, it follows that x is (2)(2
...
Therefore, x = 8 + 5 = 13, and the correct answer is
13
...
Unlawful distribution of this ebook is prohibited
...
Radiology
3%
Pathology
3%
Other Pediatrics
21%
15%
Psychiatry
6%
Anesthesiology
3%
14
...
Which of the following sectors of the circle graph represent more
than 40,000 physicians?
Indicate all such sectors
...
2, it follows that 40,000 is 20% of 200,000, and any
graph
...
This is true for the specialties of pediatrics, internal medicine, and
surgery
...
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GRE Quantitative Reasoning Practice Questions
SET 2
...
Machine R, working alone at a constant rate,
produces x units of a product in 30 minutes, and
machine S, working alone at a constant rate,
produces x units of the product in 48 minutes, where
x is a positive integer
...
Quantity B
The number of units of
the product that machine
R, working alone at its
constant rate, produces
in 3 hours
The number of units of
the product that machine
S, working alone at its
constant rate, produces
in 4 hours
A
B
C
D
Explanation
In this question you are given that machine R, working alone at its constant rate,
produces x units of a product in 30 minutes
...
You can compare 6x with Quantity B in two ways
...
8 hours
...
4
Two: First, convert 48 minutes to hour, then find the number of 48-minute
5
4
5
periods there are in 4 hours by computing
= (4)
= 5
...
Either way, Quantity A is greater than Quantity B, and the correct answer is
Choice A
...
Unlawful distribution of this ebook is prohibited
...
Frequency
distributions for each list are given above
...
7, and the average of the numbers in list Y is 7
...
List Z contains 120 numbers: the 60 numbers in list
X and the 60 numbers in list Y
...
Quantity B
The average of the 120
numbers in list Z
The median of the 120
numbers in list Z
A
B
C
D
Explanation
In this problem you are asked to compare the average with the median of the
120 numbers in list Z
...
To determine the average of the 120 numbers in list Z, you can use the
information given about the individual averages of the numbers in lists X and Y
...
2
...
1
, or 4
...
Thus, the average of the numbers in list Z is
2
To determine the median of the 120 numbers in list Z, first note that list Z
contains an even number of numbers, so the median of the numbers in list Z is
the average of the middle two numbers when the numbers are listed in
increasing order
...
Thus, the two middle numbers in list Z are 5
5+6
, or 5
...
Therefore, the median
and 6, and the average of these numbers is
2
of the numbers in list Z is 5
...
9
...
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GRE Quantitative Reasoning Practice Questions
C
B
D
A
In the figure above, the diameter of the circle is 10
...
Quantity B
The area of quadrilateral
ABCD
40
A
B
C
D
Explanation
You are given that the circle has a diameter of 10, and from the figure you can
assume that points A, B, C, and D lie on the circle in the order shown
...
Therefore, to get
an idea of how various possible positions of these four points could affect the
area of quadrilateral ABCD, it is a good idea to see how the figure can vary but
still have points A, B, C, and D in the same order as in the figure above
...
C
B
D
A
Another way is to draw points A and C opposite each other, with points B
and D close to point C, as shown below
...
If points A and C are opposite each other, with points B and D very close to
point C, the area of quadrilateral ABCD is very close to 0
...
If points A, B, C, and D are evenly spaced, the area is not close to 0
...
Unlawful distribution of this ebook is prohibited
...
The two diameters are perpendicular
bisectors of each other, so they divide ABCD into four right triangles, as shown
...
5
...
5), or 50
...
The correct answer is Choice D
...
Quantity B
y
A
B
C
D
Explanation
You are given that x2y > 0, which means that the product of the two numbers x2
and y is positive
...
The square of a number is
always greater than or equal to 0
...
Thus, x2 is positive and it follows that y is also positive
...
The product of two numbers is negative only if one
of the numbers is negative and the other number is positive
...
Thus, y2 is positive and so x must be negative
...
Among the 9,000 people attending a football game at
College C, there were x students from College C and y
students who were not from College C
...
Quantity B
The number of people
attending the game who
were not students
9,000 − x − y
A
B
C
D
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GRE Quantitative Reasoning Practice Questions
Explanation
In this question you are not told whether all of the 9,000 people attending the
game were students
...
The people attending the game can be broken down into three
groups: students from College C, students not from College C, and people who
were not students
...
Therefore, 9,000 − x − y = z is the number of people attending the
game who were not students
...
Multiple-choice Questions—Select One Answer Choice
For Questions 6 to 10, select a single answer choice
...
If x ≠ 0, which of the following is equivalent to
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
x(x2)3
?
x2
x2
x3
x4
x5
x6
Explanation
x(x2)3
, it can be helpful to write (x2)3 as (x2)(x2)(x2) in the given
x2
x(x2)3 x(x2)(x2)(x2)
expression; that is,
=
...
Another way to simplify the expression using the rules of exponents directly
is as follows
...
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GRE Quantitative Reasoning Practice Questions
y
1
O
7
...
What is
the value of f ( f (−1)) ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
−2
−1
0
1
2
Explanation
Note that to find f ( f (−1)), you must apply the function f twice, first to find the
value of f (−1) and then to find the value of f ( f (−1))
...
This point has y-coordinate y = 2
...
Next you need to find the value of f (2)
...
This point has
y-coordinate y = 1
...
The correct answer is Choice D
...
If
d − 3n
= 1, which of the following statements describes d in terms of n ?
7n − d
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
d is 4 less than n
...
3
d is of n
...
d is 5 times n
...
To
7n − d
simplify the equation, you can begin by multiplying both sides by 7n − d and
then proceed as follows
...
To describe d in terms of n, you need to solve the equation
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GRE Quantitative Reasoning Practice Questions
9
...
If 3 grams of solution R are mixed with 7 grams of solution S,
then liquid A accounts for what percent of the weight of the resulting
solution?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
10%
13%
15%
19%
26%
Explanation
Liquid A makes up 8 percent of the weight of solution R and 18 percent of the
weight of solution S
...
08)(3), or 0
...
18)(7), or 1
...
When the two solutions are mixed, the resulting solution weighs 3 + 7,
or 10 grams and contains 0
...
26, or 1
...
This means that
1
...
The correct answer is Choice C
...
Of the 700 members of a certain organization, 120 are lawyers
...
Which of the
following is closest to the probability that neither of the members selected
will be a lawyer?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
0
...
6
0
...
8
0
...
Since there are 120 members who are lawyers, there must be 700 − 120, or
580 members who are not lawyers
...
Multiplying these two numbers gives the number of ways to
select 2 members who are not lawyers
...
You can see this by
considering 2 members, A and B
...
To adjust for double counting, you
need to divide (580)(579) by 2
...
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...
Thus, the desired probability is
(580)(579)
2
(580)(579)
=
(700)(699)
(700)(699)
2
Since the answer choices are all tenths, you need to approximate the value of
this fraction to the nearest tenth
...
One way is to use your calculator to convert the fraction to a decimal and round
the decimal to the nearest tenth
...
2
36 36
= 49 Ϸ 50 = 0
...
7
...
Another approach to this problem is to consider the random selections as
two separate but successive events
...
For the second selection, there are only 699
members left to select from, because one member has already been selected
...
So the probability of selecting a second member who is not
a lawyer, given the condition that the first member selected was not a lawyer, is
579
...
72
...
Numeric Entry
For Questions 11 and 12, use the directions for Numeric Entry questions
...
Walkway
The figure above represents a rectangular garden with a walkway around it
...
The walkway is uniformly 3
feet wide, and its edges meet at right angles
...
Unlawful distribution of this ebook is prohibited
...
Looking at the shaded region in this way suggests that the area of the
walkway can be calculated as the difference between the area of the larger
rectangle and the area of the smaller rectangle
...
Since the
garden is 18 feet long and 12 feet wide, its area is (18)(12), or 216 square feet
...
The length of the region is the length of the garden plus twice the
width of the walkway, or 18 + (2)(3) = 24 feet
...
Therefore, the area of the region represented by the larger rectangle is (24)(18),
or 432 square feet, and the area of the walkway is 432 − 216, or 216 square feet
...
Garden
Walkway
Each of the four squares is 3 feet long and 3 feet wide
...
Thus, the area of the walkway is
4(3)(3) + 2(18)(3) + 2(12)(3) = 36 + 108 + 72 = 216 square feet
The correct answer is 216
...
Line k lies in the xy-plane
...
What is the slope of line k ?
Give your answer as a fraction
...
In this question you are given information about two points on line
k, namely,
¼
¼
the point at which line k crosses the x-axis has x-coordinate −4;
the midpoint of the line segment with endpoints at (2, 9) and (2, 0) is on
line k
...
Unlawful distribution of this ebook is prohibited
...
For the second point, the midpoint of the line segment is halfway between the endpoints (2, 9) and (2, 0)
...
Based on the coordinates (−4, 0) and 2, , the slope of line k
2
is
9
9
−0
2
2
3
=
=
2 − ()4מ
6
4
The correct answer is
3
(or any equivalent fraction)
...
13
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
3
5
8
15
Explanation
A good way to approach this problem is to think about how much the length of
the third side of a triangle with two fixed side lengths can vary
...
This suggests drawing two triangles, one in which the angle between
the two sides is close to 0 degrees and one in which the angle between the two
sides is close to 180 degrees, like the triangles below
...
If it
were equal to 4, the triangle would degenerate into a line segment
...
If it
were equal to 14, the triangle would degenerate into a line segment
...
Unlawful distribution of this ebook is prohibited
...
Furthermore, it is intuitive that any length between these two
numbers can be achieved by some triangle
...
x
14
...
Which
of the following statements about the numbers x, y, and z must be true?
Indicate all such statements
...
Because the tick marks are equally spaced, you can also
see that x = −y and z = 2y
...
Choice A says that the product of the three numbers x, y, and z is less than 0
...
¼
¼
All three numbers are negative
...
Choice A must be true, since x is negative and y and z are positive
...
To see whether the equation must be true,
it is a good idea to express two of the variables in terms of the third (that is, to
“get rid of” two of the variables)
...
In this form you can quickly conclude that the equation must
be true
...
Recall that the product of two numbers is positive under either of the following
two conditions
...
Both numbers are negative
...
By adding x to both sides of the inequality y − x > 0, you can see that it is equivalent to the inequality y > x, which is
clearly true from the number line
...
Therefore, the correct answer consists of Choices A, B, and C
...
Unlawful distribution of this ebook is prohibited
...
Discrete Questions: Hard
Quantitative Comparison
For Questions 1 to 6, use the directions for Quantitative Comparison questions
...
Quantity A
1
...
Since the measure of the interior angle given is 125Њ, you can
conclude that the parallelogram is not a rectangle
...
It is helpful to draw the vertical
height from vertex C to base AD of the parallelogram, as shown in the figure
below
...
The
hypotenuse of the triangle is a side of the parallelogram and has length 6
...
The area of the parallelogram is equal to the length of base AD,
which is 4, times the height, which is less than 6
...
Quantity B is greater than Quantity A, and the correct answer is
Choice B
...
Unlawful distribution of this ebook is prohibited
...
The 95 measurements were then grouped
into 7 measurement intervals
...
Quantity A
The average (arithmetic
mean) of the 95
measurements
2
...
Since in the histogram the 95 measurements have been grouped into intervals,
you cannot calculate the exact value of either the average or the median; you must
compare them without being able to determine the exact value of either one
...
The middle measurement is the 48th
measurement
...
Therefore, the
median is in the measurement interval 6–10 and could be 6, 7, 8, 9, or 10
...
Since you are asked to compare the average and the median, not necessarily
to calculate them, you may ask yourself if you can tell whether the average is
greater than or less than the median
...
The 30 measurements in the remaining four measurement intervals are all greater than 10, some
significantly greater than 10
...
Unlawful distribution of this ebook is prohibited
...
At this point it seems likely that the average of
the 95 measurements is greater than the median of the 95 measurements
...
To actually show that the average must be greater than 10, you can make the
average as small as possible and see if the smallest possible average is greater than
10
...
That is to say, all 15 measurements in the
measurement interval 1–5 are equal to 1, all 35 measurements in the measurement interval 6–10 are equal to 6, etc
...
95
Therefore, since the average of the 95 measurements is greater than 10 and
the median is in the measurement interval 6–10, it follows that the average is
greater than the median, and the correct answer is Choice A
...
Quantity A
3
...
If you plug in x = 2, you see that Quantity A is 3x+1 = 33, or 27, and Quantity B
x
is 4 = 42, or 16
...
If you plug in x = 3, you see that Quantity A is 3x+1 = 34, or 81, and Quantity B
x
is 4 = 43, or 64
...
If you plug in x = 4, you see that Quantity A is 3x+1 = 35, or 243, and Quantity
B is 4x = 44, or 256
...
Since for
x = 2 and for x = 3, Quantity A is greater than Quantity B, and for x = 4, Quantity
B is greater than Quantity A, it follows that the relationship between the two
quantities cannot be determined
...
Since both quantities are algebraic expressions, another way to approach this
problem is to set up a placeholder relationship between the two quantities and
simplify it to see what conclusions you can draw
...
Since each step in this
x
4
simplification is reversible, this reduces the problem to comparing 3 with
...
Unlawful distribution of this ebook is prohibited
...
In particular, it is greater than 3 for large enough values of x
...
For the smallest value of x, x = 2, the relationship is
3
9
Since for x = 2, Quantity A is greater than Quantity B and for large values of x,
Quantity B is greater than Quantity A, it follows that the relationship between the
two quantities cannot be determined
...
You can see that because
A, B, and C are three rectangles
...
The length and width of rectangle B are
20 percent greater and 20 percent less, respectively,
than the length and width of rectangle C
...
Quantity B
The area of rectangle B
A
B
C
D
Explanation
In this question you are asked to compare the area of rectangle A and the area of
rectangle B
...
If ℓ represents the length of rectangle C and w represents its width, then the
length and width of rectangles A and B can be translated into algebraic
expressions as follows
...
1ℓ
...
9w
...
2ℓ
...
8w
...
1ℓ)(0
...
99ℓw
...
2ℓ)(0
...
96ℓw
...
99ℓw is greater than 0
...
The random variable X is normally distributed
...
Quantity A
5
...
Unlawful distribution of this ebook is prohibited
...
Both of the values 650 and 850 are greater than the mean of the distribution
...
Note that it is not necessary to know the
exact location of 650 and 850, just that both values are above the mean
...
To say that 850 is
at the 90th percentile of the distribution means that 90 percent of the area
between the normal curve and the horizontal axis lies to the left of the vertical
line segment at 850
...
However, because the curve is
decreasing in that interval, the area between 650 and 750 is greater than the area
between 750 and 850
...
Thus you can conclude
that Quantity A, the value at the 75th percentile of the distribution of X, is less
than Quantity B
...
Set S consists of all positive integers less than 81 that are
not equal to the square of an integer
...
The number of integers in
set S
Quantity B
72
A
B
C
D
Explanation
Set S consists of all integers from 1 to 80, except those that are equal to the
square of an integer
...
Clearly, there are 80 positive integers that are less than 81
...
You can also draw this conclusion by squaring each of the positive integers,
beginning with 1, until you get to an integer n such that n2 is greater than or
equal to 81
...
191
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...
GRE Quantitative Reasoning Practice Questions
Therefore, the number of integers in set S is 80 − 8, or 72, which is equal to
Quantity B
...
Multiple-choice Questions—Select One Answer Choice
For Questions 7 to 12, select a single answer choice
...
A manager is forming a 6-person team to work on a certain project
...
In selecting the other 3 team members, how many
different combinations of 3 of the remaining candidates does the manager
have to choose from?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
6
24
56
120
462
Explanation
To determine the number of different combinations of 3 of the remaining
candidates that the manager has to choose from, you first have to know the
number of remaining candidates
...
Now you need to count how many different combinations
of 3 objects can be chosen from a group of 8 objects
...
You can
3
3!(8 − 3)!
then calculate the number of different combinations of 3 of the remaining
candidates as follows
...
8
...
Unlawful distribution of this ebook is prohibited
...
To do that you need to simplify
the inequality until you isolate x
...
Note that when you multiply by 3, the right-hand side of
the inequality becomes −(6x − 5), not −6x − 5
...
(3)(2 − 5x) ≤ −6x + 5
6 − 15x ≤ −6x + 5
− 15x ≤ −6x −1
−9x ≤ −1
1
x≥
9
Note that when an inequality is multiplied (or divided) by a negative number, the
direction of the inequality reverses
...
Therefore, you do not need to locate on the number line; it is
9
1
enough to know that is a positive number
...
Therefore, the correct answer is Choice C
...
If 1 + x + x2 + x3 = 60, then the average (arithmetic mean) of x, x2, x3, and x4
is equal to which of the following?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
12x
15x
20x
30x
60x
Explanation
A quick inspection of the answer choices shows that it is not necessary to solve
the equation 1 + x + x2 + x3 = 60 for x to answer this question
...
To express this average in terms of x, you need to add the 4 quantities and divide
x + x2 + x3 + x4
...
4
Note that the numerator of the fraction is a sum of 4 quantities, each of which
has an x term raised to a power
...
Unlawful distribution of this ebook is prohibited
...
By using the information in the
question, you can make the following simplification
...
y
Q
P
R
x
O
10
...
The
coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6)
...
Therefore, in the figure above, PQM and ORN are
congruent right triangles
...
Unlawful distribution of this ebook is prohibited
...
Thus, the lengths of the
legs ON and RN of triangle ORN are also 6 and 2, respectively
...
The correct answer is Choice E
...
The relationship between the area A of a circle and its circumference C is
given by the formula A = kC 2, where k is a constant
...
Therefore, you can pick a specific circle and substitute the
circumference and the area of that particular circle into the formula and calculate
the value of k
...
The area of the circle is
p and the circumference of the circle is 2p
...
Solving this equation for k gives k = , and the correct answer is
4p
Choice A
...
Recall the
commonly used formulas for the area and the circumference of a circle: A = pr2
and C = 2pr
...
So, in the formula A = kC2, you can substitute expressions for A and
C in terms of r
...
Now you can determine the value of k by solving the equation for k as follows
...
195
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...
GRE Quantitative Reasoning Practice Questions
12
...
What is the sum of the first 20 terms of this sequence?
The sequence of numbers a1, a2, a3,
...
is defined by an =
C
ɕ
1
1 + 1 − 20
2
1
1
1 + 1 − 21 + 22
2
1
1
1− +
20 22
D
ɕ
1−
E
ɕ
1
1
−
20 22
A
ɕ
B
ɕ
1
22
Explanation
This question asks for the sum of the first 20 terms of the sequence
...
Questions involving sequences can often be answered by
looking for a pattern
...
To look for a pattern, begin by adding the first two terms of the sequence
...
3
3
1 − 1 + 1 − 1 + 1 − 1 = 1 + 1 − 1 + 1
1 3
2 4
3 5
1 2
4 5
If you add the first four terms, you get
1 1
1 1
1 1
1 1
1 − 3 + 2 − 4 + 3 − 5 + 4 − 6
Again, you can simplify the sum by canceling
...
3
4
1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 = 1 + 1 − 1 + 1
1 3
2 4
3 5
4 6
1 2
5 6
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GRE Quantitative Reasoning Practice Questions
If you write out the next two sums and simplify them, you will see that they are
1 1
1 1
1 1
1 1
1 + 2 − 6 + 7 and 1 + 2 − 7 + 8
Working with the sums makes it clear that this pattern continues to hold as you
add more and more terms of the sequence together and that a formula for the
sum of the first k terms of the sequence is
1
1
1 + 1 − k + 1 + k + 2
1 2
Therefore, the sum of the first 20 terms of the sequence is equal to
1
1
1
1 + 1 − 201 1 + 20 1 2 = 1 + 2 − 21 + 22
1 2
+
+
The correct answer is Choice B
...
Y
1
2
2
3
4
7
5
4
8
3
2
8
7
4
13
...
What is the mean of the distribution?
Give your answer to the nearest 0
...
Explanation
The mean of distribution of the variable Y is the sum of all the values of Y divided
by the number of values of Y
...
Information about the variable is given in a table, where any repetitions of values
have been summarized in the column labeled “Frequency
...
Unlawful distribution of this ebook is prohibited
...
To sum all the values of Y, you could add the value twice, add the
2
3
value seven times, and continue the addition process in this manner
...
table, you can see that the value
1 + (7)3 + (8)5 + (8)3 + (9)7 = 4 + 21 + 40 + 48 + 63
2
4
4
2
4
4
4
4
4
4
(2)
176
4
= 44
=
To find the average, you need to divide the sum, 44, by the number of values of Y
...
The sum of the numbers in this column, 2 + 7 + 8 + 8 + 9, or 34, is the
44
number of values of Y
...
2941
...
01, the correct answer is 1
...
Multiple-choice Questions—Select One or More Answer Choices
For Questions 14 and 15, select all the answer choices that apply
...
Let S be the set of all positive integers n such that n2 is a multiple of both
24 and 108
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
12
24
36
72
Explanation
To determine which of the integers in the answer choices is a divisor of every
positive integer n in S, you must first understand the integers that are in S
...
Therefore, you must use the information about n2 to derive information about n
...
To determine the least common
multiple of 24 and 108, factor 24 and 108 into prime factors as (23)(3) and
(22)(33), respectively
...
Knowing that n2 must be a multiple of (23)(33) does not mean that every
multiple of (23)(33) is a possible value of n2, because n2 must be the square of an
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...
GRE Quantitative Reasoning Practice Questions
integer
...
Thus, the least multiple of (23)(33) that is a square is (24)(34)
...
Furthermore, since every value of n2 is a multiple of (24)(34), the values of n
are the positive multiples of 36; that is, S = {36, 72, 108, 144, 180,
...
Since Choice A, 12, is a divisor of 36,
it is also a divisor of every multiple of 36
...
Choices B and D, 24 and 72, are not divisors of 36, so they are not divisors of
every integer in S
...
15
...
2
inches, and the range of the heights of the male students in the class is 15
...
Which of the following statements individually provide(s) sufficient
additional information to determine the range of the heights of all the
students in the class?
Indicate all such statements
...
8 inches taller than the tallest
female student in the class
...
1 inches
greater than the median height of the female students in the class
...
6 inches greater than the average height of the female students in
the class
...
8 inches taller than the tallest
female student
...
15
...
2
Shortest Shortest
female
male
5
...
You can also see the difference in height
between those two students, which is the range of the heights of the entire class
...
Choice B provides information about one of the centers of the data—the
median; it does not say anything about how spread out the data are around that
center
...
1 inches greater
than that of the females
...
Unlawful distribution of this ebook is prohibited
...
Choice B gives the
difference between the medians of the male heights and the female heights,
without giving the actual medians
...
It is possible to construct examples of heights of students that satisfy all of
the information in the question and in Choice B but have different ranges for the
heights of the entire class
...
Although the examples are small, they illustrate
the fact that the range of the heights of the entire class can vary
...
2, the range of male heights is 15
...
1 inches
...
0
56
...
2
Male heights:
50
...
7
65
...
4
which have a median of 56
...
7
Example 2
Female heights: 50
...
6
63
...
0
57
...
4
Range of heights of entire class: 16
...
6
which have a median of 57
...
Choice C provides information about another center of the data—the
average
...
6 inches greater
than that of the females
...
Again, it is
possible for two different sets of data to have the same average but have very
different ranges
...
Therefore, Choice C does not
provide sufficient additional information to determine the range of the heights of
the entire class
...
200
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...
GRE Quantitative Reasoning Practice Questions
SET 4
...
Questions 1 to 3 are based on the following data
...
There are 275 students in the field of engineering at University X
...
To determine the total number of
faculty members in engineering, you need to add 2 percent of 200, which is 4, to
12 percent of 250, which is 30, to get 34
...
The correct answer is Choice A
...
Unlawful distribution of this ebook is prohibited
...
Approximately what percent of the faculty in humanities are male?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
35%
38%
41%
45%
51%
Explanation
You need to determine the numbers of female and male faculty in the
humanities field
...
Thus, the fraction of
35
35
humanities faculty who are male is
= , or approximately 0
...
As a
34 + 35 69
percent, the answer choice that is closest to 0
...
The correct
answer is Choice E
...
Hard Question
3
...
What
9
fraction of all the faculty members in those two fields combined are tenured
professors?
female and
Explanation
You need to determine the number of female faculty and the number of male
faculty in the combined group
...
Similarly, 16 percent of the female faculty, or 32, and 8 percent of the
male faculty, or 20, are in the health sciences
...
The tenured faculty are of the 42 females, or 14 females, and of
3
9
the 45 males, or 10 males
...
The correct answer is
(or any equivalent
87
87
fraction)
...
Unlawful distribution of this ebook is prohibited
...
VALUE OF IMPORTS TO AND EXPORTS FROM COUNTRY T, 2000 –2009
(in United States dollars)
16
Billions* of Dollars
14
12
Exports
Imports
10
8
6
4
2
0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Year
*1 billion = 1,000,000,000
For Question 4, select all the answer choices that apply
...
For which of the eight years from 2001 to 2008 did exports exceed imports
by more than $5 billion?
Indicate all such years
...
For each year, the difference between the dollar value of
exports and the dollar value of imports can be read directly from the graph
...
The correct answer consists of Choices A, B, C, F, G, and H
...
Unlawful distribution of this ebook is prohibited
...
Which of the following is closest to the average (arithmetic mean) of the 9
changes in the value of imports between consecutive years from 2000 to
2009 ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
$260 million
$320 million
$400 million
$480 million
$640 million
Explanation
The average of the 9 changes in the value of imports between consecutive years
can be represented as follows, where the function v(year) represents the value of
imports for the indicated year
...
+ (v(2009) − v(2008))
9
Note that in the numerator of the fraction, each term, with the exception of
v(2000) and v(2009), appears first as positive and then again as negative
...
9
Reading the values from the graph, you can approximate the value of the
9
...
2 5
...
644 billion dollars
...
644 billion is $640 million
...
Medium Question
6
...
5
5
204
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...
GRE Quantitative Reasoning Practice Questions
Since the fraction is greater than 1, expressing it as a percent will give a
percent greater than 100
...
4, or 140 percent
...
Hard Question
7
...
The average value of imports for the 10 years shown in the graph is found by
adding the 10 values and then dividing the sum by 10
...
If that amount were $5 billion instead, then the sum of
the values would be $2 billion less
...
The average would therefore be $200 million less,
10
and the correct answer is Choice A
...
The average of the 10 values is
S
...
The average of the adjusted sum is
...
2 billion dollars, or $200 million
...
205
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...
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This ebook was issued to Diane Massey, order #11560922926
...
7
GRE ®
Math Review
Your goal
for this
chapter
g Review the math topics likely to appear on the
GRE® revised General Test
g Study examples with worked-out solutions
g Test your skills with practice exercises
T
his Math Review will familiarize you with the mathematical skills and concepts that are important to understand in order to solve problems and to reason quantitatively on the Quantitative Reasoning measure of the GRE revised
General Test
...
Note, however, that this review is not intended to be all-inclusive — there may be some
concepts on the test that are not explicitly presented in this review
...
The Math Review covers the following topics:
1
...
Geometry
1
...
2
1
...
4
1
...
6
1
...
1
3
...
3
3
...
5
3
...
Algebra
4
...
1 Operations with Algebraic
Expressions
2
...
3 Solving Linear Equations
2
...
5 Solving Linear Inequalities
2
...
7 Applications
2
...
9 Graphs of Functions
4
...
2
4
...
4
4
...
6
Graphical Methods for
Describing Data
Numerical Methods for
Describing Data
Counting Methods
Probability
Distributions of Data, Random
Variables, and Probability
Distributions
Data Interpretation Examples
207
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...
GRE Math Review
1
...
The basic arithmetic operations of addition, subtraction,
multiplication, and division are discussed, along with exponents and roots
...
1
...
, and 0
...
, −3, −2, −1, 0, 1, 2, 3,
...
When integers are added, subtracted, or multiplied,
the result is always an integer; division of integers is addressed below
...
Here are some general facts regarding multiplication of integers
...
The product of two negative integers is a positive integer
...
When integers are multiplied, each of the multiplied integers is called a factor or
divisor of the resulting product
...
The integers 4, 15, 5, and 12 are also factors of 60, since (4)(15) = 60
and (5)(12) = 60
...
The negatives of these integers are also factors of 60, since, for example,
(−2)(−30) = 60
...
We say that 60 is a multiple of
each of its factors and that 60 is divisible by each of its divisors
...
¼
¼
¼
¼
¼
The positive factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100
...
The list of positive multiples of 25 has no end: 25, 50, 75, 100, 125, 150, etc
...
1 is a factor of every integer; 1 is not a multiple of any integer except 1 and −1
...
The least common multiple of two nonzero integers a and b is the least positive
integer that is a multiple of both a and b
...
This is because the positive multiples of 30 are 30, 60, 90, 120,
150, 180, 210, 240, 270, 300, etc
...
Thus, the common positive multiples of 30 and 75 are 150, 300,
450, etc
...
The greatest common divisor (or greatest common factor) of two nonzero integers a and b is the greatest positive integer that is a divisor of both a and b
...
This is because the positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, and the positive divisors of 75 are
1, 3, 5, 15, 25, and 75
...
When an integer a is divided by an integer b, where b is a divisor of a, the result
is always a divisor of a
...
If b is not a divisor of a, then the result
208
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...
GRE Math Review
can be viewed in three different ways
...
Each view is useful, depending on the
context
...
Regarding quotients with remainders, consider two positive integers a and b for
which b is not a divisor of a; for example, the integers 19 and 7
...
Because 19 is 5 more than (2)(7), we say that the result of 19 divided by 7 is the
quotient 2 with remainder 5, or simply “2 remainder 5
...
That multiple of b can be expressed as the product qb,
where q is the quotient
...
The remainder is always greater than or equal
to 0 and less than b
...
¼
¼
¼
100 divided by 45 is 2 remainder 10, since the greatest multiple of 45 that’s less
than or equal to 100 is (2)(45), or 90, which is 10 less than 100
...
In general, the remainder is 0
if and only if a is divisible by b
...
Here are some other examples
...
100 divided by 25 is 4 remainder 0, since 100 = (4)(25) + 0
...
When you divide 100 by 2, the remainder is 0
...
If an integer is divisible by 2, it is called an even integer; otherwise it is an odd
integer
...
The set of even integers is {
...
}, and the set of odd
integers is {
...
There are several useful facts regarding the
sum and product of even and odd integers
...
sum of two odd integers is an even integer
...
product of two even integers is an even integer
...
product of an even integer and an odd integer is an even integer
...
The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
...
The integer 1 is not a prime number, and the integer 2 is the only prime number
that is even
...
Unlawful distribution of this ebook is prohibited
...
Such an
expression is called a prime factorization
...
12 = (2)(2)(3) = (22)(3)
14 = (2)(7)
81 = (3)(3)(3)(3) = 34
338 = (2)(13)(13) = (2)(132)
800 = (2)(2)(2)(2)(2)(5)(5) = (25)(52)
1,155 = (3)(5)(7)(11)
An integer greater than 1 that is not a prime number is called a composite
number
...
1
...
The
b
integer a is called the numerator of the fraction, and b is called the denominator
...
Such numbers are also called rational numbers
...
For example,
b
−7 (−7)(4) −28
=
=
5
(5)(4)
20
−7 (−7)(−1)
7
=
=
5
(5)(−1)
−5
A fraction with a negative sign in either the numerator or denominator can be
−7
7
7
written with the negative sign in front of the fraction; for example,
=
=−
...
For example,
40 (8)(5) 5
=
=
72 (8)(9) 9
To add two fractions with the same denominator, you add the numerators and
keep the same denominator
...
Then convert both
fractions to equivalent fractions with the same denominator
...
For example, to add the fractions and
3
2
− , use the common denominator 15:
5
1 −2
1 5
−2 3
5
−6 5 + (−6)
1
+
=
+
=
+
=
=−
3
5
3 5
5 3
15 15
15
15
210
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...
GRE Math Review
The same method applies to subtraction of fractions
...
For example,
10−1 = (10)(−1) = −10 = − 10
7
3
(7)(3)
21
21
8 7
56
33 = 9
To divide one fraction by another, first invert the second fraction—that is, find
its reciprocal—then multiply the first fraction by the inverted fraction
...
It consists of an integer
8
3
3
part and a fraction part; the mixed number 4 means 4 +
...
For example,
An expression such as 4
3
3
4 8
3 32 3 35
4 =4+ =
+ =
+ =
8
8
1 8
8
8
8
8
a
, where either a or b is not an integer and
b
b ≠ 0, are fractional expressions that can be manipulated just like fractions
...
2
3
Note that numbers of the form
p p
p 3
p 2
3p 2p 5p
+ =
+
=
+
=
2 3
2 3
3 2
6
6
6
1
And the number
Ί2 can be simplified as follows
...
3 Exponents and Roots
Exponents are used to denote the repeated multiplication of a number by itself; for
example, 34 = (3)(3)(3)(3) = 81 and 53 = (5)(5)(5) = 125
...
” So 5 to the third power is 125
...
Thus, 6 squared is 36, 62 = (6)(6) = 36, and 7 squared is 49,
72 = (7)(7) = 49
...
Unlawful distribution of this ebook is prohibited
...
For example, (−3)2 = (−3)(−3) = 9, while (−3)5 = (−3)(−3)(−3)(−3)(−3) = −243
...
Note that without the parentheses,
the expression −32 means “the negative of ‘3 squared’ ”; that is, the exponent is applied before the negative sign
...
Exponents can also be negative or zero; such exponents are defined as follows
...
The expression 00 is undefined
...
Note that
a
a
a
1
(a)(a−1) = (a)
= 1
...
For
example, 4 is a square root of 16 because 42 = 16
...
All positive numbers have two square roots, one positive and one
negative
...
The symbol Ίn is used to denote the nonnegative square root of the nonnegative number n
...
Square roots of negative numbers are not defined in the real number
system
...
Examples
Rule
2
2
2
Ίa = a
Ί3 = 3
2
Ίp = p
Ίp2 = p
Ίa = a
Ί4 = 2
ΊaΊb = Ίab
Ί3Ί10 = Ί30
Ίa
Ίb
=
Ί
a
b
Ί5
Ί15
=
Ί Ί
5
=
15
Ί24 = Ί4Ί6 = 2Ί6
1
3
Ί18
Ί2
=
Ί 2 = Ί9 = 3
18
A square root is a root of order 2
...
For orders 3 and 4, the cube root 3 n and fourth root 4 n
Ί
Ί
represent numbers such that when they are raised to the powers 3 and 4,
respectively, the result is n
...
There are some notable
differences between odd-order roots and even-order roots (in the real number
system):
¼
¼
For odd-order roots, there is exactly one root for every number n, even when n is
negative
...
For example, 8 has exactly one cube root, 3 8 = 2, but 8 has two fourth roots: 4 8 and
Ί
Ί
−4 8; and −8 has exactly one cube root, 3 −8 = −2, but −8 has no fourth root, since
Ί
Ί
it is negative
...
Unlawful distribution of this ebook is prohibited
...
4 Decimals
Thousandths
Hundredths
Tenths
Ones or Units
Tens
Hundreds
Thousands
The decimal number system is based on representing numbers using powers of 10
...
For example, the digits
of the number 7,532
...
That is,
1
1
1
10 + 1100 + 81,000
7,532
...
Since each place value is a power of 10, every decimal
can be converted to an integer divided by a power of 10
...
17 = 90 +
=
=
100
100
100
612
153
0
...
3 = 2 +
Conversely, every fraction with integers in the numerator and denominator can
be converted to an equivalent decimal by dividing the numerator by the denominator
using long division (which is not in this review)
...
08, or the decimal will
long division will either terminate, as in = 0
...
111
...
0454545
...
08333
...
Here are some examples of fractions converted to
decimals
...
375
8
259
19
=6+
= 6
...
3
3
15
= 1
...
That is, every rational number can be expressed
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...
GRE Math Review
as a terminating or repeating decimal
...
Not all decimals are terminating or repeating; for instance, the decimal that is
equivalent to Ί2 is 1
...
, and it can be shown that this decimal does not
terminate or repeat
...
010110111011110111110
...
Since these two decimals do not terminate or repeat,
they are not rational numbers
...
1
...
The real numbers include all integers, fractions, and decimals
...
– 5
–3
–2
–
3
2
1
2
–0
...
6
2
1
2
3
Every real number corresponds to a point on the number line, and every point
on the number line corresponds to a real number
...
Only the
number 0 is neither negative nor positive
...
A real number y is greater than x if y is to the
right of x on the number line, which is written as y > x
...
The set
of all real numbers that are between 2 and 3 is called an interval, and the double
inequality 2 < x < 3 is often used to represent that interval
...
Sometimes one or both of
the endpoints are to be included in an interval
...
2
2
There are also four types of intervals with only one endpoint, each of which consists of all real numbers to the right or to the left of the endpoint, perhaps including
the endpoint
...
x<4
x≤4
x>4
x≥4
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GRE Math Review
The entire real number line is also considered to be an interval
...
Therefore, ⎪3⎪ = 3 and ⎪−3⎪ = 3 because each of the
numbers 3 and −3 is a distance of 3 from 0
...
It follows that the absolute value
of any nonzero number is positive
...
⎪Ί5⎪ = Ί5
⎪−23⎪ = −(−23) = 23
⎪−10
...
2
There are several general properties of real numbers that are used frequently
...
For example, 8 + 2 = 2 + 8 = 10 and (−3)(17) = (17)(−3) = −51
...
For example, (7 + 3) + 8 = 7 + (3 + 8) = 18 and (7Ί2 )Ί2 = 7(Ί2Ί2 ) = (7)(2) = 14
...
a + 0 = a, (a)(0) = 0, and (a)(1) = a
...
For example, if −2b = 0, then b = 0
...
Division by 0 is not defined; for example, 5 ,0 נ
0
0
If both a and b are positive, then both a + b and ab are positive
...
If a is positive and b is negative, then ab is negative
...
This is known as the triangle inequality
...
Therefore, ⎪5 + (−2)⎪ ≤ ⎪5⎪ + ⎪−2⎪
...
For example, ⎪5⎪
⎪−2⎪ = ⎪(5)(−2)⎪ = ⎪−10⎪ = 10
...
If 0 < b < 1, then b2 < b
...
5
25 5
1
...
Thus, if s and t are positive quantities, then the ratio of
s
s to t can be written as the fraction
...
For example, if there are 2 apples and 3 oranges in a basket, we
2
can say that the ratio of the number of apples to the number of oranges is or that
3
it is 2 to 3 or that it is 2:3
...
For
example, if there are 8 apples and 12 oranges in a basket, then the ratio of the numbers of apples to oranges is still 2 to 3
...
If three or more positive quantities are being considered, say r, s, and t, then
their relative sizes can also be expressed as a ratio with the notation “r to s to t
...
Unlawful distribution of this ebook is prohibited
...
This ratio can be reduced
to 1 to 6 to 4 by dividing each number by the greatest common divisor of 5, 30, and
20, which is 5
...
To solve a
A proportion is an equation relating two ratios; for example,
12 4
problem involving ratios, you can often write a proportion and solve it by cross
multiplication
...
6
...
21
1
...
Percents are ratios that are often used to represent parts of a whole, where the whole is considered as having 100
parts
...
100
¼ 32 percent means 32 parts out of 100 parts, or 32
...
2
Note that the part is the numerator of the ratio and the whole is the denominator
...
1
= 0
...
32
100
50
50% =
= 0
...
3
0
...
003
100
1% =
Be careful not to confuse 0
...
01%
...
For exam0
...
01 = 1% but 0
...
0001
...
The result will be the decimal equivalent, so multiply the result by 100 to convert
to percent
...
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...
7
...
part
13
=
= 0
...
7
...
9?
Solution: Here the whole is 150 and the part is 12
...
part
12
...
086 = 8
...
Example 1
...
3: To find 30% of 350, multiply 350 by the decimal equivalent of 30%,
or 0
...
x = (350)(0
...
You want a number x that satisfies the proportion
part
30
=
whole 100
x
30
=
350 100
Solving for x yields x =
¼
(30)(350)
= 105, so 30% of 350 is 105
...
To do this you can
either use the decimal equivalent of the percent or you can set up a proportion
and solve it
...
7
...
Because 60% of some number z is 15,
multiply z by the decimal equivalent of 60%, or 0
...
0
...
6 as follows
...
6
Using a proportion, look for a number z such that
part
60
=
whole 100
15
60
=
z
100
Hence, 60z = (15)(100), and therefore, z =
(15)(100) 1, 500
=
= 25
...
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GRE Math Review
Although the discussion about percent so far assumes a context of a part and a
whole, it is not necessary that the part be less than the whole
...
When the numerator of a percent is greater than
the base, the percent is greater than 100%
...
5)(16) = 40
...
5
...
This is called percent change
...
25 = 25%
base
600
600 100
We say the percent increase is 25%
...
For example, if a
quantity changes from 150 to 300, then the percent increase is
change 300 − 150 150
=
=
= 100%
base
150
150
If a quantity decreases from 500 to 400, calculate the percent decrease as follows
...
20 = 20%
base
500
500 100
The quantity decreased by 20%
...
When computing a percent decrease, the base is the larger number
...
Example 1
...
5: An investment in a mutual fund increased by 12% in a single day
...
Therefore, the value of the increase is 12%
of $1,300, or, using the decimal equivalent, the increase is (0
...
Thus, the value of the investment after the change is
$1,300 + $156 = $1,456
Because the final result is the sum of the initial investment—100% of $1,300—and
the increase—12% of $1,300—the final result is 100% + 12% = 112% of $1,300
...
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...
12:
($1,300)(1
...
The base of each successive
percent change is the result of the preceding percent change
...
7
...
What was the cumulative percent change for the two months?
Solution: If E is the enrollment before the first month, then the enrollment as a
result of the 8% decrease can be found by multiplying the base E by the decimal
equivalent of 100% − 8% = 92%, which is 0
...
92E
The enrollment as a result of the second percent change—the 6% increase—can be
found by multiplying the new base 0
...
06:
(1
...
92)E = 0
...
9752 is 97
...
48% less than 100%
...
48% decrease
...
Evaluate the following
...
15 − (6 − 4)(−2)
(2 − 17) 5 נ
(60 )4 + 7−( − )21 נ
(3)4 − (−2)3
Evaluate the following
...
Which of the integers 312, 98, 112, and 144 are divisible by 8?
4
...
6
...
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GRE Math Review
8
...
1
(b) Ί16 = 4
(c) 7 0 = 0 נ
1
(d) 0 < −
7
1
(e) 0
...
Find the following
...
6% of 800
10
...
12
...
14
...
If the value increases by 20
percent and then decreases by 25 percent, what will be the value of the
stock per share after the decrease?
If the ratio of the number of men to the number of women on a committee
of 20 members is 3 to 2, how many members of the committee are women?
The integer a is even and the integer b is odd
...
Integer
Even
Odd
a + 2b
2a + b
ab
ab
(a + b)2
a2 − b2
15
...
What is the least possible value of n?
ANSWERS TO ARITHMETIC EXERCISES
1
...
Unlawful distribution of this ebook is prohibited
...
(a)
(b) −
3
...
5
...
7
...
9
...
11
...
13
...
9
1, 600
4
(d) −
9
1
4
(c)
5
14
312, 112, and 144
(a) 372 = (22)(3)(31)
(b) The positive divisors of 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, and
372
...
(b) 144 = (24)(32), so the prime divisors are 2 and 3
...
8
(d) 50
(e) 20%
17%
5%
$36 per share
8 women
Integer
Even
Odd
a + 2b
2a + b
ab
ab
(a + b)2
a2−b2
15
...
Unlawful distribution of this ebook is prohibited
...
ALGEBRA
Basic algebra can be viewed as an extension of arithmetic
...
The letters x and y are often used as
variables, although any letter can be used
...
This section reviews these algebraic tools and then progresses to several examples of applying them to solve real-life word problems
...
2
...
Here are some examples of algebraic expressions
...
In the expression
n+p
w3z + 5z2 − z2 + 6, the terms 5z2 and −z2 are called like terms because they have
the same variables, and the corresponding variables have the same exponents
...
A number that is multiplied by
variables is called the coefficient of a term
...
The same rules that govern operations with numbers apply to operations with
algebraic expressions
...
w3z + 5z2 − z2 + 6 has four terms, and
2x + 5x = 7x
w3z + 5z2 − z2 + 6 = w3z + 4z2 + 6
3xy + 2x − xy − 3x = 2xy − x
A number or variable that is a factor of each term in an algebraic expression can
be factored out, as the following examples show
...
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(x + 2)(3x − 7) = x(3x) + x(−7) + 2(3x) + 2(−7)
= 3x2−7x + 6x − 14
= 3x2−x−14
A statement of equality between two algebraic expressions that is true for all
possible values of the variables involved is called an identity
...
Here are some standard identities
that are useful
...
For example, the identity a2 − b2 = (a + b)(a−b) can be used to simplify the
following algebraic expression
...
The values are called
the solutions of the equation
...
3x + 5 = −2
A linear equation in one variable, x
x − 3y =10
A linear equation in two variables, x and y
2
20y + 6y − 17 = 0
A quadratic equation in one variable, y
2
...
For some equations involving bases and exponents, the
following property is very useful: if xa = xb, then a = b
...
For example, if 2y = 64, then
since 64 is 26, you have 2y = 26, and you can conclude that y = 6
...
1
x−a = a
1
...
3
...
5
...
Note that 00 is not defined
...
Unlawful distribution of this ebook is prohibited
...
a
=x
y
x
y
a
a
2
Examples:
7
...
Sometimes
algebraic expressions look like they can be simplified in similar ways, but in fact
they cannot
...
¼
¼
¼
¼
xayb ≠ (xy)a+b
Note that the bases are not the same
...
(x + y)a ≠ xa + ya
Recall that (x + y)2 = x2 + 2xy + y2; that is, the correct expansion contains
terms such as 2xy
...
Note carefully where each minus sign appears
...
a
a a
2
...
Two equations that have the same
solutions are called equivalent equations
...
The general method for solving an equation is to find successively simpler equivalent equations so that the simplest equivalent equation makes the solutions obvious
...
¼
¼
When the same constant is added to or subtracted from both sides of an
equation, the equality is preserved and the new equation is equivalent to the
original equation
...
A linear equation is an equation involving one or more variables in which each
term in the equation is either a constant term or a variable multiplied by a coefficient
...
For
example, 2x + 1 = 7x and 10x − 9y−z = 3 are linear equations, but x + y2 = 0 and
xz = 3 are not
...
Unlawful distribution of this ebook is prohibited
...
Then use the rules for producing simpler equivalent equations
...
3
...
Note that it is possible for a linear equation to have no solutions
...
Also, it is possible that what looks to be a linear equation turns
out to be an identity when you try to solve it
...
Linear Equations in Two Variables
A linear equation in two variables, x and y, can be written in the form
ax + by = c
where a, b, and c are real numbers and a and b are not both zero
...
A solution of such an equation is an ordered pair of numbers (x, y) that makes
the equation true when the values of x and y are substituted into the equation
...
A linear equation in two variables has infinitely many solutions
...
Two equations with the same variables are called a
system of equations, and the equations in the system are called simultaneous equations
...
There are two basic methods for solving systems of linear equations, by substitution or by elimination
...
Then the expression is substituted in the
other equation
...
Then substitute
2 − 2y for x in the first equation to find the value of y
...
Unlawful distribution of this ebook is prohibited
...
We use the
second equation:
x + 2y = 2
x + 2(−1) = 2
x−2=2
x = 4 (2 added to both sides)
In the elimination method, the object is to make the coefficients of one variable
the same in both equations so that one variable can be eliminated either by adding
the equations together or by subtracting one from the other
...
Now you have two equations with the same coefficient of x
...
Thus,
y = −1, and substituting −1 for y in either of the original equations yields x = 4
...
2
...
When such an equation has solutions,
they can be found using the quadratic formula:
x=
−b עΊb2 − 4ac
2a
where the notation עis shorthand for indicating two solutions—one that uses the
plus sign and the other that uses the minus sign
...
4
...
Therefore, the quadratic formula yields
x=
=
−(−1) עΊ(−1)2 − 4(2)(−6)
2(2)
1 עΊ49
4
17ע
=
4
Hence the two solutions are x =
1+7
1−7
3
= 2 and x =
=−
...
Unlawful distribution of this ebook is prohibited
...
However, some quadratic equations have only one real solution
...
In this case, the
expression under the square root symbol in the quadratic formula is equal to 0, and
so adding or subtracting 0 yields the same result
...
In this case, the expression under the
square root symbol is negative, so the entire expression is not a real number
...
For example,
the quadratic equation 2x2 − x − 6 = 0 in example 2
...
1 can be factored as
(2x + 3)(x − 2) = 0
...
Therefore,
2x + 3 = 0
2x = −3
3
x=−
2
and the solutions are −
OR
x−2=0
x
=2
3
and 2
...
4
...
5x2 + 3x − 2 = 0
(5x − 2)(x + 1) = 0
Therefore,
5x − 2 = 0
2
x=
5
OR
x+1=0
x = −1
2
...
Ͻ
Ͼ
≤
≥
less than
greater than
less than or equal to
greater than or equal to
Inequalities can involve variables and are similar to equations, except that the two
sides are related by one of the inequality signs instead of the equality sign used in
equations
...
” To solve an inequality means to
find the set of all values of the variable that make the inequality true
...
Two inequalities that have the
same solution set are called equivalent inequalities
...
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GRE Math Review
¼
¼
When the same constant is added to or subtracted from both sides of an
inequality, the direction of the inequality is preserved and the new inequality
is equivalent to the original
...
In either case,
the new inequality is equivalent to the original
...
5
...
−3x + 5 ≤ 17
−3x ≤ 12
−3x 12
≥
−3 −3
(5 subtracted from both sides)
(both sides divided by −3, which reverses
the direction of the inequality)
x ≥ −4
Therefore, the solution set of −3x + 5 ≤ 17 consists of all real numbers greater than
or equal to −4
...
5
...
5
Therefore, the solution set of
4x + 9
< 5 consists of all real numbers less than 11
...
11
2
...
Functions are usually denoted by letters such as f, g, and h
...
For example, if x = 1 is substituted in the expression above, the
result is f (1) = 8
...
For
any function, each input x gives exactly one output f (x)
...
For example, if g is the function defined by
g(x) = x2 − 2x + 3, then g(0) = 3 and g(2) = 3
...
For the functions f and g defined above, the domain is the
set of all real numbers
...
Unlawful distribution of this ebook is prohibited
...
For example, we can define the function h
by h(x) = x2 − 4 for −2 ≤ x ≤ 2
...
Example 2
...
1: Let f be the function defined by f (x) =
fined at x = 6 because
2x
...
Hence, the domain of f consists of all real
0
numbers except for 6
...
6
...
In this case,
g(x) is not a real number if x < −2
...
Example 2
...
3: Let h be the function defined by h(x) = ⎪x⎪, the absolute value of x,
which is the distance between x and 0 on the number line (see section 1
...
The domain of h is the set of all real numbers
...
2
...
Some examples are given below
...
If John’s present salary s is increased by 14 percent, then his new salary is
1
...
If y gallons of syrup are to be distributed among 5 people so that one
particular person gets 1 gallon and the rest of the syrup is divided equally
y−1
among the remaining 4, then each of those 4 people will get
gallons of
4
syrup
...
Example 2
...
1: Ellen has received the following scores on 3 exams: 82, 74, and 90
...
This initial step of assigning
a variable to the quantity that is sought is an important beginning to solving the
problem
...
Now simplify the expression and set it equal to 85:
82 + 74 + 90 + x 246 + x
=
= 85
4
4
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...
GRE Math Review
Solving the resulting linear equation for x, you get
246 + x = 340
x = 94
Therefore, Ellen will need to attain a score of 94 on the next exam
...
7
...
How many ounces of oil must be
added to the mixture to produce a new mixture that is only 25 percent vinegar?
Solution: Let x represent the number of ounces of oil to be added
...
40)(12)
...
40)(12)
= 0
...
40)(12) = (12 + x)(0
...
8 = 3 + 0
...
8 = 0
...
2 = x
Thus, 7
...
Example 2
...
3: In a driving competition, Jeff and Dennis drove the same course at
average speeds of 51 miles per hour and 54 miles per hour, respectively
...
The
distance d, in miles, is equal to the product of the rate r, in miles per hour, and the
time t, in hours; that is,
d = rt
Note that since the rates are given in miles per hour, it is necessary to express the
40
times in hours; for example, 40 minutes equals
of an hour
...
Since the dis60
tances are equal,
x
40 = (54)60
60
(51)
(51)(40) = 54x
(51)(40)
x=
Ϸ 37
...
8 minutes to drive the course
...
Unlawful distribution of this ebook is prohibited
...
7
...
Working alone at its constant rate, machine B takes 2 hours to produce an identical batch of parts
...
Similarly, machine B can produce of the batch in 1 hour
...
When the two machines work together, adding their individual production
1
1
1
rates, and , gives their combined production rate
...
Example 2
...
5: At a fruit stand, apples can be purchased for $0
...
20 each
...
80
...
0
...
20p = 3
...
Substituting 21 − p into the first equation for
a gives
0
...
20p = 3
...
15)(21) − 0
...
20p = 3
...
15 − 0
...
20p = 3
...
05p = 0
...
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Example 2
...
6: To produce a particular radio model, it costs a manufacturer $30 per
radio, and it is assumed that if 500 radios are produced, all of them will be sold
...
Therefore, we set
500(y − 30) > 8,200
Solving the inequality, we get
500y − 15,000 Ͼ 8,200
500y Ͼ 23,200
y Ͼ 46
...
40 to ensure that the profit is greater
than $8,200
...
The interest can be computed as simple interest or compound
interest
...
If the
amount P is invested at a simple annual interest rate of r percent, then the value V of
the investment at the end of t years is given by the formula
V=P 1+
rt
100
where P and V are in dollars
...
Each time interest is added to
the principal, the interest is said to be compounded
...
If the amount P is invested at an annual interest rate of r percent,
compounded annually, then the value V of the investment at the end of t years is given
by the formula
V=P 1+
t
r
100
If the amount P is invested at an annual interest rate of r percent, compounded n
times per year, then the value V of the investment at the end of t years is given by the
formula
V=P 1+
nt
r
100n
Example 2
...
7: If $10,000 is invested at a simple annual interest rate of 6 percent,
what is the value of the investment after half a year?
Solution: According to the formula for simple interest, the value of the investment
1
after year is
2
1
$10,000 1 + 0
...
03) = $10,300
2
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GRE Math Review
Example 2
...
8: If an amount P is to be invested at an annual interest rate of 3
...
5 percent annual interest, compounded annually, the value of the investment after 3 years is
P(1 + 0
...
035)3 = $1,000
To find the value of P, we divide both sides of the equation by (1 + 0
...
P=
$1,000
Ϸ $901
...
035)3
Thus, an amount of approximately $901
...
Example 2
...
9: A college student expects to earn at least $1,000 in interest on an initial investment of $20,000
...
05
r
400
r
1+
400
$20,000 1 +
4
We can use the fact that taking the positive fourth root of each side of an inequality
preserves the direction of the inequality
...
1+
r
≥ 4 1
...
05 − 1
Ί
To compute the fourth root, we can use the fact that 4 x = ΊΊx for x ≥ 0; that is, we
Ί
can compute a fourth root by taking a square root twice:
r ≥ 400 4 1
...
05 − 1 Ϸ 4
...
91 percent
...
8 Coordinate Geometry
Two real number lines that are perpendicular to each other and that intersect at their
respective zero points define a rectangular coordinate system, often called the
xy-coordinate system or xy-plane
...
Unlawful distribution of this ebook is prohibited
...
The point where the two axes intersect is called the origin, denoted by O
...
The two axes divide
the plane into four regions called quadrants I, II, III, and IV, as shown in the figure
below
...
The first number is called the x-coordinate, and
the second number is called the y-coordinate
...
Also, the point is located ⎪y⎪ units above the x-axis if y is positive or below
the x-axis if y is negative
...
The origin has coordinates (0, 0)
...
In the figure above, the point P(4, 2) is 4 units to the right of the y-axis and 2 units
above the x-axis, and the point P ′′′(−4, −2) is 4 units to the left of the y-axis and 2
units below the x-axis
...
These points are geometrically related to P as follows
...
P ″ is the reflection of P about the y-axis, or P ″ and P are symmetric about
the y-axis
...
The distance between two points in the xy-plane can be found by using the Pythagorean theorem
...
5) in the figure at the top of the following page is the length of line segment QR
...
5 − (−3) = 4
...
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GRE Math Review
Since line segment QR is the hypotenuse of the triangle, you can apply the Pythagorean theorem:
QR = Ί62 + 4
...
25 = 7
...
3
...
In the xy-plane, the graph of an equation in the variables x and y is the set of all
points whose ordered pairs (x, y) satisfy the equation
...
The x-intercepts of a graph are the x-coordinates of the points at which the graph
intersects the x-axis
...
Sometimes the terms x-intercept and
y-intercept refer to the actual intersection points
...
A horizontal
line has a slope of 0, since the rise is 0 for any two points on the line
...
The slope of a
vertical line is not defined, since the run is 0
...
Two lines are parallel if their slopes are equal
...
For example, the line with equation
1
y = 2x + 5 is perpendicular to the line with equation y = − x + 9
...
8
...
5) is
1
...
5
=
= 0
...
Unlawful distribution of this ebook is prohibited
...
5), so the y-intercept
of the line must be close to −1
...
To get the exact value of the y-intercept, substitute
the coordinates of any point on the line, say Q(−2, −3), into the equation y = 0
...
y = 0
...
75)(−2) + b
b = −3 + (0
...
5
Therefore, the equation of line QR is y = 0
...
5
...
More generally, you can find the x-intercept by setting y = 0
in an equation of the line and solving it for x as follows
...
75x − 1
...
5 = 0
...
5
x=
=2
0
...
Example 2
...
2: Consider the system of linear equations in two variables in section
2
...
y
4
x + 2y = 2
4x + 3y = 13
2
–2
O
2
4
x
(4, –1)
–2
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GRE Math Review
Example 2
...
3: Consider the following system of linear inequalities
...
Therefore, the graph of y ≤ x + 2 consists of the line y = x + 2 and the en3
3
3
tire region below it
...
Thus, the solution set of the system of
inequalities consists of all of the points that lie in the shaded region shown in the
figure below, which is the intersection of the two regions described
...
Another important symmetry is symmetry with respect to the line with equation
y = x
...
For any point with coordinates (a, b), the point with interchanged coordinates (b, a) is the reflection of (a, b) about the line y = x; that is, (a, b)
and (b, a) are symmetric about the line y = x
...
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Example 2
...
4: Consider the line whose equation is y = 2x + 5
...
Solving this equation for y yields y = x −
...
2
2
y
y = 2x + 5
10
y=x
y = 1x − 5
2
2
5
45°
−10
−5
5
10
x
−5
−10
1
5
The line y = x is a line of symmetry for the graphs of y = 2x + 5 and y = x −
...
The x-intercepts of the parabola are the solutions of the equation ax2 + bx + c = 0
...
If a is negative, the parabola opens downward and the
vertex is the highest point
...
In particular, the two x-intercepts are equidistant
from this line of symmetry
...
Unlawful distribution of this ebook is prohibited
...
8
...
y
y = x 2 – 2x – 3
6
4
2
−2
O
2
x
4
−2
−4
(1, − 4)
The graph indicates that the x-intercepts of the parabola are −1 and 3
...
The point (1, −4) is the vertex of the parabola, and the line
x = 1 is its line of symmetry
...
The graph of an equation of the form (x − a)2 + (y − b)2 = r2 is a circle with its
center at the point (a, b) and with radius r
...
8
...
The smaller circle has center (6, −5)
and radius 3, so its equation is (x − 6)2 + (y + 5)2 = 9
...
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...
9 Graphs of Functions
The coordinate plane can be used for graphing functions
...
In other words, you use the x-axis for the input and the y-axis for
the output
...
1
Example 2
...
1: Consider the linear function defined by f (x) = − x + 1
...
Example 2
...
2: Consider the quadratic function defined by g(x) = x2
...
y
y = x2
4
3
2
1
–3 –2 –1 O
1
x
2
y = –1 x + 1
2
Note that the graphs of f and g from the two examples above intersect at two points
...
We can find these points algebraically by setting
g(x) = f (x)
1
x2 = − x + 1
2
and solving for x, using the quadratic formula, as follows
...
78
and
x=
−1 − Ί17
4
Ϸ −1
...
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...
61
and
g
−1 − Ί17
4
=
4
2
−1 − Ί17
Ϸ 1
...
78, 0
...
28, 1
...
Example 2
...
3: Consider the absolute value function defined by h(x) = ⎪x⎪
...
5), h can be expressed as a piecewisedefined function:
h(x) =
x,
≥
Ά−x, xx< 0
0
The graph of this function is V-shaped and consists of two linear pieces, y = x and
y = −x, joined at the origin, as shown in the figure below
...
9
...
Also consider the negative
square-root function defined by k(x) = −Ίx for x ≥ 0, whose graph is the other half
of the parabola lying on its side—the dashed curve below the x-axis
...
y
y = x2
4
3
y= x
2
1
–3 –2 –1 O
–1
–2
1
2
3
4
x
y=– x
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GRE Math Review
The graphs of y = Ίx and y = −Ίx are halves of a parabola because they are reflections of the right and left halves, respectively, of the parabola y = x2 about the line
y = x
...
Also note that y = −Ίx is the reflection of y = Ίx about the x-axis
...
Example 2
...
5: Consider the functions defined by f (x) = ⎪x⎪ + 2 and g(x) = (x + 1)2
...
The graph of f is the graph of ⎪x⎪ shifted upward by 2 units, as shown in the
figure below
...
The graph of g is the graph of x2 shifted to the left by 1 unit, as shown in the
figure below
...
To double-check the direction of the shift, you can
plot some corresponding values of the original function and the shifted function
...
¼
¼
¼
¼
The graph of h(x) + c is the graph of h(x)
The graph of h(x) − c is the graph of h(x)
The graph of h(x + c) is the graph of h(x)
The graph of h(x − c) is the graph of h(x)
shifted upward by c units
...
shifted to the left by c units
...
x2
...
The graph of f is the graph of ⎪x⎪ shifted to the right by 1 unit and then stretched
vertically away from the x-axis by a factor of 2, as shown in the figure on the next
1
page
...
Example 2
...
6: Consider the functions defined by f (x) = 2⎪x − 1⎪ and g(x) = −
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GRE Math Review
The graph of g is the graph of x2 shrunk vertically by a factor of
1
and then reflected
4
in the x-axis, as shown in the figure below
...
¼
¼
The graph of ch(x) is the graph of h(x) stretched vertically by a factor of c if
c > 1
...
ALGEBRA EXERCISES
1
...
(a) The square of y is subtracted from 5, and the result is multiplied by 37
...
(c) The product of (x + 4) and y is added to 18
...
Simplify each of the following algebraic expressions
...
(a) What is the value of f (x) = 3x2 − 7x + 23 when x = −2 ?
(b) What is the value of h(x) = x3 − 2x2 + x − 2 when x = 2 ?
5
(c) What is the value of k(x) = x − 7 when x = 0 ?
3
4
...
(a) g(2)
(b) g(−2)
(c) g(2) − g(−2)
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5
...
(a) (n5)(n−3)
(e) (w5)−3
(b) (s7)(t7)
(f ) (50)(d3)
(c)
r12
r4
(g)
(d)
2a
b
(x10)( y−1)
(x−5)( y5)
(h)
3x 1 נ
y
y
5
2
5
6
...
(a) 5x − 7 = 28
(b) 12 − 5x = x + 30
(c) 5(x + 2) = 1 − 3x
(d) (x + 6)(2x − 1) = 0
(e) x2 + 5x − 14 = 0
(f ) x2 − x − 1 = 0
7
...
(a)
x + y = 24
x − y = 18
(b)
3x − y = −5
x + 2y = 3
(c)
15x − 18 − 2y = −3x + y
10x + 7y + 20 = 4x + 2
8
...
(a) −3x > 7 + x
(b) 25x + 16 ≥ 10 − x
(c) 16 + x > 8x − 12
9
...
The sum of the digits is 11
...
10
...
Kathleen’s weekly salary was increased by 8 percent to $237
...
What was
her weekly salary before the increase?
12
...
If 5 adult
tickets and 8 children’s tickets cost a total of $27, what is the cost of an adult
ticket?
13
...
Part of the money was invested in a money
market account that paid 10 percent simple annual interest, and the
remainder of the money was invested in a fund that paid 8 percent simple
annual interest
...
Two cars started from the same point and traveled on a straight course in
opposite directions for exactly 2 hours, at which time they were 208 miles
apart
...
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...
A group can charter a particular aircraft at a fixed total cost
...
(a) What is the fixed total cost to charter the aircraft?
(b) What is the cost per person if 40 people charter the aircraft?
16
...
The dealer
sold each chair for y dollars
...
(b) Write an algebraic expression for the profit per chair
...
In the coordinate system below, find the following
...
In the xy-plane, find the following
...
For the parabola y = x2 − 4x − 12 in the xy-plane, find the following
...
For the circle (x − 1)2 + ( y + 1)2 = 20 in the xy-plane, find the following
...
Unlawful distribution of this ebook is prohibited
...
For each of the following functions, give the domain and a description of the
graph y = f (x) in the xy-plane, including its shape, and the x- and y-intercepts
...
(a) 37(5 − y2), or 185 − 37y2
(3x)2
9x2
(b)
, or
7
7
(c) 18 + (x + 4)( y), or 18 + xy + 4y
2
...
(a) 49
(b) 0
(c) −7
4
...
(a) n2
(c) x + 4
(d) 6x2 + 13x−5
1
w15
(f ) d3
x15
(g) 6
y
(h) 9x2y3
(e)
(b) (st)7
(c) r8
32a5
(d) 5
b
6
...
8
...
9
8
x = 21
(a)
y=3
x = −1
(b)
y=2
1
(c)
2
y = −3
x=
7
4
3
(b) x ≥ −
13
(c) x < 4
(a) x < −
83
10
...
$220
12
...
$800 at 10% and $2,200 at 8%
14
...
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...
(a) $4,320
(b) $108
16
...
(a) (−2, 0)
P cy − x
x
=
=y−
c
c
c
(b) PQ = 6, QR = 7, PR = Ί85
(c) 13 + Ί85
(d) 21
18
...
(a) x = −2 and x = 6
(b) y = −12
(c) (2, −16)
20
...
(a) Domain: the set of all real numbers
...
(b) Domain: the set of all real numbers
...
9
(c) Domain: the set of all real numbers
...
(d) Domain: the set of numbers greater than or equal to −2
...
(e) Domain: the set of all real numbers
...
Every nonpositive number is an
x-intercept, and the y-intercept is 0
...
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...
GEOMETRY
The review of geometry begins with lines and angles and progresses to other plane
figures, such as polygons, triangles, quadrilaterals, and circles
...
Coordinate geometry is covered in the Algebra
section
...
1 Lines and Angles
Plane geometry is devoted primarily to the properties and relations of plane figures,
such as angles, triangles, other polygons, and circles
...
A point has no size and is the simplest geometric figure
...
A line is understood to be a
straight line that extends in both directions without ending
...
Given any two points on a line, a line segment is the part of the line that contains the two points and all the points between them
...
Line segments that have equal lengths are called congruent line segments
...
In the figure below, A, B, C, and D are points on line ℓ
...
Sometimes the notation AB denotes line segment AB, and sometimes
it denotes the length of line segment AB
...
According to the figure above, the lengths of line segments
AB, BC, and CD are 8, 6, and 6, respectively
...
Since C is halfway between B and D, point C is the midpoint of line segment BD
...
Each angle has a vertex at point P, which is the point of intersection of the two
lines
...
Angles APD and CPB are also opposite angles
...
Hence, opposite angles are congruent
...
Sometimes the angle symbol ∠ is used instead of the word “angle
...
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Two lines that intersect to form four congruent angles are called perpendicular
lines
...
An angle with a measure of 90Њ
is called a right angle
...
ℓ1
90°
90° 90°
90°
ℓ1 Ќ ℓ2
ℓ2
A common way to indicate that an angle is a right angle is to draw a small
square at the vertex of the angle, as shown below, where PON is a right angle
...
Two lines in the same plane that do not intersect are called parallel lines
...
The two
lines are intersected by a third line, ℓ3, forming eight angles
...
y°
x°
y°
ℓ1
x°
ℓ1 ℓ2
y°
x°
y°
ℓ2
x°
ℓ3
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3
...
Each side is joined to two other sides at its endpoints, and the endpoints are called
vertices
...
The figures
below are examples of such polygons
...
Note that a quadrilateral can be divided into
2 triangles, and a pentagon can be divided into 3 triangles, as shown below
...
Since the sum of
the measures of the interior angles of a triangle is 180Њ, it follows that the sum of
the measures of the interior angles of an n-sided polygon is (n − 2)(180Њ)
...
A polygon in which all sides are congruent and all interior angles are congruent
is called a regular polygon
...
Therefore, the measure
1,080Њ
= 135Њ
...
The area of a
polygon refers to the area of the region enclosed by the polygon
...
3
...
The measures of the interior
angles add up to 180Њ
...
For example, the sides of a triangle could not have
the lengths 4, 7, and 12 because 12 is greater than 4 + 7
...
¼
¼
A triangle with three congruent sides is called an equilateral triangle
...
A triangle with at least two congruent sides is called an isosceles triangle
...
Unlawful distribution of this ebook is prohibited
...
The converse is also true
...
Also, since
50 + 50 + x = 180, the measure of ∠ B is 80Њ
...
The side
opposite the right angle is called the hypotenuse; the other two sides are
called legs
...
The
Pythagorean theorem states that in a right triangle, the square of the length of the
hypotenuse is equal to the sum of the squares of the lengths of the legs
...
For example, if one leg of a right triangle has length 5 and the hypotenuse has length 8, then the length of the other side
can be determined as follows
...
2
...
One special right triangle is an isosceles right
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GRE Math Review
triangle
...
x
y2 = x2 + x2
y2 = 2x2
y = Ί2x
x
45°
45°
y
The other special right triangle is a 30Њ- 60Њ- 90Њ right triangle, which is half of
an equilateral triangle, as indicated below
...
By the Pythagorean theorem, the ratio of x to y is 1 to Ί3 because
x2 + y2 = (2x)2
x2 + y2 = 4x2
y2 = 4x2 − x2
y2 = 3x2
y = Ί3x
Hence, the ratio of the lengths of the three sides of such a triangle is 1 to Ί3 to 2
...
In the figure below, the base is denoted by b
and the corresponding height is denoted by h
...
The examples below show three different configurations of a
base and the corresponding height
...
2
Two triangles that have the same shape and size are called congruent triangles
...
The following three propositions can be used to determine whether two triangles
are congruent by comparing only some of their sides and angles
...
Unlawful distribution of this ebook is prohibited
...
If two sides and the included angle of one triangle are congruent to two sides
and the included angle of another triangle, then the triangles are congruent
...
¼
¼
Two triangles that have the same shape but not necessarily the same size are
called similar triangles
...
For example, all 30Њ- 60Њ- 90Њ right triangles, discussed above, are similar triangles, though they may differ in size
...
In other words, the order of the letters indicates
the correspondences
...
By cross mulDE EF DF
AB DE
tiplication, we can obtain other proportions, such as
...
4 Quadrilaterals
Every quadrilateral has four sides and four interior angles
...
The following are special quadrilaterals
...
Opposite sides of
a rectangle are parallel and congruent, and the two diagonals are also
congruent
...
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GRE Math Review
¼
A quadrilateral in which both pairs of opposite sides are parallel is called a
parallelogram
...
Q
x°
y°
R
PQ SR and PS QR
PQ = SR and PS = QR
P
¼
y°
x°
S
A quadrilateral in which two opposite sides are parallel is called a trapezoid
...
The height corresponding to the base is the
perpendicular line segment from any point of a base to the opposite side (or to an
extension of that side)
...
10
8
20
6
A = (6)(10) = 60
A = (20)(8) = 160
The area A of a trapezoid equals half the product of the sum of the lengths of
the two parallel sides b1 and b2 and the corresponding height h; that is,
1
A = (b1 + b2)(h)
2
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For example, for the trapezoid below with bases of length 10 and 18 and a
height of 7
...
5) = 105
2
10
7
...
5 Circles
Given a point O in a plane and a positive number r, the set of points in the plane
that are a distance of r units from O is called a circle
...
The diameter of the circle is twice the radius
...
Any line segment joining two points on the circle is called a chord
...
In the figure below, O is the center of the circle, r is the radius, PQ is a chord, and ST is a diameter
...
The ratio of the circumference C to the diameter d is the same for all circles and is denoted by the Greek letter p; that is,
C
=p
d
The value of p is approximately 3
...
7
C C
If r is the radius of a circle, then = = p, and so the circumference is related
d 2r
to the radius by the equation
C = 2pr
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GRE Math Review
For example, if a circle has a radius of 5
...
2) = (10
...
4)(3
...
7
...
Two points on a circle are always the
endpoints of two arcs
...
In the figure below, arc ABC is the shorter arc between A and C, and arc
ADC is the longer arc between A and C
...
The measure of an arc is the measure of its central angle, which is the angle
formed by two radii that connect the center of the circle to the two endpoints of the
arc
...
In the figure
above, the measure of arc ABC is 50Њ and the measure of arc ADC is 310Њ
...
The circumference of the circle above is 10p
...
14)
length of arc ABC =
(10p) =
Ϸ
Ϸ 4
...
For example, the area of the circle
above with radius 5 is p(5)2 = 25p
...
In
the circle above, the region bounded by arc ABC and the two dashed radii is a sector
with central angle 50Њ
...
Therefore, if S represents the area of the sector
with central angle 50Њ, then
S
50
=
25p 360
50
125p (125)(3
...
9
360
36
36
A tangent to a circle is a line that intersects the circle at exactly one point,
called the point of tangency, denoted by P in the figure at the top of the following
page
...
The converse is also true; that is, if a line is perpendicular to a radius at its endpoint on the circle, then the line is a tangent to the
circle at that endpoint
...
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...
Triangles RST and XYZ below
are inscribed in the circles with centers O and W, respectively
...
Conversely, if an inscribed triangle is a
right triangle, then one of its sides is a diameter of the circle
...
In the figure below, quadrilateral ABCD is circumscribed about the circle with center O
...
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3
...
In this section, we look at some properties of rectangular solids and right circular cylinders
...
Adjacent faces are perpendicular to each other
...
There are 12 edges and 8 vertices
...
h
ℓ
w
A rectangular solid with six square faces is called a cube, in which case ℓ = w = h
...
5, width 5, and height 10, then
its volume is
V = (8
...
5)(5) + (8
...
The latter line segment is called the axis of the cylinder
...
The right circular cylinder shown in the figure below has circular bases with
centers P and Q
...
The length of PQ is called the height of the cylinder
...
Unlawful distribution of this ebook is prohibited
...
5 and a base with radius 3,
then its volume is
V = p(3)2(6
...
5p
and its surface area is
A = (2)(p)(3)2 + (2)(p)(3)(6
...
Lines ℓ and m below are parallel
...
ℓ
57°
y°
x°
m
2
...
Find the values of x and y
...
x°
C
In the figure below, what is the relationship between x, y, and z?
x°
y°
z°
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GRE Math Review
4
...
6
...
8
...
What are the possible values of the perimeter?
Triangles PQR and XYZ are similar
...
10
P
40
In the figure below, AB = BC = CD
...
G
In rectangle ABCD below, AB = 5, AF = 7, and FD = 3
...
(a) Area of ABCD
(b) Area of triangle AEF
(c) Length of BD
(d) Perimeter of ABCD
E
B
A
F
C
D
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...
GRE Math Review
11
...
(a) Area of ABCD
(b) Perimeter of ABCD
(c) Length of diagonal BD
B
C
4
A
12
...
Find the following
...
The figure below shows two concentric circles, each with center O
...
(a) Circumference of the larger circle
(b) Area of the smaller circle
(c) Area of the shaded region
O
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GRE Math Review
14
...
(a) Surface area of the solid
(b) Length of diagonal AB
7
B
2
10
A
ANSWERS TO GEOMETRY EXERCISES
1
...
x = 70 and y = 125
3
...
1,440Њ
5
...
52 and 59
7
...
NO = 30 and OP = 10Ί34
9
...
(a) 50
(b) 17
...
(a) 48
(b) 24 + 4Ί5
(c) 2Ί29
12
...
(a) 24p
(b) 49p
(c) 95p
14
...
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...
DATA ANALYSIS
The goal of data analysis is to understand data well enough to describe past and
present trends, predict future events with some certainty, and thereby make better
decisions
...
4
...
Tables are
commonly used, and there are many graphical and numerical methods as well
...
In this
section, we review some common graphical methods for describing and summarizing data
...
In data analysis, variables also play an important role but with a
somewhat different meaning
...
For example,
both gender and age represent variables among people
...
The distribution of a variable, or
distribution of data, indicates the values of the variable and how frequently the values are observed in the data
...
A frequency distribution is
a table or graph that presents the categories or numerical values along with their
associated frequencies
...
Relative frequencies
may be expressed in terms of percents, fractions, or decimals
...
Example 4
...
1: A survey was taken to find the number of children in each of 25
families
...
1 2 0 4 1 3 3 1 2 0 4 5 2 3 2 3 2 4 1 2 3 0 2 3 1
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GRE Math Review
Here are the resulting frequency and relative frequency distributions of the data
...
If decimals were used instead
of percents, the total would be 1
...
Bar Graphs
A commonly used graphical display for representing frequencies, or counts, is a bar
graph, or bar chart
...
All of the bars are drawn with the same width, and the
bars can be presented either vertically or horizontally
...
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GRE Math Review
Example 4
...
2:
FALL 2009 ENROLLMENT AT FIVE COLLEGES
8,000
7,000
Enrollment
6,000
5,000
4,000
3,000
2,000
1,000
0
College A College B College C
College D College E
From the graph, we can conclude that the college with the greatest fall 2009 enrollment was College E, and the college with the least enrollment was College A
...
A segmented bar graph is used to show how different subgroups or subcategories contribute to an entire group or category
...
Each bar is divided
into segments that represent the different subcategories
...
Example 4
...
3:
FALL 2009 ENROLLMENT AT FIVE COLLEGES
8,000
Full-Time
Part-Time
7,000
Enrollment
6,000
5,000
4,000
3,000
2,000
1,000
0
College A College B College C
College D College E
Different values can be estimated from the segmented bar graph above
...
265
This ebook was issued to Diane Massey, order #11560922926
...
GRE Math Review
Bar graphs can also be used to compare different groups using the same categories
...
1
...
Also, the greatest decrease in the enrollment from fall 2009
to spring 2010 occurred at College B
...
Also, the categories sometimes are numerical in nature, such as years or
other time intervals
...
They illustrate how a whole is separated into parts
...
266
This ebook was issued to Diane Massey, order #11560922926
...
GRE Math Review
Example 4
...
5:
UNITED STATES PRODUCTION OF PHOTOGRAPHIC
EQUIPMENT AND SUPPLIES IN 1971
Total: $3,980 million
Sensitized Goods
47%
5%
Office
Copiers
25%
12%
7%
4%
Motion-Picture
Equipment
Still-Picture
Equipment
Prepared Photochemicals
Microfilm Equipment
The graph shows that of all United States production of photographic equipment
and supplies in 1971, Sensitized Goods was the category with the greatest dollar
value
...
Because the area of each sector is
proportional to the percent of the whole that the sector represents, the measure of the
central angle of a sector is proportional to the percent of 360 degrees that the sector
represents
...
2 degrees
...
To do this, divide the entire interval of values into smaller intervals of equal
length and then count the values that fall into each interval
...
The intervals and their frequencies (or relative frequencies) are often displayed in a histogram
...
Also, in a histogram, there are no regular spaces between the bars
...
Example 4
...
1 in section 4
...
Numerical variables with just a few values can also be displayed using histograms, where the frequency or relative frequency of each value is represented by a bar centered over the
value, as in the histogram in the following example
...
Unlawful distribution of this ebook is prohibited
...
1
...
1
...
Relative Frequency
Relative Frequency Distribution
30%
25%
20%
15%
10%
5%
0%
0
1
2
3
4
Number of Children
5
Histograms are useful for identifying the general shape of a distribution of data
...
From the histogram above, you can see
that the distribution is shaped like a mound with one peak; that is, the data are frequent in the middle and sparse at both ends
...
Because the bars all have
the same width, the area of each bar is proportional to the amount of data that the
bar represents
...
Finally, note that because each bar has a width of 1, the sum of the areas of the
bars equals the sum of the relative frequencies, which is 100% or 1, depending on
whether percents or decimals are used
...
5
...
These types of data are referred to as univariate, that is, data observed for
one variable
...
Such data are called bivariate data
...
If the variables were to be analyzed separately, each of the graphical
methods for univariate numerical data presented above could be applied
...
In a scatterplot, the values of one variable appear on the horizontal axis of a rectangular coordinate system and the values of the other variable appear on the vertical axis
...
A scatterplot makes it possible to observe an overall pattern, or trend, in the relationship between the two variables
...
In many cases, a line or a curve that best represents the trend is also displayed in the graph and is used to make predictions about
the population
...
Unlawful distribution of this ebook is prohibited
...
1
...
To measure the amount of training, the trainer developed a training index, measured in “units” and based on the intensity of each
bicyclist’s training
...
FINISHING TIMES AND TRAINING INDICES
FOR 50 BICYCLISTS IN A RACE
6
...
5
Finishing Time
(hours)
5
...
5
4
...
5
3
...
0
0
10
20
30
40 50 60 70
Training Index
(units)
80
90 100
In addition to the given trend line, you can see how scattered or close the data are to
the trend line; or to put it another way, you can see how well the trend line fits the
data
...
Several types of predictions can be based on the trend line
...
This value is obtained by noting that the vertical line at the training index of 70 units intersects the trend line
very close to 4 hours
...
This prediction is basically the ratio of the change in finishing time to
the change in training index, or the slope of the trend line
...
To estimate the slope, estimate the coordinates of any two points on the
line—for instance, the points at the extreme left and right ends of the line: (0, 5
...
2)
...
2 − 5
...
6
=
= −0
...
The slope can be interpreted as follows: the
finishing time is predicted to decrease 0
...
Unlawful distribution of this ebook is prohibited
...
Since we want to know how much the finishing time decreases
for an increase of 10 units, we multiply the rate by 10 to get 0
...
To compute the decrease in minutes per 10 units, we multiply 0
...
Based on the trend line, the bicyclist can expect to decrease
the finishing time by 16 minutes for every increase of 10 training index units
...
For
example, sales for a department store may be collected monthly or yearly
...
A time plot of a variable plots each observation corresponding to the time at which it was measured
...
Additionally, consecutive observations are connected by a line segment to emphasize increases and decreases over
time
...
1
...
One way to determine this is by noting that the slope of the line segment joining the values for 2008 and 2009 is greater
than the slopes of the line segments joining all other consecutive years, because the
time intervals are regular
...
4
...
These statistical measures are often grouped in three categories: measures of central
tendency, measures of position, and measures of dispersion
...
There are three common
measures of central tendency: (i) the arithmetic mean—usually called the average or
simply the mean, (ii) the median, and (iii) the mode
...
Unlawful distribution of this ebook is prohibited
...
Example 4
...
1: For the five numbers 6, 4, 7, 10, and 4, the mean is
6 + 4 + 7 + 10 + 4 31
=
= 6
...
Example 4
...
2: Consider the following list of 16 numbers
...
The mean of the numbers in the list can be computed as
1(2) + 2(4) + 1(5) + 6(7) + 2(8) + 4(9) 109
=
= 6
...
So the mean of the 16 numbers is the weighted mean of the values 2, 4, 5, 7, 8, and 9, where the respective weights are 1, 2, 1, 6, 2, and 4
...
The mean can be affected by just a few values that lie far above or below the rest
of the data, because these values contribute directly to the sum of the data and therefore to the mean
...
To calculate the median of n numbers, first order the numbers from least to greatest
...
If n is even, then there are two middle numbers, and the median is the average of
these two numbers
...
2
...
2
...
Note that if the number 10 in the list
is replaced by the number 24, the mean increases from 6
...
This example shows how the median is relatively
unaffected by an unusually large value
...
However, if the median is equal to one of the data values
and it is repeated in the list, then the numbers of data above and below the median
may be rather different
...
2
...
The mode of a list of numbers is the number that occurs most frequently in the
list
...
Unlawful distribution of this ebook is prohibited
...
2
...
A list of numbers may have more than one mode
...
Measures of Position
The three most basic positions, or locations, in a list of data ordered from least to
greatest are the beginning, the end, and the middle
...
Aside from these, the most
common measures of position are quartiles and percentiles
...
There
are three quartile numbers that divide the data into four roughly equal groups, and
there are 99 percentile numbers that divide the data into 100 roughly equal groups
...
The first quartile Q1, the second quartile Q2 (which is simply the median M),
and the third quartile Q3 divide a group of data into four roughly equal groups as
follows
...
Because the number of data in a list may not be
divisible by 4, there are various rules to determine the exact values of Q1 and Q3 and
some statisticians use different rules, but in all cases Q2 = M
...
Example 4
...
5: To find the quartiles for the list of 16 numbers 2, 4, 4, 5, 7, 7, 7, 7, 7,
7, 8, 8, 9, 9, 9, 9 (already listed in order), first divide the data into two groups of 8
numbers each
...
To find the other
quartiles, you can take each of the two smaller groups and find its median: the first
quartile is Q1 = 6 (the average of 5 and 7) and the third quartile is Q3 = 8
...
In example 4
...
5, note that the number 4 is in the lowest 25 percent of the distribution of data
...
We can say that 4 is below
the first quartile, that is, below Q1; we can also say that 4 is in the first quartile
...
Percentiles are mostly used for very large lists of numerical data ordered from
least to greatest
...
, P99 divide the data into 100 groups
...
Because the number of data in a list may not be divisible by 100, statisticians apply various rules to determine values of percentiles
...
Unlawful distribution of this ebook is prohibited
...
The most common statistics used as measures of dispersion are the range, the interquartile range,
and the standard deviation
...
The range of the numbers in a group of data is the difference between the greatest number G in the data and the least number L in the data, that is, G − L
...
The simplicity of the range is useful in that it reflects that maximum spread of the
data
...
Such data are
called outliers because they lie so far out that in most cases, they are ignored when
analyzing the data
...
A measure of dispersion that is not affected by outliers is the interquartile range
...
Thus, the interquartile range measures the spread of the middle half of the
data
...
2
...
5
...
5 − 6 = 2
...
One way to summarize a group of numerical data and to illustrate its center and
spread is to use the five numbers L, Q1, Q2, Q3, and G
...
Such plots are
called boxplots or box-and-whisker plots, because a box is used to identify each of
the two middle quartile groups of data, and “whiskers” extend outward from the
boxes to the least and greatest values
...
2
...
Q1
L
0
1
2
3
4
5
6
7
Q3 G
M
8
9
10
There are a few variations in the way boxplots are drawn—the position of the
ends of the boxes can vary slightly, and some boxplots identify outliers with certain
symbols—but all boxplots show the center of the data at the median and illustrate the
spread of the data in each of the four quartile groups
...
Example 4
...
7: Two large lists of numerical data, list I and list II, are summarized by
the following boxplots
...
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...
First, the median of list II, which is approximately 550, is greater than the median of
list I, which is approximately 450
...
For list I, these measures are
approximately 520 and 430, respectively; and for list II, they are approximately 500
and 220, respectively
...
Using the mean as the center of the
data, the standard deviation takes into account how much each value differs from the
mean and then takes a type of average of these differences
...
The standard deviation of a group of n numerical data is computed by (1) calculating the mean of the n values, (2) finding the difference between the mean and each
of the n values, (3) squaring each of the differences, (4) finding the average of the n
squared differences, and (5) taking the nonnegative square root of the average
squared difference
...
2
...
First, the mean of the data is 7, and the squared differences
from the mean are
(7 2)01 מ 7( ,2)01 מ 7( ,2)8 מ 7( ,2)7 מ 7( ,2)0 מ
or 49, 0, 1, 9, 9
...
6, and the
5
positive square root of 13
...
7
...
The latter term is qualified with the word “sample” and is computed by dividing the sum of
the squared differences by n − 1 instead of n
...
Sometimes the standard deviation is called the population standard deviation to help distinguish it
from the sample standard deviation
...
2
...
The ratings had a mean of 32
...
1 points
...
1 points
...
5 + d = 32
...
1 = 39
...
5 + 2d = 32
...
1) = 46
...
Since 48 is actually
15
...
5
Ϸ 2
...
Thus, to answer the question, we first found the difference from
mean is
7
...
Unlawful distribution of this ebook is prohibited
...
The number of standard
deviations that a rating of 30 is away from the mean is
30 − 32
...
5
=
Ϸ − 0
...
1
7
...
4 standard deviation below the
mean
...
5 −12
...
8
7
...
1
where the negative sign indicates that the rating is 1
...
To summarize:
¼
¼
¼
48 points is 15
...
2 standard
deviations above the mean
...
5 points below the mean, or approximately 0
...
20 points is 12
...
8 standard
deviations below the mean
...
5 points is 0 points from the mean, or 0 standard deviations from the
mean
...
2
...
The process of subtracting the mean from each value and then dividing the result by the standard deviation is
called standardization
...
Note that the standardized values 2
...
4, and −1
...
2
...
This is not surprising, based on the following fact about the standard deviation
...
Thus, when any group of data are standardized, most of the data are transformed
to an interval on the number line centered about 0 and extending from about −3 to 3
...
4
...
Uncertainty is addressed with the ideas and methods of probability theory
...
When a set of objects is small, it is easy to list the objects and count them one by
one
...
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...
Sets and Lists
The term set has been used informally in this review to mean a collection of objects
that have some property, whether it is the collection of all positive integers, all points
in a circular region, or all students in a school that have studied French
...
Some sets are finite, which means that
their members can be completely counted
...
Sets that are not finite are called infinite sets, such as the set of all integers
...
A set with
one or more members is called nonempty
...
For example, {2, 8} is a subset of
{0, 2, 4, 6, 8}
...
A list is like a finite set, having members that can all be listed, but with two differences
...
Thus, the terms “first element,” “second element,” etc
...
Also, elements can be repeated in a list and the repetitions matter
...
In contrast to a list, when the elements of a set are given, repetitions are not
counted as additional elements and the order of the elements does not matter
...
For
any finite set S, the number of elements of S is denoted by ⎪S⎪
...
2, −9, p, 0
...
Also, ⎪л⎪ = 0
...
If S and T are sets, then the intersection of S
and T is the set of all elements that are in both S and T and is denoted by S ∩ T
...
If sets S and T have no elements in common, they are called disjoint or mutually exclusive
...
In a Venn diagram, sets are represented by circular regions that overlap if they have elements in common but do not overlap if they are disjoint
...
Example 4
...
1: The sets A, B, and C are represented in the Venn diagram below,
where U represents a universal set
...
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...
The regions with horizontal
stripes represent the set B
...
The sets B and C are mutually exclusive, often written B ∩ C = л
...
This
principle relates the numbers of elements in the union and intersection of two finite
sets: The number of elements in the union of two sets equals the sum of their individual numbers of elements minus the number of elements in their intersection
...
3
...
For the union of B and C, we have
⎪B ʜ C⎪ = ⎪B⎪ + ⎪C⎪
because B ∩ C = л
...
Suppose also that there are k different possibilities for
the first choice and m different possibilities for the second choice
...
For example, suppose that a meal is to be ordered from a restaurant menu and
that the meal consists of one entree and one dessert
...
The multiplication principle applies in more complicated situations as well
...
Example 4
...
2: Suppose that a computer password consists of four characters such
that the first character is one of the 10 digits from 0 to 9 and each of the next 3 characters is any one of the uppercase letters from the 26 letters of the English alphabet
...
Thus, there are
10 possible choices for the first character in the password and 26 possible choices
for each of the next 3 characters in the password
...
Note that if repetitions of letters are not allowed in the password, then the
choices are not all independent, but a modification of the multiplication principle
can still be applied
...
Therefore, the number of possible
passwords is (10)(26)(25)(24) = 156,000
...
3
...
Using this fact and the multiplication principle, you can
conclude that if a coin is tossed 8 times, there are (2)(2)(2)(2)(2)(2)(2)(2) = 28 = 256
possible outcomes
...
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...
The following is a list of all the possible orders
in which the letters can be placed
...
Now suppose you want to determine the number of different ways the 4 letters A,
B, C, and D can be placed in order from 1st to 4th
...
To order the 4 letters, one of the 4 letters must be placed first, one of the remaining 3 letters must be placed second, one of the remaining 2 letters must be placed
third, and the last remaining letter must be placed fourth
...
More generally, suppose n objects are to be ordered from 1st to nth, and we want
to count the number of ways the objects can be ordered
...
Thus, applying the multiplication
principle, the number of ways to order the n objects is equal to the product
n(n − 1)(n − 2)⋅⋅⋅(3)(2)(1)
Each order is called a permutation, and the product above is called the number of
permutations of n objects
...
For example,
1! = 1
2! = (2)(1) = 2
3! = (3)(2)(1) = 6
4! = (4)(3)(2)(1) = 24
As a special definition, 0! = 1
...
Example 4
...
4: Suppose that 10 students are going on a bus trip, and each of the
students will be assigned to one of the 10 available seats
...
Reasoning
as in the preceding examples, you find that there are (5)(4)(3), or 60, ways to select
and order them
...
Then there are n
choices for the first object, n − 1 choices for the second object, n − 2 choices for the
third object, and so on, until there are n − k + 1 choices for the kth object
...
Unlawful distribution of this ebook is prohibited
...
It is useful to note that
(n − k)!
n(n − 1)(n − 2)⋅⋅⋅(n − k + 1) = n(n − 1)(n − 2)⋅⋅⋅(n − k + 1)
(n − k)!
n!
=
(n − k)!
This expression represents the number of permutations of n objects taken k at a
time, that is, the number of ways to select and order k objects out of n objects
...
3
...
According to the counting principle above, there
are (7)(6)(5)(4)(3) = 2,520 ways to do this
...
(7 − 5)!
2!
Combinations
Given the five letters A, B, C, D, and E, suppose that you want to determine the number of ways in which you can select 3 of the 5 letters, but unlike before, you do not
want to count different orders for the 3 letters
...
ABC
ABD ABE ACD ACE ADE BCD BCE BDE CDE
There are 10 ways of selecting the 3 letters without order
...
The number of ways to select 3 of the 5 letters without order, which is 10, multiplied by the number of ways to order the 3 letters, which is 3!, or 6, is equal to the
5!
number of ways to select 3 of the 5 letters and order them, which is = 60
...
(number of ways to select with order)
(number of ways to order)
5!
2!
5!
=
=
= 10
3!
3!2!
(number of ways to select without order) =
More generally, suppose that k objects will be chosen from a set of n objects, where
k ≤ n, but that the k objects will not be put in order
...
k!(n − k)!
Another way to refer to the number of combinations of n objects taken k at a time
is n choose k, and two notations commonly used to denote this number are nCk
n
and
...
Unlawful distribution of this ebook is prohibited
...
3
...
How many ways are there to do this?
Solution: Since the 3 students on the committee are not ordered, you can use the
formula for the combination of 9 objects taken 3 at a time, or “9 choose 3”:
9!
9!
(9)(8)(7)
=
=
= 84
3!(9 − 3)! 3!6! (3)(2)(1)
Using the terminology of sets, given a set S consisting of n elements, n choose k is
n!
simply the number of subsets of S that consist of k elements
...
¼ n choose 0 is n! = 1, which corresponds to the fact that there is only one
0!n!
subset of S with 0 elements, namely the empty set
...
Finally, note that n choose k is always equal to n choose n − k, because
n!
n!
n!
=
=
(n − k)!(n − (n − k))! (n − k)!k! k!(n − k)!
4
...
In this section we
review some of the terminology used in elementary probability theory
...
We assume that all of the possible outcomes of an experiment are known before the experiment is performed, but which
outcome will actually occur is unknown
...
For example, consider a cube with faces numbered 1 to 6, called a 6-sided
die
...
The sample space for this experiment is the set of numbers 1, 2, 3, 4, 5, and 6
...
The probability of an event is a number from 0 to 1, inclusive, that indicates the
likelihood that the event occurs when the experiment is performed
...
Example 4
...
1: Consider the following experiment
...
The instructor will shake the box for
a while and then, without looking, choose a piece of paper at random and read the
name
...
The assumption of random
selection means that each of the names is equally likely to be selected
...
Unlawful distribution of this ebook is prohibited
...
For any event E, the probability that E occurs, denoted by P(E), is de15
fined by the ratio
equal to
P(E) =
the number of names in the event E
15
7
...
So the probability of rolling a 4 is , and the probability of rolling an odd
6
3 1
number—rolling a 1, 3, or 5—can be calculated as =
...
¼
¼
¼
¼
¼
¼
If an event E is certain to occur, then P(E) = 1
...
If an event E is possible but not certain to occur, then 0 < P(E) < 1
...
If E is an event, then the probability of E is the sum of the probabilities of the
outcomes in E
...
If E and F are two events of an experiment, we consider two other events related
to E and F
...
The event that E or F, or both, occur, that is, all outcomes in the set E ʜ F
...
For
example, if a 6-sided die is rolled once, the event of rolling an odd number and the
event of rolling an even number are mutually exclusive
...
For events E and F, we have the following rules
...
If E and F are mutually exclusive, then P (both E and F occur) = 0, and
therefore, P (E or F, or both, occur) = P(E) + P(F)
...
If two events E and F are independent, then
P(both E and F occur) = P(E)P(F)
...
In this example, the experiment is actually
rolls is P(E)P(F) =
6 6
36
281
This ebook was issued to Diane Massey, order #11560922926
...
GRE Math Review
“rolling the die twice,” and each outcome is an ordered pair of results like “4
on the first roll and 1 on the second roll
...
Note that if P(E) ≠ 0 and P(F) ≠ 0, then events E and F cannot be both
mutually exclusive and independent
...
It is common to use the shorter notation “E and F” instead of “both E and F occur” and use “E or F” instead of “E or F, or both, occur
...
¼
¼
¼
P(E or F) = P(E) + P(F) − P(E and F)
P(E or F) = P(E) + P(F) if E and F are mutually exclusive
...
Example 4
...
2: If a fair 6-sided die is rolled once, let E be the event of rolling a 3 and
let F be the event of rolling an odd number
...
This
is because rolling a 3 makes certain that the event of rolling an odd number occurs
...
4
...
The probability of rolling
1
1
11
a 4 is
, so the probability of rolling a number that is not a 4 is 1 −
=
...
So by
7
...
4
...
23,
P(B) = 0
...
85
...
What are the probabilities P(A or B) and P(B or C)?
Solution: Since A and B are mutually exclusive,
P(A or B) = P(A) + P(B) = 0
...
40 = 0
...
Unlawful distribution of this ebook is prohibited
...
So,
P(B or C) = P(B) + P(C) − P(B and C) = P(B) + P(C) − P(B)P(C)
Therefore,
P(B or C) = 0
...
85 − (0
...
85) = 1
...
34
= 0
...
4
...
When you roll the die once, the 6 outcomes are not equally likely
...
Then
each of the probabilities of rolling a 2, 3, 4, or 5 is equal to p, and the probability of
rolling a 6 is 2p
...
7
Example 4
...
6: Suppose that you roll the weighted 6-sided die from example 4
...
5
twice
...
To calculate the probability that both occur, you must multiply the probabilities of the two independent
events
...
3
7
4
P(even) = P(2) + P(4) + P(6) =
7
P(odd) = P(1) + P(3) + P(5) =
Then, P(first roll is odd and second roll is even) = P(odd)P(even) =
3 4
12
77 = 49
...
The occurrence
of one event may affect the occurrence of a following event
...
Example 4
...
7: A box contains 5 orange disks, 4 red disks, and 1 blue disk
...
What is the
probability that the first disk you select will be red and the second disk you select
will be orange?
283
This ebook was issued to Diane Massey, order #11560922926
...
GRE Math Review
Solution: To solve, you need to calculate the following two probabilities and then
multiply them
¼
¼
The probability that the first disk selected from the box will be red
The probability that the second disk selected from the box will be orange,
given that the first disk selected from the box is red
4
2
=
...
Therefore, the probability that the second disk you select
5
will be orange, given that the first disk you selected is red, is
...
5 9
9
The probability that the first disk you select will be red is
4
...
Such variables are called random variables
...
Distributions of Data
Recall that relative frequency distributions given in a table or histogram are a common way to show how numerical data are distributed
...
The histogram in example 4
...
6 illustrates a small group of data, with only 6 possible values and only 25 data altogether
...
Example 4
...
1: The lifetimes of 800 electric devices were measured
...
, 1,091–1,100 hours
...
Relative Frequency Distribution for Lifetimes of 800 Electric Devices
600
700
m–d
800
M m
900
m+d
m + 2d
1,000
1,100
m + 3d
284
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GRE Math Review
Note that the tops of the bars of the histogram have a relatively smooth appearance and begin to look like a curve
...
Consequently, the distribution can be modeled by a smooth curve that is close to the tops of the bars
...
Recall from example 4
...
6 that the sum of the areas of the bars of a relative frequency histogram is 1
...
With this vertical scale adjustment, the
area under the curve that models the distribution is also 1
...
The purpose of the distribution curve is to give a good illustration of a large distribution of numerical data that doesn’t depend on specific classes
...
Before leaving this histogram, note that the mean m and the median M of the data
are marked on the horizontal axis
...
The standard deviation marks show how most of the data are within about 3 standard deviations
above or below the mean (that is, between the numbers m − 3d (not shown) and
m + 3d)
...
On the other hand, m takes into
account the exact value of each of the data, not just whether a value is high or low
...
That is why m is somewhat to the right of M
...
” To summarize, the median is the “halving point” and the mean is the “balance point
...
4
...
Given
a distribution of data, a variable, say X, may be used to represent a randomly chosen
value from the distribution
...
Example 4
...
2: In the data from example 4
...
1 consisting of numbers of children, let
X represent the number of children in a randomly chosen family among the 25 families
...
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...
Number of
Children
Frequency
0
1
2
3
4
5
3
5
7
6
3
1
Total
25
Since there are 6 families with 3 children and each of the 25 families is equally likely
6
to be chosen, the probability that a family with 3 children will be chosen is
...
24
...
24
...
This
indicates how probability is related to area in a histogram for a relative frequency
distribution
...
Because X = 4 and
X = 5 are mutually exclusive events, we can use the rules of probability from section
4
...
P(X > 3) = P(4) + P(5) =
3
1
+
= 0
...
04 = 0
...
0(3) + 1(5) + 2(7) + 3(6) + 4(3) + 5(1) 54
=
= 2
...
16) = P(0) + P(1) + P(2) =
3
5
7
15
+ +
=
= 0
...
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...
Probability Distribution of the Random Variable X
X
P(X)
0
1
2
3
4
5
0
...
20
0
...
24
0
...
04
Note that the probabilities are simply the relative frequencies of the 6 possible values expressed as decimals instead of percents
...
For a random variable that represents a randomly chosen value from a distribution
of data, the probability distribution of the random variable is the same as the relative
frequency distribution of the data
...
Also, all of the descriptive statistics—such as mean, median, and standard deviation—
that apply to the distribution of data also apply to the probability distribution
...
16, a median
of 2, and a standard deviation of about 1
...
These statistics are similarly defined for the random variable X above
...
16
...
So we would also say that the expected
value of X is 2
...
Note that the mean of X can be expressed in terms of probabilities
as follows
...
The preceding example involves a common type of random variable—one that
represents a randomly chosen value from a distribution of data
...
A random variable can be any quantity whose
value is the result of a random experiment
...
So any random experiment with numerical outcomes naturally has a random variable associated with it, as in the following example
...
Unlawful distribution of this ebook is prohibited
...
5
...
4
...
Then Y is a random variable with 6 possible values,
the numbers 1 through 6
...
Probability Distribution of the Random Variable Y
Y
1
2
3
4
5
6
P(Y)
1
7
1
7
1
7
1
7
1
7
2
7
Probability
3
7
Histogram for the Random Variable Y
2
7
1
7
0
1
2
3
4
Value of Y
5
6
The mean, or expected value, of Y can be computed as
P(1) + 2P(2) + 3P(3) + 4P(4) + 5P(5) + 6P(6) =
1 + 21 + 31 + 41 + 51 + 62
7
7
7
7
7
7
1 2 3 4 5 12
= + + + + +
7 7 7 7 7 7
27
=
Ϸ 3
...
A basic fact about probability from section 4
...
Also, the sum of the areas of the bars in a histogram for the probability
distribution of a random variable is 1
...
In the histogram for a random variable, the area of each bar is proportional to the
probability represented by the bar
...
4
...
Such a flat histogram indicates a uniform distribution, since the probability is distributed uniformly over all possible outcomes
...
Unlawful distribution of this ebook is prohibited
...
Approximately Normal Relative Frequency Distribution
m – 3d
m – 2d
m–d
m
m+d
m + 2d
m + 3d
Such data are said to be approximately normally distributed and have the following
properties
...
The data are grouped fairly symmetrically about the mean
...
Almost all of the data are within 2 standard deviations of the mean
...
If X is such a
random variable for the distribution above, we say that X is approximately normally
distributed
...
5
...
The region below such a curve represents a distribution,
called a continuous probability distribution
...
Normal Distribution
m – 3d
m – 2d
m–d
m
m+d
m + 2d
m + 3d
289
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GRE Math Review
Just as a data distribution has a mean and standard deviation, the normal probability
distribution has a mean and standard deviation
...
A normal distribution, though always shaped like a bell, can be centered around
any mean and can be spread out to a greater or lesser degree, depending on the standard deviation
...
From left to right, the means of the three distributions are −10, 1, and 20;
and the standard deviations are 5, 10, and 2
...
This is also true for a continuous probability
distribution: the area of the region under the curve is 1, and the areas of vertical slices
of the region—similar to the bars of a histogram—are equal to probabilities of a random variable associated with the distribution
...
The main difference
is that we seldom consider the event in which a continuous random variable is equal
to a single value like X = 3; rather, we consider events that are described by intervals
of values such as 1 < X < 3 and X > 10
...
(Consequently, the probability of an event such
as X = 3 would correspond to the area of a line segment, which is 0
...
5
...
5, 0
...
05, or 0
...
Unlawful distribution of this ebook is prohibited
...
So P(W > 5) =
...
Since about two-thirds of the area is within one standard deviation of
2
the mean, P(3 < W < 7) is approximately
...
Since the graph makes it fairly clear that the area of the region under the normal
curve to the left of −1 is much less than 5 percent of all of the area, the best of the
four estimates given for P(W < −1) is 0
...
The standard normal distribution is a normal distribution with a mean of 0 and
standard deviation equal to 1
...
2
...
Very precise values for probabilities associated with normal distributions can be
computed using calculators, computers, or statistical tables for the standard normal
distribution
...
683 and 0
...
Such calculations are beyond the scope of this review
...
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...
6 Data Interpretation Examples
Example 4
...
1:
DISTRIBUTION OF CUSTOMER COMPLAINTS
RECEIVED BY AIRLINE P, 2003 AND 2004
Category
2003
2004
Flight problem
20
...
1%
Baggage
18
...
8
Customer service
13
...
3
Oversales of seats
10
...
8
Refund problem
10
...
1
Fare
6
...
0
Reservation and ticketing
5
...
6
Tours
3
...
3
Smoking
3
...
9
Advertising
1
...
1
Credit
1
...
8
Special passenger accommodation
0
...
9
Other
6
...
3
Total
100
...
0%
Total number of complaints
22,998
13,278
(a) Approximately how many complaints concerning credit were received by Airline
P in 2003?
(b) By approximately what percent did the total number of complaints decrease
from 2003 to 2004?
(c) Based on the information in the table, which of the following statements are
true?
I
...
II
...
III
...
292
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GRE Math Review
Solutions:
(a) According to the table, in 2003, 1 percent of the total number of complaints
concerned credit
...
By converting 1 percent to its decimal equivalent,
you obtain that the number of complaints in 2003 is equal to (0
...
(b) The decrease in the total number of complaints from 2003 to 2004 was
9,720
(100%),
22,998 − 13,278, or 9,720
...
(c) Since 20
...
3 + 13
...
1 + 21
...
3 are both greater than 50,
statement I is true
...
Thus, statement II is false
...
The total number of
complaints in 2004 was much lower than the total number of complaints in
2003, and clearly 20 percent of 22,998 is greater than 22
...
So,
the number of flight problem complaints actually decreased from 2003 to 2004,
and statement III is false
...
6
...
Unlawful distribution of this ebook is prohibited
...
Therefore, the ratio is 47 to 12, or
approximately 4 to 1
...
25 times $3,980 million, or
$995 million
...
3x = 995 million
...
3
copiers produced in 1970 was approximately $765 million
...
6
...
0
5
...
0
4
...
0
Trend line
3
...
0
0
...
To measure the amount of training, the trainer developed a training
index, measured in “units” and based on the intensity of each bicyclist’s training
...
(a) How many of the 50 bicyclists had both a training index less than 50 units and a
finishing time less than 4
...
Unlawful distribution of this ebook is prohibited
...
5 hours is equal to the number of points on the graph
to the left of 50 and below 4
...
Since there are five data points that are both to
the left of 50 units and below 4
...
(b) The 10 lowest data points represent the 10 fastest bicyclists
...
Example 4
...
4:
TRAVELERS SURVEYED: 250
Africa
93
Asia
155
70
In a survey of 250 European travelers, 93 have traveled to Africa, 155 have traveled
to Asia, and of these two groups, 70 have traveled to both continents, as illustrated in
the Venn diagram above
...
(a) The set described here is represented by the part of the left circle that is not
shaded
...
(b) The set described here is represented by that part of the rectangle that is in at
least one of the two circles
...
But the 70 travelers who have traveled to both continents would be
counted twice in the sum 93 + 155
...
Unlawful distribution of this ebook is prohibited
...
Let N be the number of these travelers
...
The first part represents N travelers and
the second part represents 93 + 155 − 70 = 178 travelers (from question (b))
...
The daily temperatures, in degrees Fahrenheit, for 10 days in May were 61,
62, 65, 65, 65, 68, 74, 74, 75, and 77
...
(b) If each day had been 7 degrees warmer, what would have been the mean,
median, mode, and range of those 10 temperatures?
2
...
The standard deviation of these 9 numbers is approximately
equal to 10
...
(a) Find the mean, median, mode, range, and interquartile range of the 9
numbers
...
A group of 20 values has a mean of 85 and a median of 80
...
(a) What is the mean of the 50 values?
(b) What is the median of the 50 values?
4
...
X
Relative Frequency
0
1
2
3
4
0
...
33
0
...
06
0
...
Unlawful distribution of this ebook is prohibited
...
Eight hundred insects were weighed, and the resulting measurements, in
milligrams, are summarized in the boxplot below
...
In how many different ways can the letters in the word STUDY be ordered?
7
...
There are 120 different
ways in which they can sit together in a row of 5 seats, one person per seat
...
How many 3-digit positive integers are odd and do not contain the digit 5 ?
9
...
How many different sets of
4 lightbulbs could you remove?
10
...
Judges must award prizes for first, second,
and third places, with no ties
...
If an integer is randomly selected from all positive 2-digit integers, what is
the probability that the integer chosen has
(a) a 4 in the tens place?
(b) at least one 4 in the tens place or the units place?
(c) no 4 in either place?
12
...
(a) If you choose one part at random from the box, what is the probability
that it is not defective?
(b) If you choose two parts at random from the box, without replacement,
what is the probability that both are defective?
13
...
Sophomores
Males
Females
Juniors
Seniors
6
10
10
9
2
3
If one student is randomly selected from this group, find the probability that
the student chosen is
(a) not a junior
(b) a female or a sophomore
(c) a male sophomore or a female senior
297
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GRE Math Review
14
...
6, P(A) = 0
...
6, and P(C) = 0
...
The events A and B are mutually exclusive,
and the events C and D are independent
...
Lin and Mark each attempt independently to decode a message
...
80 and the probability that
Mark will decode the message is 0
...
2%
34%
34%
14%
m – 2d m – d
14%
m
2%
m + d m + 2d
The figure above shows a normal distribution with mean m and standard
deviation d, including approximate percents of the distribution
corresponding to the six regions shown
...
(a) Approximately how many of the adult penguins are between 65
centimeters and 75 centimeters tall?
(b) If an adult penguin is chosen at random from the population,
approximately what is the probability that the penguin’s height will be
less than 60 centimeters? Give your answer to the nearest 0
...
298
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GRE Math Review
17
...
DISTRIBUTION OF WORKFORCE BY OCCUPATIONAL CATEGORY
FOR REGION Y IN 2001 AND PROJECTED FOR 2015
Total workforce: 150 million
Total workforce: 175 million
Professional 2%
Professional 1%
Manufacturing
28%
15%
Service
18%
Clerical
20%
Service
Manufacturing
Agricultural
Clerical
10%
Managerial
8%
Sales
20%
18%
Sales
2001
7%
16%
24%
13%
Agricultural
Managerial
2015 (Projected)
(a) In 2001, how many categories each comprised more than 25 million
workers?
(b) What is the ratio of the number of workers in the Agricultural category in
2001 to the projected number of such workers in 2015 ?
(c) From 2001 to 2015, there is a projected increase in the number of
workers in which of the following categories?
I
...
Service
III
...
Unlawful distribution of this ebook is prohibited
...
A FAMILY’S EXPENDITURES AND SAVINGS
AS A PERCENT OF ITS GROSS ANNUAL INCOME*
33
30
2003
27
2004
24
Percent
21
18
15
12
9
6
M
s
ng
vi
Sa
es
iti
til
E
U
o
xp bile
en
se
s
s
to
ne
Au
lla
ce
m
ou
od
Fo
is
M
ag
or
tg
In
co
m
e
Ta
0
xe
e
s
Pr , In
op su
er ra
ty nc
Ta e,
xe
s
3
*2003 Gross annual income: $50,000
2004 Gross annual income: $45,000
(a) In 2003 the family used a total of 49 percent of its gross annual income
for two of the categories listed
...
In degrees Fahrenheit, the statistics are
(a) mean = 68
...
5, mode = 65, range = 16
(b) mean = 75
...
5, mode = 72, range = 16
2
...
7
9
standard deviation = 3
(c) interquartile range = 17, standard deviation Ϸ 10
...
(a) mean = 79
(b) The median cannot be determined from the information given
...
mean = 2
...
(a) range = 41, Q1 = 114, Q2 = 118, Q3 = 126, interquartile range = 12
(b) 40 measurements
300
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...
GRE Math Review
6
...
24
8
...
210
10
...
(a)
1
9
(b)
1
5
12
...
(a)
21
40
(b)
7
10
14
...
4
(b) 0
...
(a) 0
...
94
16
...
15
17
...
(a) Three
(b) 9 to 14, or
19
...
06
9
14
(c) I, II, and III
301
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...
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8
GRE ®
Practice Test 1
Your goals
for this
chapter
g Take the first full-length authentic GRE® revised
General Test under actual test time limits
...
g Use your results to identify your strengths and
weaknesses
...
Practice Test 1 begins on the following pages
...
The time allotted
for each section appears at the beginning of that section
...
Find a quiet place to work, and
set aside enough time to complete the test without being disturbed
...
Use your watch or a timer to keep track of the time limit for each section
...
However, when you take the real GRE revised
General Test on computer, you will click on your answer choices
...
If you plan to take the actual test on computer, you should type your responses
...
You will need a supply of lined paper for this task
...
As a result, the number of questions and time allowed per section are not the same as in
the computer-based test
...
Following this practice test you will find an answer key
...
You will also find explanations for each test question
...
Once you have worked your way through Practice Test 1, you will have a better idea
of how ready you are to take the actual GRE revised General Test
...
After you
have evaluated your test-taking performance, you can determine what type of additional preparation you might want to do for the test
...
ets
...
Once you
feel you have sufficiently prepared, you can take Practice Test 2 (Chapter 9)
...
Unlawful distribution of this ebook is prohibited
...
You will then have 30 minutes to plan and compose
a response according to the specific instructions
...
Make sure that you respond according to the specific instructions and support your position on the
issue with reasons and examples drawn from such areas as your reading, experience, observations,
and/or academic studies
...
Be sure to develop your position fully and organize
it coherently, but leave time to reread what you have written and make any revisions you think are
necessary
...
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...
Analytical Writing
Issue Topic
The best way to teach is to praise positive actions and ignore negative ones
...
In developing and supporting your position, describe specific circumstances in
which adopting the recommendation would or would not be advantageous and
explain how these examples shape your position
...
Unlawful distribution of this ebook is prohibited
...
You will then have 30 minutes to plan and compose a response in which
you evaluate the passage according to the specific instructions
...
Note that you are NOT being asked to present your own views on the subject
...
Trained GRE readers will evaluate your response for its overall quality, based on how well you:
b
b
b
b
b
Respond to the specific task instructions
Identify and analyze features of the argument relevant to the assigned task
Organize, develop, and express your ideas
Support your analysis with relevant reasons and/or examples
Control the elements of standard written English
Before you begin writing, you may want to think a few minutes about the argument passage and
the specific task instructions and then plan your response
...
306
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...
Section 2
...
Karp, an anthropologist
...
Field, a noted anthropologist, visited the island of Tertia and
concluded from his observations that children in Tertia were reared by an entire village
rather than by their own biological parents
...
This
research of mine proves that Dr
...
The
interview-centered method that my team of graduate students is currently using in Tertia will
establish a much more accurate understanding of child-rearing traditions there and in other
island cultures
...
307
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GRE Practice Test 1
NO TEST MATERIAL ON THIS PAGE
308
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Section 3
...
Questions 1 to 3 are based on the following reading passage
...
Nahuatl,
like Greek and German, is a language that allows the formation of extensive compounds
...
The tlamatinime (those who know) were able to use this rich stock of abstract terms
to express the nuances of their thought
...
Of these forms, the most characteristic in Nahuatl is the juxtaposition
of two words that, because they are synonyms, associated terms, or even contraries,
complement each other to evoke one single idea
...
For the following question, consider each of the choices separately and select all that
apply
...
Which of the following can be inferred from the passage regarding present-day
research relating to Nahuatl?
A
Ȟ Some record or evidence of the thought of the tlamatinime is available
...
C
Ȟ Researchers believe that in Nahuatl, abstract universal concepts are
always expressed metaphorically
...
Select the sentence in the passage in which the author introduces a specific
Nahuatl mode of expression that is not identified as being shared with certain
European languages
...
In the context in which it appears, “coinages” (line 9) most nearly means
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
adaptations
creations
idiosyncrasies
pronunciations
currencies
GO ON TO NEXT PAGE g
309
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...
GRE Practice Test 1
Question 4 is based on the following reading passage
...
As a way of reconciling these
two facts, scientists have hypothesized that nearly all of the oxygen being produced was
taken up by iron on Earth’s surface
...
New studies show that the amount of iron on Earth’s surface was not sufficient to
absorb anywhere near as much oxygen as was being produced
...
4
...
The first is a judgment made by the argument about a certain explanation;
the second is that explanation
...
The first sums up the argument’s position with regard to a certain
hypothesis; the second provides grounds for that position
...
For Questions 5 to 8, select one entry for each blank from the corresponding column
of choices
...
5
...
Blank (i)
A
ɕ anachronistic
B
ɕ accepted
C
ɕ exotic
6
...
A
ɕ imitation
B
ɕ reaction
C
ɕ dogmatism
D
ɕ invention
E
ɕ caution
310
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...
Section 3
...
The (i)__________ of Vladimir Nabokov as one of North America’s literary giants
has thrown the spotlight on his peripheral activities and has thus served to
(ii)__________ his efforts as an amateur entomologist
...
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
foreground
transcend
obscure
Mathematicians have a distinctive sense of beauty: they strive to present their
ideas and results in a clear and compelling fashion, dictated by __________ as
well as by logic
...
Unlawful distribution of this ebook is prohibited
...
Questions 9 to 12 are based on the following reading passage
...
A bird, by singing,
may forfeit time that could otherwise be spent on other important behaviors such as
foraging or resting
...
Although these types of cost may
be important, discussions of the cost of singing have generally focused on energy costs
...
To obtain empirical data regarding the energy costs of singing, Thomas examined
the relationship between song rate and overnight changes in body mass of male
nightingales
...
If singing has important energy costs, nightingales should lose more body mass
on nights when their song rate is high
...
These results suggest that there may be several costs of singing at night associated
with body reserves
...
The strategic regulation of evening body
reserves is also likely to incur additional costs, as nightingales must spend more time
foraging in order to build up larger body reserves
...
This metabolic cost may arise from
the muscular and neural activity involved in singing or from behaviors associated with
singing
...
Thomas’s data therefore show that whether or not singing per se has an
important metabolic cost, metabolic costs associated with singing can have an important measurable effect on a bird’s daily energy budget, at least in birds with high song
rates such as nightingales
...
The primary purpose of the passage is to
A
ɕ
B
ɕ
compare the different types of cost involved for certain birds in singing
question a hypothesis regarding the energy costs of singing for certain
birds
C
ɕ present evidence suggesting that singing has an important energy cost for
certain birds
D
ɕ discuss the benefits provided to an organism by a behavior that is costly in
energy
E
ɕ describe an experiment that supports an alternative model of how
birdsong functions
312
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...
Section 3
...
10
...
Select the sentence in the first or second paragraph that presents empirical
results in support of a hypothesis about the energy costs of singing
...
12
...
B
Ȟ They have generally received more attention from scientists
...
Question 13 is based on the following reading passage
...
These improvements have made the sport both safer and more enjoyable
for experienced climbers
...
13
...
Some mountain-climbing injuries are caused by unforeseeable weather
conditions
...
In the past ten years there have been improvements in mountain-climbing
techniques as well as in mountain-climbing equipment
...
GO ON TO NEXT PAGE g
313
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...
GRE Practice Test 1
For Questions 14 to 17, select one entry for each blank from the corresponding
column of choices
...
14
...
A
ɕ demur
B
ɕ schism
C
ɕ cooperation
D
ɕ compliance
E
ɕ shortsightedness
15
...
A
ɕ didactic
B
ɕ syntactical
C
ɕ irrelevant
D
ɕ sartorial
E
ɕ frivolous
16
...
Blank (i)
Blank (ii)
A
ɕ undemonstrative panache
B
ɕ unrestrained enthusiasm
C
ɕ unattractive gawkiness
D
ɕ
E
ɕ
F
ɕ
focus
overwhelm
deflect
17
...
He does not,
however, piously (ii)__________ political principles only to betray them in
practice
...
Blank (i)
Blank (ii)
Blank (iii)
A
ɕ quixotic
D
ɕ brandish
G
ɕ profound
B
ɕ self-righteous
E
ɕ flout
H
ɕ deeply felt moral
C
ɕ strategic
F
ɕ follow
I
ɕ thoroughgoing
cynicism
code
pragmatism
314
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...
Section 3
...
Questions 18 to 20 are based on the following reading passage
...
Recent years have witnessed the posthumous inflation of the role of the
hobbyist Alice Austen into that of a pioneering documentarian while dozens of notable
senior figures — Marion Palfi, whose photographs of civil-rights activities in the South
served as early evidence of the need for protective legislation, to name one — received
scant attention from scholars
...
18
...
19
...
Alice Austen has achieved greater notoriety than has Marion Palfi
primarily because the subjects that Austen photographed were more
familiar to her contemporaries
...
20
...
Unlawful distribution of this ebook is prohibited
...
21
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
innocuous
feasible
practicable
minimal
remedial
benign
22
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
antedated
cloaked
portrayed
preceded
renewed
represented
23
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
commonplace
disparate
divergent
fundamental
trite
trivial
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...
Section 3
...
During the opera’s most famous aria, the tempo chosen by the orchestra’s
conductor seemed __________, without necessary relation to what had gone
before
...
Because they had expected the spacecraft Voyager 2 to be able to gather data only
about the planets Jupiter and Saturn, scientists were __________ the wealth of
information it sent back from Neptune twelve years after leaving Earth
...
This is the end of Section 3
...
Unlawful distribution of this ebook is prohibited
...
1
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
2
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
3
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
synoptic
abridged
sensational
copious
lurid
understated
318
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...
Section 4
...
Always circumspect, she was reluctant to make judgments, but once arriving at a
conclusion, she was __________ in its defense
...
Unlawful distribution of this ebook is prohibited
...
Questions 5 and 6 are based on the following reading passage
...
However, phytoplankton flourish only in surface waters where iron levels are sufficiently high
...
While experiments subsequently confirmed that such a
procedure increases phytoplankton growth, field tests have shown that such growth
does not significantly lower atmospheric carbon dioxide
...
For the following question, consider each of the choices separately and select all that
apply
...
It can be inferred from the passage that Martin’s hypothesis includes which of the
following elements?
A
Ȟ A correct understanding of how phytoplankton photosynthesis utilizes
B
Ȟ
C
Ȟ
6
...
Unlawful distribution of this ebook is prohibited
...
Verbal Reasoning
Question 7 is based on the following reading passage
...
Clearly, Sparva’s less restrictive policy must be the explanation for the fact
that altogether insurers there pay for far more treatments after accidents than insurers
in other provinces, even though Sparva does not have the largest population
...
Which of the following, if true, most strengthens the argument?
A
ɕ
B
ɕ
C
ɕ
Car insurance costs more in Sparva than in any other province
...
Different insurance companies have different standards for determining
what constitutes emergency treatment
...
E
ɕ There are fewer traffic accidents annually in Sparva than in any of the
provinces of comparable or greater population
...
Unlawful distribution of this ebook is prohibited
...
Elements of the Philosophy of Newton, published by Voltaire in 1738, was an early
attempt to popularize the scientific ideas of Isaac Newton
...
Voltaire’s book commanded a wide audience, according to Feingold, because “he was neither a mathematician nor a physicist,
but a literary giant aloof from the academic disputes over Newtonian ideas
...
”
For the following question, consider each of the choices separately and select all that
apply
...
Which of the following statements about Voltaire’s Elements of the Philosophy of
Newton can be inferred from the passage?
A
Ȟ Voltaire’s literary stature helped secure a large audience for this attempt to
B
Ȟ
C
Ȟ
9
...
Voltaire’s status as a nonscientist was an advantage in this effort to bring
Newtonian science to the attention of the general public
...
Select the sentence that describes an allegory for Voltaire’s acquisition of
knowledge concerning Newton’s ideas
...
Fill all blanks in the way that best completes the text
...
Ironically, the writer so wary of (i)__________ was (ii)__________ with ink and
paper, his novel running to 2,500 shagreen-bound folio pages — a fortune in
stationery at the time
...
Unlawful distribution of this ebook is prohibited
...
Verbal Reasoning
11
...
Yet Mill had another reason for encouraging the
liberty of thought and discussion: the danger of partiality and incompleteness
...
Blank (i)
Blank (ii)
Blank (iii)
A
ɕ tendentiousness
D
ɕ
embrace only a
portion of the truth
G
ɕ erroneous
B
ɕ complacency
E
ɕ
change over
time
H
ɕ antithetical
C
ɕ fractiousness
F
ɕ
focus on matters
close at hand
I
ɕ immutable
12
...
A
ɕ prevent
B
ɕ defy
C
ɕ replicate
D
ɕ inform
E
ɕ use
13
...
A
ɕ enhance
B
ɕ replace
C
ɕ produce
D
ɕ surpass
E
ɕ reconcile
GO ON TO NEXT PAGE g
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...
GRE Practice Test 1
For each of Questions 14 to 16, select one answer choice unless otherwise instructed
...
It would be expected that a novel by a figure as prominent as W
...
B
...
Additionally, when the novel subtly engages the
issue of race, as DuBois’ The Quest of the Silver Fleece (1911) does, it would be a surprise not to encounter an abundance of scholarly work about that text
...
Perhaps DuBois the novelist must wait his turn behind
DuBois the philosopher, historian, and editor
...
Which of the following can be inferred from the passage regarding DuBois’ The
Quest of the Silver Fleece?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The lack of attention devoted to The Quest of the Silver Fleece can be
attributed to the fact that it was DuBois’ first novel
...
The Quest of the Silver Fleece has at least one feature that typically would
attract the attention of literary scholars
...
Much of the scholarly work that has focused on The Quest of the Silver
Fleece has been surprisingly critical of it
...
In the fourth sentence (“Perhaps DuBois
...
”), the author of the passage is
most likely suggesting that
A
ɕ
scholars will find that DuBois’ novels are more relevant to current
concerns than is his work as philosopher, historian, and editor
B
ɕ more scholarly attention will be paid to The Quest of the Silver Fleece than
to DuBois’ other novels
C
ɕ DuBois’ novels will come to overshadow his work as philosopher,
historian, and editor
D
ɕ
DuBois’ novels may eventually attract greater scholarly interest than they
have to date
E
ɕ it will be shown that DuBois’ work as philosopher, historian, and editor
had an important influence on his work as novelist
324
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...
Section 4
...
Which of the following best describes the central issue with which the passage is
concerned?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The perfunctoriness of much of the critical work devoted to DuBois’
novels
The nature of DuBois’ engagement with the issue of race in The Quest of
the Silver Fleece
Whether DuBois’ novels are of high quality and relevant to current
concerns
The relationship between DuBois the novelist and DuBois the philosopher,
historian, and editor
The degree of consideration that has been given to DuBois’ novels,
including The Quest of the Silver Fleece
For Questions 17 to 20, select one entry for each blank from the corresponding
column of choices
...
17
...
A
ɕ a paradigm
B
ɕ a misnomer
C
ɕ a profundity
D
ɕ an inaccuracy
E
ɕ an anomaly
18
...
Blank (i)
A
ɕ undermines
B
ɕ supports
C
ɕ underscores
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
diffuse
inimical
predominant
19
...
At a moment when so many
films strive to be as (ii)__________ as possible, it is gratifying to find one that is so
subtle and puzzling
...
Unlawful distribution of this ebook is prohibited
...
Wills argues that certain malarial parasites are especially (i)__________ because
they have more recently entered humans than other species and therefore have
had (ii)__________ time to evolve toward (iii)__________
...
Blank (i)
Blank (ii)
A
ɕ populous
B
ɕ malignant
C
ɕ threatened
D
ɕ ample
E
ɕ insufficient
F
ɕ adequate
Blank (iii)
G
ɕ virulence
H
ɕ benignity
I
ɕ variability
For each of Questions 21 to 25, select one answer choice unless otherwise instructed
...
Saturn’s giant moon Titan is the only planetary satellite with a significant atmosphere
and the only body in the solar system other than Earth that has a thick atmosphere
dominated by molecular nitrogen
...
The conditions for acquiring and
retaining a thick nitrogen atmosphere are now readily understood
...
The
higher temperatures of Jupiter’s moons, which were closer to the Sun, prevented them
from acquiring such an atmosphere
...
According to the passage, Titan differs atmospherically from Ganymede and
Callisto because of a difference in
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
rate of heat loss
proximity to the Sun
availability of methane and ammonia
distance from its planet
size
326
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...
Section 4
...
Observations of the Arctic reveal that the Arctic Ocean is covered by less ice each summer than the previous summer
...
This occurrence would in
itself have little or no effect on global sea levels, since the melting of ice floating in
water does not affect the water level
...
22
...
Unlawful distribution of this ebook is prohibited
...
line
5
10
In a recent study, David Cressy examines two central questions concerning English
immigration to New England in the 1630s: what kinds of people immigrated and why?
Using contemporary literary evidence, shipping lists, and customs records, Cressy finds
that most adult immigrants were skilled in farming or crafts, were literate, and were
organized in families
...
With respect to their reasons for immigrating, Cressy does not deny the frequently
noted fact that some of the immigrants of the 1630s, most notably the organizers and
clergy, advanced religious explanations for departure, but he finds that such explanations usually assumed primacy only in retrospect
...
For the following question, consider each of the choices separately and select all that
apply
...
The passage indicates that Cressy would agree with which of the following
statements about the organizers among the English immigrants to New England
in the 1630s?
A
Ȟ Some of them offered a religious explanation for their immigration
...
C
Ȟ They were more likely than the average immigrant to be motivated by
material considerations
...
Select the sentence that provides Cressy’s opinion about what motivated English
immigrants to go to New England in the 1630s
...
In the passage, the author is primarily concerned with
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
summarizing the findings of an investigation
analyzing a method of argument
evaluating a point of view
hypothesizing about a set of circumstances
establishing categories
STOP
...
328
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...
Section 5
...
Notes: All numbers used are real numbers
...
Geometric figures, such as lines, circles, triangles, and quadrilaterals, are not
necessarily drawn to scale
...
You
should assume, however, that lines shown as straight are actually straight,
points on a line are in the order shown, and more generally, all geometric
objects are in the relative positions shown
...
Coordinate systems, such as xy-planes and number lines, are drawn to scale;
therefore, you can read, estimate, or compare quantities in such figures by
sight or by measurement
...
For each of Questions 1 to 9, compare Quantity A and Quantity B, using
additional information centered above the two quantities if such information is
given
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
A symbol that appears more than once in a question has the same meaning
throughout the question
...
Unlawful distribution of this ebook is prohibited
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity A
1
...
5
Quantity A
2
...
Quantity B
x+y+z
3
y
x
y
50°
Quantity A
4
...
Unlawful distribution of this ebook is prohibited
...
Quantitative Reasoning
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
0
5
...
Quantity A
6
...
Quantity A
7
...
Quantity A
8
...
Quantity A
9
...
Unlawful distribution of this ebook is prohibited
...
Unless otherwise directed,
select a single answer choice
...
Numeric Entry Questions
Enter your answer in the answer box(es) below the question
...
If a question asks for a fraction, there will be two boxes—one for the
numerator and one for the denominator
...
5 and 2
...
Fractions do not need to be reduced to lowest terms
...
10
...
1
3
to is equal to the ratio of
3
8
1 to 8
8 to 1
8 to 3
8 to 9
9 to 8
A reading list for a humanities course consists of 10 books, of which 4 are
biographies and the rest are novels
...
How
many selections of 4 books satisfy the requirements?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
90
115
130
144
195
For the following question, enter your answer in the box
...
In a graduating class of 236 students, 142 took algebra and 121 took chemistry
...
Unlawful distribution of this ebook is prohibited
...
Quantitative Reasoning
s°
t°
13
...
m
30
60
75
80
105
If 2x = 3y = 4z = 20, then 12xyz =
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
16,000
8,000
4,000
800
10
For the following question, select all the answer choices that apply
...
The total amount that Mary paid for a book was equal to the price of the book
plus a sales tax that was 4 percent of the price of the book
...
00
...
A
Ǣ
B
Ǣ
C
Ǣ
16
...
50
...
90
...
45
...
Unlawful distribution of this ebook is prohibited
...
VARIATION IN THE AMOUNT OF CAFFEINE IN COMMON BEVERAGES AND DRUGS*
Amount of Caffeine (milligrams)
0
25
50 75 100 125 150 175 200
Decaffeinated coffee
Percolated coffee
Coffee
Drip-brewed coffee
Instant coffee
Brewed tea
Other
beverages
Instant tea
Cocoa
Caffeinated soft drinks
Weight-loss drugs,
diuretics, and stimulants
Drugs
Pain relievers
Cold/allergy remedies
Source: Food and Drug Administration
*Based on 5-ounce cups of coffee, tea, and cocoa; 12-ounce cups of soft drinks;
and single doses of drugs
...
The least amount of caffeine in a 5-ounce cup of drip-brewed coffee exceeds
the greatest amount of caffeine in a 5-ounce cup of cocoa by approximately
how many milligrams?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
160
80
60
40
20
For the following question, enter your answer in the box
...
For how many of the 11 categories of beverages and drugs listed in the graph
can the amount of caffeine in the given serving size be less than 50 milligrams?
categories
19
...
Unlawful distribution of this ebook is prohibited
...
Quantitative Reasoning
20
...
200
Running
Walking
100
0
0
1
2 3 4 5 6 7 8
Speed (miles per hour)
9
If s is a speed, in miles per hour, at which the energy used per meter during
running is twice the energy used per meter during walking, then, according
to the graph above, s is between
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
22
...
5 and 3
...
0 and 3
...
5 and 4
...
0 and 4
...
5 and 5
...
Unlawful distribution of this ebook is prohibited
...
B
A
D
C
The length of AB is 10Ί3
...
Which of the following statements individually provide(s) sufficient additional
information to determine the area of triangle ABC above?
Indicate all such statements
...
ABD is an isosceles triangle
...
The length of BC is 10
...
For the following question, enter your answer in the box
...
, an,
...
In the sequence above, each term after the first term is equal to the preceding
term plus the constant c
...
A desert outpost has a water supply that is sufficient to last 21 days for 15
people
...
0
32
...
0
37
...
0
STOP
...
336
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...
Section 6
...
Notes: All numbers used are real numbers
...
Geometric figures, such as lines, circles, triangles, and quadrilaterals, are not
necessarily drawn to scale
...
You
should assume, however, that lines shown as straight are actually straight,
points on a line are in the order shown, and more generally, all geometric
objects are in the relative positions shown
...
Coordinate systems, such as xy-planes and number lines, are drawn to scale;
therefore, you can read, estimate, or compare quantities in such figures by
sight or by measurement
...
For each of Questions 1 to 9, compare Quantity A and Quantity B, using
additional information centered above the two quantities if such information is
given
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
A symbol that appears more than once in a question has the same meaning
throughout the question
...
Unlawful distribution of this ebook is prohibited
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
93 peso
Kenya
32
...
Quantity B
The dollar value of 1
Argentine peso according
to the table above
The dollar value of 1
Kenyan shilling according
to the table above
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
k is a digit in the decimal 1
...
3k5 is less
than 1
...
Quantity A
2
...
Quantity A
3
...
Quantity B
s2
10
t2
338
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...
Section 6
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity B
Quantity A
5
...
Quantity A
6
...
Quantity A
7
...
x
Quantity B
−
1
2
In a set of 24 positive integers, 12 of the integers are
less than 50
...
Quantity A
9
...
Unlawful distribution of this ebook is prohibited
...
Unless otherwise directed,
select a single answer choice
...
Numeric Entry Questions
Enter your answer in the answer box(es) below the question
...
If a question asks for a fraction, there will be two boxes—one for the
numerator and one for the denominator
...
5 and 2
...
Fractions do not need to be reduced to lowest terms
...
10
...
00 per yard and can be
purchased only by the full yard
...
6 yards and all of the fabric is purchased as a single length,
what is the total cost of the fabric that needs to be purchased for the 3
curtains?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
$40
...
40
$24
...
00
$12
...
11
...
Which of the following statements individually provide(s) sufficient additional
information to determine whether the slope of line k is negative?
Indicate all such statements
...
The product of the x-intercept and the y-intercept of line k is positive
...
340
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...
Section 6
...
02מt + 150
The expressions in the table above give the distance from Centerville to
each of two trains t hours after 12:00 noon
...
01מt + 115
1:30
3:30
5:10
8:50
11:30
The company at which Mark is employed has 80 employees, each of whom
has a different salary
...
If the company were to hire 8 new
employees at salaries that are less than the lowest of the 80 salaries, what
would Mark’s salary be with respect to the quartiles of the 88 salaries at the
company, assuming no other changes in the salaries?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The fourth-highest salary in the first quartile
The highest salary in the first quartile
The second-lowest salary in the second quartile
The third-lowest salary in the second quartile
The fifth-lowest salary in the second quartile
For the following question, enter your answer in the box
...
In the xy-plane, the point with coordinates (−6, −7) is the center of circle C
...
If m is the radius of C and m is an
integer, what is the value of m ?
m=
15
...
m is a positive number
...
m is an odd integer
...
GO ON TO THE NEXT PAGE b
341
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...
GRE Practice Test 1
For the following question, select all the answer choices that apply
...
The integer v is greater than 1
...
A
Ǣ
B
Ǣ
C
Ǣ
81v
25v+10Ίv+1
4v2+4Ίv+1
Questions 17 to 20 are based on the following data
...
Note: Total stopping distance is the sum of the distance traveled during reaction time
and the distance traveled after brakes have been applied
...
The speed, in miles per hour, at which the car travels a distance of 52 feet
during reaction time is closest to which of the following?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
43
47
51
55
59
342
This ebook was issued to Diane Massey, order #11560922926
...
Section 6
...
Approximately what is the total stopping distance, in feet, if the car is
traveling at a speed of 40 miles per hour when the driver is signaled to
stop?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
19
...
90
The total stopping distance for the car traveling at 60 miles per hour is
approximately what percent greater than the total stopping distance for the
car traveling at 50 miles per hour?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
21
...
130
26
28
36
56
58
If 0 < a < 1 < b, which of the following is true about the reciprocals of a
and b ?
1
A
ɕ 1<1
B
ɕ
1
1
<1<
a
b
C
ɕ
1 1
< <1
a b
D
ɕ
1
1
<1<
b
a
E
ɕ
1 1
< <1
b a
GO ON TO THE NEXT PAGE b
343
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...
GRE Practice Test 1
O
23
...
If each circle
has radius r, what is the area of the shaded region?
A
ɕ
B
ɕ
Ί2
2
Ί3
2
r2
r2
C
ɕ
Ί2r2
D
ɕ
Ί3r2
E
ɕ
2Ί3r2
For the following question, enter your answer in the boxes
...
Of the 20 lightbulbs in a box, 2 are defective
...
What is the probability
that neither of the lightbulbs selected will be defective?
Give your answer as a fraction
...
What is the perimeter, in meters, of a rectangular playground 24 meters wide
that has the same area as a rectangular playground 64 meters long and 48
meters wide?
A
ɕ 112
B
ɕ
C
ɕ
D
ɕ
E
ɕ
152
224
256
304
STOP
...
344
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...
Evaluating Your Performance
Evaluating Your Performance
Now that you have completed Practice Test 1, it is time to evaluate your performance
...
Scored sample essay
responses and rater commentary are presented starting on page 353 for the one Issue
topic and one Argument topic presented in the Analytical Writing sections of Practice
Test 1
...
To better understand the analytical writing abilities characteristic of particular
score levels, you should review the score level descriptions on page 41
...
An
answer key with the correct answers to the questions in the Verbal Reasoning and
Quantitative Reasoning sections in this practice test begins on page 347
...
Partially correct answers should be treated as incorrect
...
The answer key contains additional information to help you evaluate your performance
...
The P+ is the percent
of a group of actual GRE takers who were administered that same question at a previous test administration and who answered it correctly
...
The higher the P+, the easier the test question
...
For example, if the P+ for a question is 89, that
means that 89 percent of GRE test takers who received this question answered it correctly
...
A question with a P+ of 89
may be interpreted as a relatively easy question, and a question with a P+ of 14 may be
interpreted as a difficult question
...
Add the number of correct answers in Sections 5 and 6 to obtain your raw
Quantitative Reasoning score
...
Find the scores on the 130–170 score scales
that correspond to your Verbal Reasoning and Quantitative Reasoning raw
scores
...
345
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...
GRE Practice Test 1
Once you determine your scaled scores, you will need to evaluate your performance
...
ets
...
A percentile rank for a score indicates the percentage of examinees
who took that test and received a lower score
...
For each score you
earned on Practice Test 1, note the percent of GRE test takers who earned lower scores
...
346
This ebook was issued to Diane Massey, order #11560922926
...
Evaluating Your Performance
Answer Key
Section 3
...
AND
Choice B: For at least some Nahuatl expressions, researchers are able to
trace their derivation from another ancient American language
...
Choice B: creations
Choice D: The first sums up the argument’s position with regard to a certain
hypothesis; the second provides grounds for that position
...
Choice B: They have generally received more attention from scientists
...
Choice B: schism
Choice D: sartorial
Choice A: undemonstrative panache; Choice F: deflect
Choice C: strategic; Choice D: brandish; Choice H: deeply felt moral code
Choice C: provide an example of a way in which scholarship on the history
of women in photography has been unsatisfactory
Choice C: In addition to providing a record of certain historical events,
Marion Palfi’s photographs played a role in subsequent events
...
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...
Verbal Reasoning
Question
Number P+
1
2
3
4
5
70
80
49
68
26
6
7
26
31
8
23
9
82
10
11
60
37
12
13
14
35
43
54
15
68
16
49
17
18
19
20
21
22
50
19
54
23
53
59
Correct Answer
Choice B: fleeting AND Choice C: momentary
Choice A: diversity AND Choice C: variety
Choice A: synoptic AND Choice B: abridged
Choice B: intransigent AND Choice F: resolute
Choice A: A correct understanding of how phytoplankton photosynthesis
utilizes carbon dioxide
AND
Choice B: A correct prediction about how the addition of iron to iron-poor
waters would affect phytoplankton growth
AND
Choice C: An incorrect prediction about how phytoplankton growth would
affect the concentration of atmospheric carbon dioxide
Choice A: help explain why Martin’s hypothesis is incorrect
Choice E: There are fewer traffic accidents annually in Sparva than in any of
the provinces of comparable or greater population
...
AND
Choice B: Voltaire’s status as a nonscientist was an advantage in this effort
to bring Newtonian science to the attention of the general public
...
Sentence 2: In the book’s frontispiece, Voltaire is seen writing at his desk,
and over him a shaft of light from heaven, the light of truth, passes through
Newton to Voltaire’s collaborator Madame du Châtelet; she reflects that light
onto the inspired Voltaire
...
Choice D: DuBois’ novels may eventually attract greater scholarly interest
than they have to date
Choice E: The degree of consideration that has been given to DuBois’ novels,
including The Quest of the Silver Fleece
Choice E: an anomaly
Choice A: undermines; Choice E: inimical
Choice A: peculiarity; Choice E: assertive
Choice B: malignant; Choice E: insufficient; Choice H: benignity
Choice B: proximity to the Sun
Choice C: such a warm Arctic Ocean would trigger the melting of massive
land-based glaciers in the Arctic
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Evaluating Your Performance
Answer Key
Question
Number P+
23
24
33
94
25
64
Correct Answer
Choice A: Some of them offered a religious explanation for their immigration
...
Choice A: summarizing the findings of an investigation
Section 5
...
Choice C: The two quantities are equal
...
Choice A: Quantity A is greater
...
Choice A: Quantity A is greater
...
Choice D: The relationship cannot be determined from the information
given
...
Choice D: 8 to 9
Choice B: 115
121
Choice C: 75
Choice C: 4,000
Choice C: The sales tax was less than $0
...
Choice B: Two
Choice D: 40
9
Choice B: 190
Choice B: Decaffeinated, instant, drip-brewed, percolated
Choice A: 2
...
0
Choice D: 224
Choice A: DBC is an equilateral triangle
...
18
Choice C: 35
...
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...
Quantitative Reasoning
Question
Number P+
1
2
66
73
3
4
5
6
7
52
46
48
33
40
8
9
26
31
10
11
67
10
12
13
14
15
16
49
27
38
40
21
Correct Answer
Choice A: Quantity A is greater
...
Choice A: Quantity A is greater
...
Choice B: Quantity B is greater
...
Choice D: The relationship cannot be determined from the information
given
...
Choice D: The relationship cannot be determined from the information
given
...
00
Choice B: 3:30
Choice E: The fifth-lowest salary in the second quartile
13
Choice E: m is an even integer
...
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...
Unlawful distribution of this ebook is prohibited
...
Unlawful distribution of this ebook is prohibited
...
Write a response in which you discuss the extent to which you agree or disagree with the
recommendation and explain your reasoning for the position you take
...
Score 6 Response*
The recommendation presents a view that I would agree is successful most of the
time, but one that I cannot fully support due to the “all or nothing” impression it gives
...
It is human nature that we all want to be accepted
and achieve on some level, and when people in authority provide feedback that we
have done something well, the drive to repeat the action that was praised is bound to
be particularly strong
...
For example, if an
educator is attempting to teach students proper classroom etiquette, it would be
appropriate to openly praise a student who raises his or her hand when wishing to
speak or address the class
...
In fact, the decision to ignore students who are exhibiting inappropriate
behaviors of this type could work very well in this situation, as the stakes are not very
high and the intended outcome can likely be achieved by such a method
...
As we will discuss
below, ignoring a student who hits another student, or engages in more serious
misbehaviors, would not be effective or prudent
...
, if
any
...
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...
Take for instance a student who is misbehaving just by chatting with a fellow classmate
...
Ignoring the student might, in fact, be the best solution
...
To ignore these negative actions would
be absurd and negligent
...
In a more serious
situation, addressing the negative actions quickly and properly could stop the problem
it in its tracks
...
I do, however, greatly support the idea that the central focus of teaching should be
to build on and encourage positive actions
...
Perhaps a better
way to phrase this statement would be to say, “The best way to teach is to praise
positive actions and ignore negative ones that are not debilitating to class efficiency
or the safety of any individual”
...
Data proves that positive support
can substantially increase motivation and desire in students and contribute to positive
achievements
...
It needs to be stressed, however, that this tool is only effective at certain levels of
misbehavior
...
It is
likely to be very successful, however, when the drive behind the misbehavior is simple
attention seeking
...
Should the student choose this path, then
the ignoring has worked and when the positive behavior is exhibited, then the teacher
can utilize the first part of the theory and support or praise this behavior
...
If the student does not choose this path and instead
elects to raise the actions to a higher level that presents a more serious issue, then
ignorance alone cannot work and other methods must be employed
...
Reader Commentary
This response receives a 6 for its well-articulated, insightful analysis of the issue
...
The writer turns this idea into an insightful position by
providing examples and evidence to fully and persuasively support its nuanced argument
...
At the same time, it also highlights the recommendation’s limits using additional specific, detailed examples
...
Thus, the writer recognizes that the prompt’s
claim, as well as his/her own, is inevitably dependent on the specific context for its suc354
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Analytical Writing Sample Responses
cess or failure
...
This sentence demonstrates the level of language facility seen throughout the response: “It is
human nature that we all want to be accepted and achieve on some level, and when
people in authority provide feedback that we have done something well, the drive to
repeat the action that was praised is bound to be particularly strong
...
Children should be rewarded when they perform well;
however, they should not be ignored for performing sub-optimally
...
Utilizing positive reinforcements, such as tangible rewards, can be a good method
to teach children
...
For example, a student who completes
an assignment on time and does a good job is likely to want to do a good job on the
next assignment if he gets positive feedback
...
Conversely, children should not be ignored for negative actions
...
Ignoring something doesn’t make it go
away, actions and consequences do
...
However, the
teacher’s actions need be appropriate
...
For instance, children who leave their
seat often, stare in to space, or call out of turn may be initially viewed as having poor
behavior
...
If the child does have an attentional problem, then
the teacher can work with a related service, such as occupational therapy, to alter the
classroom environment in order to cater to the needs of the child
...
If the child becomes more attentive in class then the
teacher was able to assist the child without scorning them or ignoring them
...
On the other hand, if the child is tested, and does not have any areas of concern
that may be impacting the educational performance in the classroom, then the
negative behavior may strictly be due to defiance
...
As a result, a child who is being
disruptive to the learning process of the class should be set apart from the class so
that they do not receive the positive reinforcement of peer attention
...
It is better to address the child privately
and make sure the child is aware of the negative actions
...
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...
Perhaps the child’s parents are in the middle of a divorce and the
child is outwardly expressing his frustration in the classroom
...
Whatever the reason behind the behavior, the key factor is that the teacher
works with the child to try and identify it
...
Likewise, rather than punnishing and defeating the child, the teacher
is working with and empowering the child; a much more positive outcome to the
situation
...
In
this case the writer argues that teachers need to modify their approach based on context and observation, meaning that a blanket approach cannot be successful
...
Note that the task instructions ask writers to discuss circumstances in which
adopting the recommendation might or might not prove advantageous, and this
response does that quite clearly
...
Other examples show
circumstances in which adopting the recommendation would not be a good idea, and
these various points are brought together to support the writer’s position that teachers
have to look at the context of the situation and cannot rely on simply ignoring negative
actions
...
Sentences like this one demonstrate the writer’s command of the conventions of standard written English: “If the child does have an attentional problem, then the teacher can work with a related service, such as occupational
therapy, to alter the classroom environment in order to cater to the needs of the child
...
Although the response is clearly stronger than a 4, which would simply present a clear position on the issue according to the task instructions, it does not reach
the level of a 6 because it does not develop its points in a way that creates a cogent and
insightful position
...
Score 4 Response
I absolutely agree with the first section of the statement above, but find fault with the
latter half
...
When
a young child is learning basic social behavior, it is imperative that he is encouraged
to repeat positive actions
...
In contrast, if a child displays negative behavior by stealing a toy away from his
playmate, it would be very dangerous for the teacher to ignore this action, for then the
child may never recognize that this is unacceptable
...
Unlawful distribution of this ebook is prohibited
...
So what should a teacher do when faced with such
a situation? Punishment is not necessarily the optimal choice, either
...
In this case, rather than ignoring or punishing negative actions, the teacher
could seize the opportunity to reinforce positive behavior, and further extend the child’s
learning experience
...
However to
ignore, rather than recognize and correct negative actions, would be a disservice to
the student, for he would not know what conclusion to draw from his action
...
For instance, the discussion in the second paragraph of a teacher who reinforces the positive behavior of sharing a toy is certainly relevant and on-task (i
...
, it
describes a situation in which adopting the recommendation would be advantageous)
...
Instead, it is simply presented as an example
...
Some
of the sentences demonstrate the syntactical variety normally seen in responses that
receive higher scores (e
...
, “Rather than scolding a child for mistreating his playmates
and sending him off to a corner, a teacher would be wise to demonstrate the positive
alternative: to share his toys instead”)
...
Score 3 Response
Praising postive actions and ignoring negative ones may be a good way to teach but
not the best way
...
For instance, in a classroom full of eight-year old kids; if during a lesson they are
making alot of noise, having this ignored would tell the kids that it is okay to be
disruptive in class
...
However if the eight-year old kids
were immediately told to stop the distruption then it will never become a habit
...
In the early years of education, the way they are taught becomes a lifelong habit which
is hard to change in later years
...
The way postive actions are dealt
with should also be done with negative actions rather than being ignored which in turn
enhance the learning environment
...
Unlawful distribution of this ebook is prohibited
...
The writer
does make an attempt to follow the specific task instructions, and the response has a
clear position on the issue, arguing that it is not acceptable practice to ignore negative
behaviors
...
The example of “eight-year old kids” making noise during class can be seen as a situation in which following the recommendation is not advantageous
...
Another issue that keeps this response at the 3 level is a lack of
clarity, particularly in the final paragraph
...
” Problems with the structure of this sentence make it difficult to determine the writer’s intended meaning
...
, could be better to put more emphasis in the positive
things and if not ignore all the negative ones, do not give so much importance to them,
this is particulary important in the lowest levels of education
...
For this reason I believe that is important to praise positive actions but is also
important no to ignore the negative ones, because in a given situation the student can
have troubles recongnising what is right and what is wrong
...
Reader Commentary
This response clearly fits several characteristics of a 2, as defined by the scoring guide
...
The response repeats
itself rather than developing any of its statements, pointing to an inability to organize
a response capable of supporting any specific claims with relevant reasons or examples
...
Thus, even though the writer does seem to be making an attempt to respond to the
specific task instructions, the response merits a score of 2
...
Unlawful distribution of this ebook is prohibited
...
In
developing and supporting position, describe specific circumstances in which adopting
the recommendation would or would not be advantageous and explain how these
examples shape your position
...
I agree to this recommendation
...
Specific crimstances lead me which adopting
the recommendation as the following:
First, we will lost the good children who have negative maner if we ignore them
...
Praise in negative should not be, teaching to children to
best way
...
second, negative ones in today may be a great people in the future
...
Teenage in today is not easy for all! Negative ones
can not better, if only prainse positive actions, ignore negativeone
...
conclusion, specific circumstances are which adopting the recommendation would
not be advantage, I am not agree to the the recommendation
...
But they can, if do not ignore them
...
Reader Commentary
This response has severe and pervasive problems in language and sentence structure
that, as stated in the scoring guide, consistently interfere with meaning and result in
incoherence
...
For example, it is
not clear what the writer means by the claim that the best way to teach is “makeing
everyone to be a good ones
...
Although the writer makes an
attempt at organization, with points marked as first, second, and conclusion, the
response actually exhibits little or no evidence of the ability to develop any potential
understanding of the prompt into a logical position on the issue
...
Unlawful distribution of this ebook is prohibited
...
Karp, an anthropologist
...
Field, a noted anthropologist, visited the island of Tertia and
concluded from his observations that children in Tertia were reared by an entire village
rather than by their own biological parents
...
This
research of mine proves that Dr
...
The
interview-centered method that my team of graduate students is currently using in Tertia will
establish a much more accurate understanding of child-rearing traditions there and in other
island cultures
...
Score 6 Response
It might seem logical, at first glance, to agree with the argument in Dr
...
However, in order to fully evaluate this
argument, we need to have a significant amount of additional evidence
...
In
order to make that determination, we need to know more then analyze what we learn
...
Karp’s claims
is information about whether or not Tertia and the surrounding island group have
changed significantly in the past 20 years
...
Field conducted his observational study
20 years ago, and it is possible that Tertia has changed significantly since then
...
Karp’s argument
...
Karp’s study could be correct, as well, though his conclusion that Dr
...
Another piece of evidence that might help us evaluate this claim involves the exact
locations where Dr
...
According to this article, Dr
...
” If we were to learn that they never interviewed a single Tertian
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Analytical Writing Sample Responses
child, it would significantly weaken the conclusion
...
In order to fully evaluate this article, we would also need to learn more about the
interview questions that Dr
...
What exactly did they ask? We don’t
know, nor do we know what the children’s responses actually were
...
It would significantly undermine Dr
...
Without knowing WHAT
the children said, it is hard to accept Dr
...
It is slightly more difficult to discuss teh evidence we might need in order to
evaluate the more interesting claims in Dr
...
In order to fully evaluate this
claim, in fact, we would need to look at many more examples of interview-based and
observation-based anthropological studies and we would also need to look into
different study designs
...
Field did not conduct an effective observational
study, but other observational approaches could be effective
...
Karp really needs a lot of additional evidence (ideally a metaanalysis of hundreds of anthropological studies)
...
Karp’s article
...
We also need to know about study design (Dr
...
Field’s)
...
Reader Commentary
This outstanding response clearly addresses the specific task directions and presents a
cogent, insightful analysis by specifically detailing the impact that different pieces of
evidence would have on the argument
...
For example, after the writer
discusses possible evidence that Tertian child-rearing practices have changed over the
past 20 years, he or she clearly explains the impact information about those changes
might have on the argument, saying, “In that case, the original study could have been
accurate, and Dr
...
Field’s method is ineffective would be seriously weakened
...
There is more insightful development in the fifth paragraph, in which the writer examines Dr
...
Although there are a few typos
and minor errors here, nothing in the response distracts from the overall fluency of the
writing
...
” Because of its compelling and
insightful development and fluent and precise language, this response fits all of the bullet points for a 6
...
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...
Karp’s argument here
...
Karp’s
article
...
Karp
and his students did not actually conduct any of their interviews on the island of Tertia
itself
...
Karp claims the interviews were
conducted with children from the island group that includes Tertia
...
It would definitely weaken the
argument if we were to learn that they interviewed children only on islands close
to Tertia
...
Another piece of evidence that would weaken the argument could come from
transcripts of the interviews themselves
...
Karp’s article makes the claim that the
children “spend much more time talking about their biological parents than about
other adults,” but he gives no indication of what exactly they say about their biological
parents
...
One more important piece of evidence that might undermine the argument Dr
...
He admits that twenty years have passed since Dr
...
Any number of factors could have led to a
significant shift in how children are raised
...
Any evidence of such changes would clearly undermine Dr
...
If we went looking for evidence that could strengthen the argument, we might also
find something interesting
...
g
...
Field’s study or if there were transcripts
that showed the children spoke about how much they loved living with their biological
parents)
...
Karp’s findings, it would go a long way toward bolstering his claim
about Tertian child-rearing AND his claim about interview-centered studies being more
effective
...
Karp’s argument is
undermining Dr
...
Maybe Dr
...
Dr
...
Depending
on the evidence we find to fill it out, we may discover that it is quite convincing, or we
could determine that he is full of hot air
...
This writer
approaches the task by first discussing the evidence that might weaken Dr
...
In both cases the writer analyzes the ways in which the evidence would bear on the
argument
...
Any evidence of such changes would clearly undermine Dr
...
” Although the development presented here is strong, the response does not
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Analytical Writing Sample Responses
present the compelling development required for a 6
...
How
could a catastrophic event or a change in governmental structure have led to changes
in child-rearing traditions? The development, then, is strong but not outstanding
...
In general, the response demonstrates
strong writing skills, in spite of some minor errors like the sentence fragment that
begins paragraph three
...
” In
terms of writing skill and analysis, then, this response earns a score of 5
...
Karp’s arguments that his research proves that obervation-centered research is
invalid and that his interview-centered method “will establish a much more accurate
understanding of child-rearing traditions there and in other island cultures” need more
support
...
Karp’s interviews do challenge Dr
...
Field’s research is invalid
...
Karp can strengthen his argument
...
Karp should provide more information about the content of the interviews
...
It
is possible that while children may spend more time talking about their own biological
parents, other people from the village are still assisting in most of the rearing of the
child
...
Second, Dr
...
If there have been significant changes on the island of Tertia, it is
possible that both anthropologists are correct
...
Recents events
could explain the change - such as introduction of Western mass media or changes in
government (monarchy to democracy)
...
Not to mention, interpretting information from
children and using that information to generalize about an entire island is not the most
effective means
...
Karp needs more proof that the observation-centered approach to
studying cultures in invalid
...
Other anthropologists who employ the interview-centered
method need to dispute the work of anthropoligsts who use the observation-centered
approach
...
To conclude, Dr
...
In fact, it will take more than Dr
...
In terms of his own research, Dr
...
Field’s
research wrong
...
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...
The
response does not merit a score of 5 or 6, however, because it does not present compelling or insightful development
...
Development in paragraph four
(“Thirdly
...
The response does follow the specific task instructions, but it does
not develop its discussion of specific evidence fully
...
Also, language control in this response is merely adequate, not strong
...
g
...
Because of its adequate control
of language and competent analysis, this response earns a score of 4
...
Field’s observations and findings
...
Field’s work was not given
out
...
Fields work is invalid
...
The writer did not give any clue on what exactly the children were saying about
their biological parents
...
In fact, the argument could have been
strengthened if the writer gave what exactly the children were talking about
...
Field did his analyses to the the time writer also
conducted His or Her research
...
Field did His
analyses
...
fields
last visited and didcompleted His work at Tertia
...
It almost seems like
Dr
...
Fields look bad, instead of supporting his own research with
information
...
He needs to
have more details about his own work to really sell the reader on it
...
This will be more convincing if it is less of an attack on Dr
...
On the whole the writer’s work is incomplete and His or Her criticisms are
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...
Analytical Writing Sample Responses
unfounded
...
If done in this way the impact of His or Her findings will be
very strong and convincing
...
In particular,
this response contains occasional major errors and frequent minor errors that can
interfere with meaning
...
In addition to the problems with language control, the response demonstrates limited relevant development
...
However, the response does not explain exactly
how this evidence would strengthen the argument
...
Karp is making
...
The discussion of
Dr
...
There is an attempt to talk about evidence (“He needs to have more
details
...
Because of its limited development and language control, this
response earns a score of 3
...
Karp , an anthropologist and his study
and the new plan to study the same in the tertia region
...
Karp has written an article
on Children in Tertia and about the culture
...
They haven’t indicate the education level in the children
and the background of the children
...
The team is going to study and correlate the tradition with the other island culture
but there is a possibility of different environment of other island or differnt biological
parents
...
In that situation it is not possible to correlate the culture between to
iceland
...
Field’s interview time , lacking of infrastructure in the
tartia
...
To support the argument more information about the nature, cultural background
and also the type of infrastructure presence in the area is require, the kind of study
carring out in the study area is require
...
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...
GRE Practice Test 1
Reader Commentary
This response demonstrates serious weaknesses in analytical writing
...
Additionally, there is little
or no relevant or reasonable support for the writer’s points
...
There are basic errors in just about every
sentence of the response, and these errors frequently interfere with meaning
...
” The writer is
attempting to discuss some points that are relevant to an analysis of this argument, but
meaning is obscured by all of the errors present
...
Score 1 Response
Twenty years ago Dr field an anthropologist found result after reserch that in small
village of tertia children reared by entire village but according to dr karp he talked most
of the children that they talk about there boilogical parents
...
reared the
children by entire village is not logical but in some cultures there are some surprizing
customs
...
intrveiw with children and observing their
behaviour is important because some time the person talk one thing and behave in
different way look like either he not telling correct or he is showing his altitude in
misguiding way
...
The expert reserch scholer can easily feel their emotions and
behavour during some time stay with their culture
...
Reader Commentary
This fundamentally deficient response mainly consists of a summary of the prompt,
and although there is some evidence of understanding, the response provides little evidence of the ability to develop and organize an analysis of the argument
...
In fact, the material that
does not come directly from the prompt is more or less incomprehensible
...
Unlawful distribution of this ebook is prohibited
...
Questions 1 to 3 are based on the following reading passage
...
Nahuatl,
like Greek and German, is a language that allows the formation of extensive compounds
...
The tlamatinime (those who know) were able to use this rich stock of abstract terms
to express the nuances of their thought
...
Of these forms, the most characteristic in Nahuatl is the juxtaposition
of two words that, because they are synonyms, associated terms, or even contraries,
complement each other to evoke one single idea
...
Description
This passage claims that Nahuatl was used to express abstract universal concepts, by
combining semantic elements, and goes on to explain that the tlamatinime used these
terms to express subtle distinctions
...
1
...
B
Ȟ For at least some Nahuatl expressions, researchers are able to trace their
derivation from another ancient American language
...
Explanation
Choices A and B are correct
...
” This suggests that there is some evidence of
what those thoughts were, and therefore Choice A can be inferred
...
Unlawful distribution of this ebook is prohibited
...
” That researchers know certain Nahuatl
expressions are derived from Toltec suggests that they are able to trace the derivation
of some Nahuatl expressions from another language besides Nahuatl, and therefore
Choice B may be inferred
...
Therefore Choice C cannot be inferred
...
Select the sentence in the passage in which the author introduces a specific
Nahuatl mode of expression that is not identified as being shared with certain
European languages
...
One is the formation
of single compound words that are capable of expressing complex conceptual relations
(first paragraph); the other is the juxtaposition of two related words to evoke a single
idea (second paragraph)
...
Therefore the sixth sentence (“Of these forms
...
3
...
The fifth sentence draws a contrast between linguistic expressions
original to Nahuatl and those derived from Toltec
...
” Of the answer
choices given, “creations” is the nearest equivalent of “coinages” in the sense of “inventions,” and therefore Choice B is the best answer
...
Unlawful distribution of this ebook is prohibited
...
At a certain period in Earth’s history, its atmosphere contained almost no oxygen,
although plants were producing vast quantities of oxygen
...
Clearly, however, this explanation is inadequate
...
Therefore,
something in addition to the iron on Earth’s surface must have absorbed much of the
oxygen produced by plant life
...
In the argument given, the two portions in boldface play which of the following
roles?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The first is a claim made by the argument in support of a certain position;
the second is that position
...
The first expresses the argument’s dismissal of an objection to the position
it seeks to establish; the second is that position
...
The first is a concession by the argument that its initial formulation of the
position it seeks to establish requires modification; the second presents
that position in a modified form
...
The first step in responding is
to read through the passage quickly to get an understanding of what is being said
...
In this passage the first sentence presents two pieces of information that seem to be
in conflict — the atmosphere contained almost no oxygen even though plants were producing so much of it
...
The next sentence calls this hypothetical explanation inadequate and the following sentence gives a reason for that judgment — that there was insufficient iron for the proposed explanation to work
...
Since the highlighted portions in the passage represent the main content of the
third and fourth sentences, the task in this question is to find the answer choice whose
two parts fit those sentences’ roles
...
Therefore Choice D is the correct
answer
...
Unlawful distribution of this ebook is prohibited
...
Fill all blanks in the way that best completes the text
...
In her later years, Bertha Pappenheim was an apostle of noble but already
(i)__________ notions, always respected for her integrity, her energy, and her
resolve but increasingly out of step and ultimately (ii)__________ even her own
organization
...
The clue to the negative
aspect is in the later part of the sentence, where “out of step” leads both to “anachronistic” as the answer for the first blank and “alienated from” as the answer for the
second
...
6
...
A
ɕ imitation
B
ɕ reaction
C
ɕ dogmatism
D
ɕ invention
E
ɕ caution
Explanation
The sentence sets up two parallel, contrasting concepts
...
” The word “invention” is the best choice
...
7
...
Blank (i)
A
ɕ stigmatization
B
ɕ lionization
C
ɕ marginalization
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
foreground
transcend
obscure
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...
Answers and Explanations
Explanation
It is possible to analyze this sentence by starting with either blank
...
It would hardly make sense for what had happened to be either
stigmatization or marginalization, since both of those activities represent a turning
away from him, not a calling attention to him
...
Then, since we are told
that Nabokov is a literary giant, entomology must be one of his peripheral activities, so
the correct answer for the second blank must be “foreground,” which also means “call
attention to
...
Thus, the correct answer is lionization (Choice B) and foreground (Choice D)
...
Mathematicians have a distinctive sense of beauty: they strive to present their
ideas and results in a clear and compelling fashion, dictated by __________ as
well as by logic
...
Filling in the
blank will supply some aspect that balances “logic” and reinforces the view that mathematicians have a sense of beauty; “aesthetics” is the best choice
...
For each of Questions 9 to 13, select one answer choice unless otherwise instructed
...
line
5
10
Animal signals, such as the complex songs of birds, tend to be costly
...
Singing may also advertise an individual’s location to rivals or predators and impair the ability to detect their approach
...
Overall the evidence is equivocal: for instance, while Eberhardt found increases in
energy consumption during singing for Carolina wrens, Chappell found no effect of
crowing on energy consumption in roosters
...
Birds store energy as subcutaneous fat deposits or “body reserves”;
changes in these reserves can be reliably estimated by measuring changes in body
mass
...
Unlawful distribution of this ebook is prohibited
...
Thomas found that nightingales reached a significantly higher body mass at dusk and lost more mass overnight on nights when their
song rate was high
...
The increased metabolic cost of possessing higher body mass contributes to the increased overnight mass loss
...
The metabolic cost of singing itself
may also contribute to increased loss of reserves
...
For example, birds may expend more of their reserves on thermoregulation if
they spend the night exposed to the wind on a song post than if they are in a sheltered
roost site
...
Description
The passage mentions various ways in which singing is costly to a bird, but soon
focuses on the main topic: the energy costs of singing
...
9
...
Thus, the correct answer is
Choice C
...
Because the passage does not question any
hypotheses, discuss benefits, or advance an alternative model of birdsong, Choices B,
D, and E are incorrect
...
Unlawful distribution of this ebook is prohibited
...
10
...
Choice A is incorrect: the only reference to thermoregulation comes in line 24 and
discusses nighttime activity, not daytime activity
...
Choice C is incorrect: while the passage does say that singing exposes birds to predators (line 3), it says nothing to suggest that they make special efforts to hide before
singing, and in fact it says that nightingales spend extra time foraging (line 20)
...
Select the sentence in the first or second paragraph that presents empirical
results in support of a hypothesis about the energy costs of singing
...
The last sentence of the first paragraph
contains information about increases in energy consumption but only the last sentence
of the second paragraph provides results in support of the only hypothesis in the passage, that nightingales should lose more body mass on nights when their song rate is
high
...
high”) is the correct choice
...
12
...
B
Ȟ They have generally received more attention from scientists
...
Explanation
Choice B is correct
...
Choice B is correct: lines 4–5 say that discussions of the costs of singing have generally focused on energy costs
...
Unlawful distribution of this ebook is prohibited
...
These findings relate to energy
costs alone and, if anything, suggest that energy costs vary considerably
...
In the past ten years, there have been several improvements in mountain-climbing
equipment
...
Despite these improvements, however, the rate of mountainclimbing injuries has doubled in the past ten years
...
Which of the following, if true, best reconciles the apparent discrepancy
presented in the passage?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
Many climbers, lulled into a false sense of security, use the new equipment
to attempt climbing feats of which they are not capable
...
Mountain climbing, although a dangerous sport, does not normally result
in injury to the experienced climber
...
Although the rate of mountain-climbing injuries has increased, the rate of
mountain-climbing deaths has not changed
...
The discrepancy is that despite improvements in mountain climbing equipment that have made climbing safer, the incidence
of mountain-climbing injuries has greatly increased
...
Therefore, Choice A is the correct answer
...
Neither Choice B nor Choice C relates to conditions that have changed over the relevant
ten-year period
...
But if, as Choice D
says, techniques as well as equipment have improved, that fact by itself only makes the
increase in injuries more puzzling
...
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...
Answers and Explanations
For Questions 14 to 17, select one entry for each blank from the corresponding
column of choices
...
14
...
A
ɕ demur
B
ɕ schism
C
ɕ cooperation
D
ɕ compliance
E
ɕ shortsightedness
Explanation
The blank must be filled with a word that describes a problem that a work group can
suffer, a problem that can be a cause of (or associated with) serious conflict
...
Thus, the correct answer is schism (Choice B)
...
The novelist devotes so much time to avid descriptions of his characters’ clothes
that the reader soon feels that such __________ concerns, although worthy of
attention, have superseded any more directly literary aims
...
Although these concerns could also be described as “irrelevant” or
“frivolous,” neither of these choices is correct because the sentence identifies the concerns as “worthy of attention
...
16
...
Blank (i)
A
ɕ undemonstrative panache
B
ɕ unrestrained enthusiasm
C
ɕ unattractive gawkiness
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
focus
overwhelm
deflect
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...
GRE Practice Test 1
Explanation
The point of the sentence is to emphasize contradictory aspects of Belanger’s dancing:
we are told, for example, that he seems “at once intensely present and curiously
detached
...
The only choice that fits, therefore, is “deflect”; focusing or
overwhelming attention would certainly be expected to draw it
...
”
Thus, the correct answer is undemonstrative panache (Choice A) and deflect
(Choice F)
...
The most striking thing about the politician is how often his politics have been
(i)__________ rather than ideological, as he adapts his political positions at any
particular moment to the political realities that constrain him
...
Rather, he attempts in subtle ways to balance his political self-interest
with a (iii) __________, viewing himself as an instrument of some unchanging
higher purpose
...
” The second blank, brandishing political principles is what a politician might do piously, while flouting is not pious and following
principles does not make sense when combined with “betray[ing] them in practice
...
Thus, the correct answer is strategic (Choice C), brandish (Choice D), and deeply
felt moral code (Choice H)
...
Questions 18 to 20 are based on the following reading passage
...
Recent years have witnessed the posthumous inflation of the role of the hobbyist Alice Austen into that of a pioneering documentarian while dozens of notable
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...
Answers and Explanations
line
5
10
senior figures — Marion Palfi, whose photographs of civil-rights activities in the South
served as early evidence of the need for protective legislation, to name one — received
scant attention from scholars
...
Description
The passage expresses dismay at the current state of scholarship concerning the history
of women in photography: some figures receive disproportionate attention, and past
1920 Rosenblum’s book is too sketchy to be useful
...
The author of the passage cites Rosenblum’s book most likely in order to
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
suggest that the works documented most thoroughly by historians of
women in photography often do not warrant that attention
offer an explanation for the observation that not all aspects of the history
of women in photography have received the same level of attention
provide an example of a way in which scholarship on the history of
women in photography has been unsatisfactory
suggest that employing a strictly chronological approach when studying
the history of women in photography may be unproductive
provide support for the notion that certain personalities in women’s
photography have attained undue prominence
Explanation
As mentioned above, the topic of the passage is the unsatisfactory condition of scholarship devoted to the history of women in photography
...
Choice D may seem appealing, because a strictly chronological approach
might be inadequate to represent the explosive growth of the field in the 1920s
...
For the following question, consider each of the choices separately and select all that
apply
...
Which of the following statements about Marion Palfi is supported by the
passage?
A
Ȟ Marion Palfi’s photographs would have received greater recognition from
B
Ȟ
C
Ȟ
historians had her work been done in an era when most aspects of
photography were static rather than in a state of transition
...
In addition to providing a record of certain historical events, Marion
Palfi’s photographs played a role in subsequent events
...
Unlawful distribution of this ebook is prohibited
...
Choice A is incorrect: the passage does not state whether the period in which Palfi
was working was an era when photography was static or in transition
...
Choice C is correct: Palfi’s photographs played a role in subsequent events because
they served as early evidence of the need for protective legislation
...
In the context in which it appears, “inflation” (line 2) most nearly means
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
exaggeration
acquisition
evaluation
distortion
attenuation
Explanation
The term “hobbyist” suggests Austen’s relative lack of seriousness as a photographer
when compared with “senior figures,” yet her role has been elevated to that of a “pioneering documentarian” at the expense of these other figures
...
” Thus, Choice A, “exaggeration,” is the
correct answer
...
21
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
innocuous
feasible
practicable
minimal
remedial
benign
Explanation
If the engineers think that the reduced levels will save the aquifer, they may describe
the reduced levels as innocuous, minimal, remedial, or benign
...
The two words
“feasible” and “practicable” are similar in meaning, but do not fit the context well,
because they imply that the current levels are not feasible or practicable, conflicting
with the implication that the current levels, though perhaps undesirable, are nevertheless entirely feasible
...
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...
Answers and Explanations
22
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
antedated
cloaked
portrayed
preceded
renewed
represented
Explanation
The words that fill the blank must fit with the idea that Rainer’s film has some feminist
implications, but that those are limited compared with her other activities
...
However, only “antedated” and “preceded” make sense in the context of the sentence:
Rainer’s 1974 film exhibits feminist themes in a limited way because it came before she
became active in feminist politics
...
23
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
commonplace
disparate
divergent
fundamental
trite
trivial
Explanation
The words that fill the blank must help explain the difficulty of developing a consensus
...
Accordingly, “disparate” and “divergent” are
the best choices because they both indicate disagreement among the members
...
Thus, the correct answer is disparate (Choice B) and divergent (Choice C)
...
During the opera’s most famous aria, the tempo chosen by the orchestra’s
conductor seemed __________, without necessary relation to what had gone
before
...
Unlawful distribution of this ebook is prohibited
...
However, the phrase “without necessary relation to what had gone before” is presented as
an elaboration on the word in the blank
...
Thus, the correct answer is arbitrary (Choice A) and capricious (Choice B)
...
Because they had expected the spacecraft Voyager 2 to be able to gather data only
about the planets Jupiter and Saturn, scientists were __________ the wealth of
information it sent back from Neptune twelve years after leaving Earth
...
Therefore, the words that fill the blank
should describe a reaction to results that are better than hoped for, and the choices
“thrilled about” and “elated by” both express such a reaction
...
Thus, the correct answer is thrilled about (Choice C) and elated by (Choice E)
...
Unlawful distribution of this ebook is prohibited
...
1
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
complete
fleeting
momentary
premature
trivial
total
Explanation
The key phrases that indicate how the blank for this question should be completed are
“Only by ignoring decades of mismanagement and inefficiency” and “provide anything
other than
...
” Among the answer
choices, “complete” and “total” are quite close in meaning and would clearly create two
sentences very similar in meaning
...
“Fleeting” and “momentary” suggest that the event referred to (“a fresh infusion of
cash”) might have some beneficial effect, but that it would ultimately not resolve the
problem
...
2
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
diversity
deviation
variety
reproduction
stability
invigoration
Explanation
The key phrase that indicates how the blank for this question should be completed is
“the ability to form an unending series of different molecules
...
No other pair of choices here would produce
two sentences as similar in meaning as those created by placing “diversity” and “variety”
in the blank
...
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...
GRE Practice Test 1
3
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
synoptic
abridged
sensational
copious
lurid
understated
Explanation
The key phrase that indicates how the blank for this question should be completed is
“the only way for someone to keep abreast of the news
...
“Sensational”
and “lurid” would create two similar sentences but do not fit the logic for completing
the blank, since we would not be relying on sensational or lurid accounts in order to
keep abreast of the news
...
4
...
A
Ȟ
B
Ȟ
C
Ȟ
C
Ȟ
E
Ȟ
F
Ȟ
deferential
intransigent
lax
negligent
obsequious
resolute
Explanation
The key phrases that indicate how the blank for this question should be completed are:
“circumspect,” “reluctant,” and “but once
...
Among
the answer choices, “intransigent” and “resolute,” although not strictly synonymous,
both fit the logic of the description given here for completing the blank and create sentences that are similar in meaning
...
“Deferential” and “obsequious” are
also similar in meaning, but their emphasis on “politeness,” while not strictly synonymous with reluctance and circumspection, like “lax” and “negligent” fail to pick up on
the expected contrast
...
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...
Answers and Explanations
For each of Questions 5 to 9, select one answer choice unless otherwise instructed
...
line
5
10
When marine organisms called phytoplankton photosynthesize, they absorb carbon
dioxide dissolved in seawater, potentially causing a reduction in the concentration of
atmospheric carbon dioxide, a gas that contributes to global warming
...
Martin therefore hypothesized that adding iron to iron-poor regions of the ocean could
help alleviate global warming
...
When phytoplankton utilize
carbon dioxide for photosynthesis, the carbon becomes a building block for organic
matter, but the carbon leaks back into the atmosphere when predators consume the
phytoplankton and respire carbon dioxide
...
For the following question, consider each of the choices separately and select all that
apply
...
It can be inferred from the passage that Martin’s hypothesis includes which of the
following elements?
A
Ȟ A correct understanding of how phytoplankton photosynthesis utilizes
carbon dioxide
B
Ȟ A correct prediction about how the addition of iron to iron-poor waters
would affect phytoplankton growth
C
Ȟ An incorrect prediction about how phytoplankton growth would affect the
concentration of atmospheric carbon dioxide
Explanation
All three choices are correct
...
Choice A is correct: the passage presents Martin as using the standard understanding of how phytoplankton photosynthesize as a basis for the hypothesis
...
Therefore,
Martin’s prediction about this was correct
...
The passage states that predators who consume phytoplankton respire carbon dioxide, so that
the carbon dioxide absorbed by phytoplankton reenters the atmosphere
...
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...
GRE Practice Test 1
6
...
Lines
7–8 present field test results showing that Martin’s hypothesis is incorrect, and the last
sentence explains these results: the reason the increased phytoplankton resulting from
the addition of iron do not reduce atmospheric carbon dioxide is that while the phytoplankton absorb carbon dioxide, the gas reenters the atmosphere when it is respired by
phytoplankton predators
...
Choice B is not correct because while
predators’ consumption of phytoplankton and respiration of carbon dioxide might be
considered one indirect consequence of adding iron to iron-poor waters, identifying a
consequence is not the primary function of the mention of predators
...
Choice E is not correct because it is
Martin who did not anticipate this factor, rather than the scientists who conducted the
field tests
...
Sparva, unlike Treland’s other provinces, requires automobile insurers to pay for any
medical treatment sought by someone who has been involved in an accident; in the
other provinces, insurers pay for nonemergency treatment only if they preapprove the
treatment
...
Description
The passage tells us that in Sparva automobile insurers pay for far more medical treatments after accidents than they do in Treland’s other provinces
...
7
...
The cost of medical care in Sparva is higher than the national average
...
D
ɕ Fewer insurance companies operate in Sparva than in any other province
...
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...
Answers and Explanations
Explanation
The question asks you to identify among the answer choices a fact that would support
the passage’s argument
...
One obvious explanation for there being more medical treatments in
Sparva is that there are more accidents there
...
So
Choice E strengthens the argument in the passage and is the correct answer
...
But neither bears on the cause of insurers having to
pay for more treatments
...
A higher cost of medical care provides additional motivation for people to seek insurance payments to cover whatever post-accident care they receive
...
According to the passage, whether treatment is
emergency treatment is, in other provinces, an important criterion in determining insurers’ responsibility
...
Questions 8 and 9 are based on the following reading passage
...
In the book’s frontispiece,
Voltaire is seen writing at his desk, and over him a shaft of light from heaven, the light
of truth, passes through Newton to Voltaire’s collaborator Madame du Châtelet; she
reflects that light onto the inspired Voltaire
...
” In other
words, Voltaire’s amateurism in science “was a source of his contemporary appeal,
demonstrating for the first time the accessibility of Newton’s ideas to nonspecialists
...
For the following question, consider each of the choices separately and select all that
apply
...
Which of the following statements about Voltaire’s Elements of the Philosophy of
Newton can be inferred from the passage?
A
Ȟ Voltaire’s literary stature helped secure a large audience for this attempt to
popularize Newton’s ideas
...
C
Ȟ The frontispiece of the book implies that Voltaire’s understanding of
Newton’s ideas was not achieved without assistance
...
Choice A is correct: the paragraph states that one of the reasons Voltaire’s book
commanded a wide audience is that he was “a literary giant
...
Unlawful distribution of this ebook is prohibited
...
Choice C is correct: the paragraph refers to Voltaire’s collaborator, Madame du
Châtelet
...
9
...
Explanation
In the image described in the second sentence, Voltaire acquires his knowledge of Newton through Madame du Châtelet, who conveys Newton’s ideas — his “light of truth” —
to Voltaire
...
from disputes
...
Therefore sentence 2 (“In the
book’s
...
For Questions 10 to 13, select one entry for each blank from the corresponding
column of choices
...
10
...
Blank (i)
A
ɕ probity
B
ɕ extravagance
C
ɕ disapprobation
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
acquisitive
illiberal
profligate
Explanation
The last part of the sentence provides most of the context needed to fill in the two
blanks
...
Among the
choices for the second blank, only “profligate” matches this lack of restraint
...
Thus, the correct answer is extravagance (Choice B) and profligate (Choice F)
...
Unlawful distribution of this ebook is prohibited
...
What readers most commonly remember about John Stuart Mill’s classic
exploration of the liberty of thought and discussion concerns the danger of
(i)__________: in the absence of challenge, one’s opinions, even when they are
correct, grow weak and flabby
...
Since one’s opinions, even under the best circumstances, tend to (ii)__________,
and because opinions opposed to one’s own rarely turn out to be completely
(iii)__________, it is crucial to supplement one’s opinions with alternative points
of view
...
The colon after the first blank signals that what follows will define the
word in the blank and will explain what danger Mill was concerned about
...
A quick reading of the next two sentences
suggests that the topic will be another danger that Mill described, “the danger of partiality and incompleteness
...
” The other choices for the second and
third blanks deal with change, immediacy, or antithesis, none of which relate to the
second danger of “partiality” or “incompleteness
...
12
...
A
ɕ prevent
B
ɕ defy
C
ɕ replicate
D
ɕ inform
E
ɕ use
Explanation
The “just as” structure indicates that the second half of the sentence should somehow
parallel the idea presented in the first half (i
...
, the idea that the authors’ book on eels
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...
GRE Practice Test 1
is a “key text” in marine vertebrate zoology)
...
“Prevent” and “defy” work in the opposite direction, while “use”
and “replicate” would suggest that the authors’ ideas are drawing upon the teaching in
this area rather than the other way around
...
Thus, the correct answer is inform (Choice D)
...
Mechanisms develop whereby every successful species can __________ its innate
capacity for population growth with the constraints that arise through its
interactions with the natural environment
...
This analysis suggests that
the correct answer will have something to do with adjusting that capacity in the face of
these constraints
...
None of
the other options make for a meaningful, coherent sentence
...
”
Thus, the correct answer is reconcile (Choice E)
...
Questions 14 to 16 are based on the following reading passage
...
E
...
DuBois would
attract the attention of literary critics
...
But though
valuable scholarship has examined DuBois’ political and historical thought, his novels
have received scant attention
...
But what if the truth lies elsewhere: what
if his novels do not speak to current concerns?
Description
The paragraph first presents reasons for critical interest in DuBois’ novels, but then
goes on to explain that there has in fact been very little such interest and speculates as
to why that might be
...
Unlawful distribution of this ebook is prohibited
...
Which of the following can be inferred from the passage regarding DuBois’ The
Quest of the Silver Fleece?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The lack of attention devoted to The Quest of the Silver Fleece can be
attributed to the fact that it was DuBois’ first novel
...
The Quest of the Silver Fleece has at least one feature that typically would
attract the attention of literary scholars
...
Much of the scholarly work that has focused on The Quest of the Silver
Fleece has been surprisingly critical of it
...
The second sentence states that The Quest of the Silver Fleece subtly engages the issue of race and implies that such an issue would attract the attention
of literary scholars
...
15
...
editor
...
None of the other choices fits the metaphor
in “Perhaps DuBois the novelist must wait his turn
...
Unlawful distribution of this ebook is prohibited
...
Which of the following best describes the central issue with which the passage is
concerned?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The perfunctoriness of much of the critical work devoted to DuBois’
novels
The nature of DuBois’ engagement with the issue of race in The Quest of
the Silver Fleece
Whether DuBois’ novels are of high quality and relevant to current
concerns
The relationship between DuBois the novelist and DuBois the philosopher,
historian, and editor
The degree of consideration that has been given to DuBois’ novels,
including The Quest of the Silver Fleece
Explanation
The passage focuses on the scant attention given to DuBois’ novels, The Quest of the Silver Fleece in particular
...
Thus, Choice E is correct
...
For Questions 17 to 20, select one entry for each blank from the corresponding
column of choices
...
17
...
A
ɕ a paradigm
B
ɕ a misnomer
C
ɕ a profundity
D
ɕ an inaccuracy
E
ɕ an anomaly
Explanation
The sentence offers a contrast between “many evasive statements” and a single “forthright statement
...
” Do any of the other options make for a meaningful, coherent sentence? “A
paradigm” is appealing, as is “a profundity,” since the forthright statement is clearly
presented as something positive
...
” The
same reasoning allows us to eliminate “inaccuracy” and “misnomer
...
Thus, the correct answer is an anomaly (Choice E)
...
Unlawful distribution of this ebook is prohibited
...
The activists’ energetic work in the service of both woman suffrage and the
temperance movement in the late nineteenth century (i)__________ the assertion
that the two movements were (ii)__________
...
The second blank, however, obscures the nature of that assertion
...
“Supports” is offered as a choice
for the first blank (as is the somewhat similar “underscores”), but there is no corresponding term in the second blank, nothing along the lines of “similar” or “compatible
...
Thus, the correct answer is undermines (Choice A) and inimical (Choice E)
...
There is nothing quite like this movie, and indeed I am not altogether sure there
is much more to it than its lovely (i) __________
...
Blank (i)
A
ɕ peculiarity
B
ɕ pellucidity
C
ɕ conventionality
Blank (ii)
D
ɕ
E
ɕ
F
ɕ
indirect
assertive
enigmatic
Explanation
The two sentences provide the reader with quite a bit of information about the movie
...
” “Peculiarity” is clearly a
solid fit for the first blank, while “conventionality” clearly does not work, given the fact
that there is “nothing quite like it
...
” The second blank needs simply to provide a contrast with “subtle and puzzling
...
Thus, the correct answer is peculiarity (Choice A) and assertive (Choice E)
...
Unlawful distribution of this ebook is prohibited
...
Wills argues that certain malarial parasites are especially (i)__________ because
they have more recently entered humans than other species and therefore have
had (ii)__________ time to evolve toward (iii)__________
...
Blank (i)
Blank (ii)
A
ɕ populous
B
ɕ malignant
C
ɕ threatened
D
ɕ ample
E
ɕ insufficient
F
ɕ adequate
Blank (iii)
G
ɕ virulence
H
ɕ benignity
I
ɕ variability
Explanation
The “Yet” that begins the second sentence indicates that Wills’ position would be supported by evidence that the newer parasites are in humans, the more harmful they are
...
What follows “therefore” is a
potential explanation for the trend that Wills expects, namely an evolution toward
harmlessness, implying “benignity” for the third blank, with newer species having had
“insufficient” time (second blank) to evolve toward harmlessness
...
For each of questions 21 to 25, select one answer choice unless otherwise instructed
...
Saturn’s giant moon Titan is the only planetary satellite with a significant atmosphere
and the only body in the solar system other than Earth that has a thick atmosphere
dominated by molecular nitrogen
...
The conditions for acquiring and
retaining a thick nitrogen atmosphere are now readily understood
...
The
higher temperatures of Jupiter’s moons, which were closer to the Sun, prevented them
from acquiring such an atmosphere
...
21
...
Unlawful distribution of this ebook is prohibited
...
Because the reason for this difference
in temperature was their respective distances from the Sun, Choice B is correct
...
Question 22 is based on the following reading passage
...
If this warming trend continues, within 50 years the
Arctic Ocean will be ice free during the summer months
...
However, serious consequences to sea levels
would eventually result, because __________
...
Which of the following most logically completes the passage?
A
ɕ
B
ɕ
large masses of floating sea ice would continue to form in the wintertime
significant changes in Arctic sea temperatures would be accompanied by
changes in sea temperatures in more temperate parts of the world
C such a warm Arctic Ocean would trigger the melting of massive landɕ
based glaciers in the Arctic
D an ice-free Arctic Ocean would support a very different ecosystem than it
ɕ
does presently
E in the spring, melting sea ice would cause more icebergs to be created and
ɕ
to drift south into shipping routes
Explanation
To logically complete the passage’s open-ended “because,” something is needed that
will explain why the continuation of the warming trend would have serious consequences for sea levels
...
But Choice C
points to a way in which increasing temperatures in the Arctic could add water to the
ocean, namely by melting ice on the land
...
Given that the passage has already explained that melting sea ice does not affect
sea levels, the formation of sea ice described in Choice A does not explain why there
would be consequences for sea levels
...
So none of these options provides a logical completion for the
passage
...
Unlawful distribution of this ebook is prohibited
...
line
5
10
In a recent study, David Cressy examines two central questions concerning English
immigration to New England in the 1630s: what kinds of people immigrated and why?
Using contemporary literary evidence, shipping lists, and customs records, Cressy finds
that most adult immigrants were skilled in farming or crafts, were literate, and were
organized in families
...
With respect to their reasons for immigrating, Cressy does not deny the frequently
noted fact that some of the immigrants of the 1630s, most notably the organizers and
clergy, advanced religious explanations for departure, but he finds that such explanations usually assumed primacy only in retrospect
...
Description
The passage discusses Cressy’s answers to the questions posed in the first sentence
...
For the following question, consider each of the choices separately and select all that
apply
...
The passage indicates that Cressy would agree with which of the following
statements about the organizers among the English immigrants to New England
in the 1630s?
A
Ȟ Some of them offered a religious explanation for their immigration
...
They were more likely than the average immigrant to be motivated by
material considerations
...
Choice A is correct: the organizers are mentioned in the second paragraph, where
the passage says that Cressy “does not deny” that organizers “advanced religious explanations” for leaving England and immigrating to New England in the 1630s
...
Choice B is incorrect: in lines 10–11, the passage says that Cressy finds that religious reasons for immigration “assumed primacy” only in retrospect, but this is not the
same as Cressy’s concluding that no reasons were given at the time of immigration
...
Choice C is incorrect: the passage refers in lines 13–14 to “promises of material
improvement” as a factor that in Cressy’s view motivated most immigrants other than
“the principal actors
...
Therefore it cannot be inferred that Cressy would agree with
the statement in Choice C
...
Unlawful distribution of this ebook is prohibited
...
Select the sentence that provides Cressy’s opinion about what motivated English
immigrants to go to New England in the 1630s
...
” Because this suggests that
Cressy believes immigrants were motivated by these promises to go to New England,
sentence 5 (“When he
...
The preceding sentence
suggests that Cressy does not believe religion was a primary motive influencing immigrants’ decision to immigrate in the 1630s
...
25
...
Choice A, “summarizing the findings of an investigation,” is therefore the best description of the author’s primary concern in the passage
...
Choice C is incorrect because the passage is not primarily concerned with evaluating a point of view: it does not assess the
merits or demerits of Cressy’s viewpoint
...
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...
GRE Practice Test 1
SECTION 5
Quantitative Reasoning
25 Questions with Explanations
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
3
x
3
O
4
O is the center of the circle above
...
A
B
C
D
Explanation
In this question you are asked to compare x with 5, where x is the length of a
line segment from the center of the circle to a point inside the circle
...
Looking at
the figure in the question, you can see that you can draw two radii, each of
which “completes” a right triangle, as shown in the figure below
...
The triangle has
legs of length 3 and 4
...
You could also see that the two triangles are congruent, and so x = 4, again
yielding Choice B
...
Unlawful distribution of this ebook is prohibited
...
5
Quantity A
2
...
It would be easier to compare these
measurements if they were both given in meters or both given in kilometers
...
1,000
1
4
Since B ran 800 meters, it follows that B ran (800)
, or kilometer, which
1,000
5
is the same distance that A ran
...
4
4
(1,000), or 800 meters, which is
Since A ran kilometer, it follows that A ran
5
5
the same distance that B ran
...
x
Quantity B
x+y+z
3
y
3
...
3
Two approaches that you could use to solve this problem are:
1: Search for a mathematical relationship between the two quantities
...
x+y+z
Approach 1: Note that
is the average of the three numbers x, y, and
3
z and that y is the median
...
Therefore, the correct answer is Choice D
...
x+y+z
Since
is the average of the three numbers x, y, and z and you are
3
comparing it to the median, you may want to try plugging in numbers that are
evenly spaced and plugging in numbers that are not evenly spaced
...
Unlawful distribution of this ebook is prohibited
...
For example, you can plug in x = 1, y = 2, and z = 3
...
3
3
3
3
You can also plug in numbers that not are not evenly spaced and are easy to
work with
...
In this case,
x + y + z 3 + 6 + 12 21
x+y+z
x+y+z
=
=
= 7, and
> y
...
The correct answer is Choice D
...
A
B
C
D
Explanation
One way you can solve this problem is by using the following fact:
¼
If ABC is a triangle and the measure of angle A is greater than the
measure of angle B, then the side opposite angle A is longer than the side
opposite angle B
...
So x > y, and > 1, which yields Choice A
...
Instead, you
can use the strategy of adapting solutions to related problems to determine the
relationship between x and y
...
How do the lengths of the legs of a 45Њ − 45Њ − 90Њ triangle compare to the lengths of the legs of the triangle in the question? To make
the comparison, add a line segment to the triangle so that the line segment cuts
the 50Њ angle in two parts, making a 45Њ angle with the horizontal base, as
shown in the following figure:
398
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...
Answers and Explanations
45°
x
z
45°
y
The 45Њ − 45Њ − 90Њ triangle has two 45Њ angles, so z = y, and
z
= 1
...
The correct answer is Choice A
...
A
B
C
D
Explanation
Two approaches that you could use to solve this problem are:
1: Translate from algebra to a number line
...
Approach 1: The following figure represents the information given in the
problem on a number line
...
If y is exactly halfway between x and 1, then 1 − y is
equal to y − x; and if y is not halfway between x and 1, then 1 − y is not equal to
y − x
...
Approach 2: Since this problem involves subtraction, it is a good idea to
choose values for x and y that are close to each other as well as values that are
far apart
...
4 and y = 0
...
5 and y − x = 0
...
1 and y = 0
...
1 and y − x = 0
...
This shows that the
relationship cannot be determined, and the correct answer is Choice D
...
Unlawful distribution of this ebook is prohibited
...
Quantity A
Quantity B
p+s
ps
6
...
Since Quantity B is the product of the two
probabilities p and s, you need to look at its value for the cases p = 1, p = 0, and
0 < p < 1
...
In both cases, ps is equal
to 0
...
Since Quantity A is equal to 1 and Quantity B is less than 1, the
correct answer is Choice A
...
Quantity A
7
...
For example,
⎪−2⎪ = ⎪2⎪ = 2
...
Thus, the set X consists of
the integers −5, −4, −3, −2, 2, 3, 4, and 5
...
The least of these integers is −5, and its absolute
value is also 5
...
The correct answer
is Choice C
...
Quantity A
8
...
Since the base in both
x3
expressions is the same, a good strategy to use to solve this problem is to plug in
numbers for m in both expressions and compare them
...
Since
400
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...
Answers and Explanations
If m = 3, then xm−3 = 1 and xm/3 = x
...
This example
xm
is sufficient to show that the relationship between 3 and xm/3 cannot be
x
determined from the information given
...
A random variable Y is normally distributed with a
mean of 200 and a standard deviation of 10
...
The probability of the event
that the value of Y is
greater than 220
1
6
A
B
C
D
Explanation
This problem involves a normal distribution with mean 200 and standard
deviation 10
...
To compare Quantity A
with Quantity B, it is not necessary to exactly determine the probability of the
event that the value of Y is greater than 220
...
This means that less than 5% of
the values in this distribution will be greater than 220
...
The correct answer is Choice B
...
170
180
190
200
210
220
230
The curve is symmetric about the mean 200
...
Similarly, the values of 190, 180, and
170 are 1, 2, and 3 standard deviations, respectively, below the mean
...
From the figure, you can see that the area under the normal curve has been
divided into 6 regions and that these regions are not equal in area
...
Unlawful distribution of this ebook is prohibited
...
The correct answer is Choice B
...
The ratio of
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
1
3
to
is equal to the ratio of
3
8
1 to 8
8 to 1
8 to 3
8 to 9
9 to 8
Explanation
Multiplying both parts of a ratio by the same number produces an equivalent
ratio
...
1
3
1
3
Thus, multiplying both and by 24, you get that the ratio of to is equal to
3
8
3
8
the ratio of 8 to 9
...
1
3
An alternate approach to this problem is to express the ratio of to as the
3
8
1
3
1 8
8
...
The correct answer is
fraction
3
3 3
9
8
Choice D
...
A reading list for a humanities course consists of 10 books, of which 4 are
biographies and the rest are novels
...
How
many selections of 4 books satisfy the requirements?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
90
115
130
144
195
Explanation
The requirement to select 4 books, including 2 or more biographies, means that
you have to consider three cases
...
Case 1: Choose 4 biographies
...
In the other two cases, you have to find the number of ways of choosing the
biographies and the number of ways of choosing the novels and then multiply
these two numbers
...
Unlawful distribution of this ebook is prohibited
...
First, you need to find the number
of ways of choosing 3 biographies out of 4
...
The number of ways of choosing 1
novel out of the 6 novels is 6
...
Case 3: Choose 2 biographies and 2 novels
...
This number is sometimes
called “4 choose 2” or the number of combinations of 4 objects taken 2 at a
time
...
The
2
2!(4−2)!
4!
(4)(3)(2!) (4)(3)
value of
is
=
= 6
...
Similarly, the number of ways to choose 2 novels out of 6 is
6!
(6)(5)
=
= 15
...
Adding the number of ways to choose the books for each of the three cases,
you get a total of 1 + 24 + 90 = 115
...
For the following question, enter your answer in the box
...
In a graduating class of 236 students, 142 took algebra and 121 took chemistry
...
The Venn diagram below is one you could draw to represent the information
given in the question
...
It is a good idea,
therefore, to redraw the Venn diagram with the number of students who took
403
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...
GRE Practice Test 1
both algebra and chemistry separated out
...
Total Students: 236
Algebra
only
142 – x
Chemistry
only
121 – x
x
Algebra and
Chemistry
To solve this problem you want the greatest possible value of x
...
Hence, x must be less than or
equal to 121
...
s°
m
t°
13
...
Since corresponding angles have equal measures, you
could place two more angle measures on the figure, as shown below
...
Unlawful distribution of this ebook is prohibited
...
Therefore, since it is given
that s = t + 30, you can substitute t + 30 for s into the equation s + t = 180 and
get that (t + 30) + t = 180, which can be simplified as follows
...
14
...
2x = 20, or x = 10
20
3y = 20, or y =
3
4z = 20, or z = 5
20(5) = 4,000, and the correct answer is Choice C
...
Therefore, the correct answer is
2
2
Choice C
...
15
...
Mary paid for the
book with a $10 bill and received the correct change, which was less than $3
...
Which of the following statements must be true?
Indicate all such statements
...
50
...
90
...
45
...
Since the price of the book is unknown, you can call it x
dollars, and then the total amount that Mary paid is x dollars plus 4% of x
dollars, or 1
...
The problem states that Mary received some change
from a $10 bill, so 1
...
Since the change was less
405
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 1
than $3
...
00
...
00 < 1
...
00
Solving the inequality for x by dividing by 1
...
73 < x < 9
...
73 and $9
...
With
this information, you can quickly examine the first two statements
...
61, and Choice B is
not necessarily true because the price could be as low as $6
...
To examine Choice C, you could compute the tax for the greatest possible
price, which would be 4% of 9
...
04)(9
...
38
...
45, Choice C must be true
...
00 would only be $0
...
00, the tax
must be less than $0
...
The correct answer consists of Choice C
...
1
is expressed as a terminating decimal, how many nonzero digits
(211)(517)
will the decimal have?
If
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
One
Two
Four
Six
Eleven
Explanation
To convert the fraction to a decimal, it is helpful to first write the fraction in
powers of 10
...
1
1
17 =
11
(2 )(5 ) (2 )(511+pl6)
11
=
1
(2 )(511)(56)
=
1
(1011)(56)
=
5 (10
11
1
6
)
−11
= (0
...
The correct answer is Choice B
...
Unlawful distribution of this ebook is prohibited
...
VARIATION IN THE AMOUNT OF CAFFEINE IN COMMON BEVERAGES AND DRUGS*
Amount of Caffeine (milligrams)
0
25
50 75 100 125 150 175 200
Decaffeinated coffee
Percolated coffee
Coffee
Drip-brewed coffee
Instant coffee
Brewed tea
Other
beverages
Instant tea
Cocoa
Caffeinated soft drinks
Weight-loss drugs,
diuretics, and stimulants
Drugs
Pain relievers
Cold/allergy remedies
Source: Food and Drug Administration
*Based on 5-ounce cups of coffee, tea, and cocoa; 12-ounce cups of soft drinks;
and single doses of drugs
...
The least amount of caffeine in a 5-ounce cup of drip-brewed coffee exceeds
the greatest amount of caffeine in a 5-ounce cup of cocoa by approximately
how many milligrams?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
160
80
60
40
20
Explanation
Each horizontal bar in the bar graph shows the possible number of milligrams
of caffeine in each of the common beverages and drugs
...
So, the difference is approximately 60 − 20, or 40
milligrams
...
To check your answer, it is useful to try to solve the problem using another
method as well to see if you get the same answer
...
Therefore, the answer is
between 25 and 50
...
407
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 1
For the following question, enter your answer in the box
...
For how many of the 11 categories of beverages and drugs listed in the graph
can the amount of caffeine in the given serving size be less than 50 milligrams?
categories
Explanation
In the graph, the left edge of each bar tells you what is the least possible amount
of caffeine in the corresponding beverage or drug
...
From the graph, you see
that there are 9 bars for which this is true
...
So there are 9 categories of
beverages and drugs that can have less than 50 milligrams of caffeine in the
given serving size
...
19
...
Therefore, the minimum
amount of caffeine in two 10-ounce cups of percolated coffee, which is the same
as the minimum amount of caffeine in four 5-ounce cups, is approximately
(40)(4), or 160 milligrams
...
So, the minimum amount
of caffeine in two 10-ounce mugs of percolated coffee and one 12-ounce
caffeinated soft drink is approximately 160 + 30, or 190 milligrams
...
20
...
Unlawful distribution of this ebook is prohibited
...
In the graph, this
difference is represented by the length of the corresponding bar, so you can
order the four types of coffee according to the lengths of their corresponding
bars, from shortest to longest
...
The
correct answer is Choice B
...
300
200
Running
Walking
100
0
0
1
2 3 4 5 6 7 8
Speed (miles per hour)
9
If s is a speed, in miles per hour, at which the energy used per meter during
running is twice the energy used per meter during walking, then, according
to the graph above, s is between
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
2
...
0
3
...
5
3
...
0
4
...
5
4
...
0
Explanation
This question is about the speed at which the energy used per meter during
running is twice that used per meter during walking
...
Looking at the graph, you can see that for speeds greater than or equal to 3
...
0
...
0 (the
lowest speed on the graph) and 3
...
Looking at the answer choices, you see that
there is only one answer choice that is between 2
...
0; namely, Choice A,
which says the desired speed is between 2
...
0
...
409
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 1
22
...
In this question the answer choices are all in the form 2 raised to a
power, so you should try to achieve that form
...
Therefore, nn = (23)8 = 224
...
For the following question, select all the answer choices that apply
...
23
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
DBC is an equilateral triangle
...
The length of BC is equal to the length of AD
...
The length of AD is 10
...
You also know that point D is on the hypotenuse AC
...
However, because the figure is not necessarily drawn to
scale, you don’t know the lengths of AD, DC, and BC
...
1
The area of a triangle is (base)(height)
...
You already know that
2
the length of AB is 10Ί3
...
You need to consider each of the five statements individually, as follows
...
This statement implies that angle
DCB is a 60Њ angle; and therefore, triangle ABC is a 30Њ−60Њ−90Њ triangle
...
Unlawful distribution of this ebook is prohibited
...
Statement B: ABD is an isosceles triangle
...
Below are two redrawn figures showing
triangle ABD as isosceles
...
B
B
A
A
D
C
D
C
Either of the figures could have been drawn with the length of BC even
longer
...
Statement C: The length of BC is equal to the length of AD
...
Statement D: The length of BC is 10
...
Statement D provides sufficient additional
information to determine the area of triangle ABC
...
The relationship between AD and BC is
not known, so statement E does not provide sufficient additional information to
determine the area of triangle ABC
...
Therefore, the correct answer consists of
Choices A and D
...
a1, a2, a3,
...
24
...
If a1 + a3 + a5 = 27, what is the value of a2 + a4 ?
a2 + a4 =
Explanation
Note that answering this question requires information only about the first five
terms of the sequence
...
Since you are given that in this sequence each term after a1 is c greater than
the previous term, you can rewrite the first five terms of the sequence in terms of
a1 and c as follows
...
Unlawful distribution of this ebook is prohibited
...
So you can conclude
that 3a1 + 6c = 27, or a1 + 2c = 9
...
a2 + a4 = (a1 + c) + (a1 + 3c)
= 2a1 + 4c
= 2(a1 + 2c)
But a1 + 2c = 9, so a2 + a4 = 2(9) = 18
...
25
...
At the same average rate of water consumption per person, how
many days would the water supply last for 9 people?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
28
...
5
35
...
5
42
...
Assuming the same
average rate of water consumption per person, 1 person would have enough
water to last for (15)(21) = 315 days
...
The correct answer is Choice C
...
9
Therefore, since the water supply would last 21 days for 15 people, it would last
15
(21), or 35 days for 9 people
...
9
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...
Answers and Explanations
SECTION 6
Quantitative Reasoning
25 Questions with Explanations
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
Country
Value of 1 United States Dollar
Argentina
Kenya
0
...
08 shillings
Quantity A
1
...
In the table accompanying this question, both the value of the Argentine
peso and the value of the Kenyan shilling are compared to the United States
dollar
...
On the other hand, 1 United States
dollar is worth 32
...
The correct answer is Choice A
...
3k5, and 1
...
33
...
A
B
C
D
Explanation
In this question, you are given that k is a digit in the decimal 1
...
3k5 is less than 1
...
So you can see that 1
...
3k5 < 1
...
Therefore, 1
...
305 or 1
...
325, and the digit k must be 0, 1, or 2
...
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...
GRE Practice Test 1
C B D
A
AB is a diameter of the circle above
...
Quantity B
The average (arithmetic
mean) of the lengths of AC
and AD
A
B
C
D
Explanation
Recall that in a circle, any diameter is longer than any other chord that is not a
diameter
...
It follows that AC and
AD are chords that are not diameters, since there is only one diameter with
endpoint A
...
Note that the average of
two numbers is always less than or equal to the greater of the two numbers
...
The correct answer is Choice A
...
A
B
C
D
Explanation
10
...
Dividing both sides of the
10
equation s2t2 = 10 by t2, you get s2 = 2
...
t
You can look at this problem in another way
...
Since st = Ί10, it follows that
In this question you are asked to compare s2 with
s=
Ί10
, and Quantity A is equal to
t
The correct answer is Choice C
...
t
t
2
414
This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
Three consecutive integers have a sum of −84
...
The least of the three
integers
−28
A
B
C
D
Explanation
Two approaches you could use to solve this problem are:
1: Translate from words to algebra
...
Approach 1: You can represent the least of the three consecutive integers by
x, and then the three integers would be represented by x, x + 1, and x + 2
...
You can solve this equation for x as follows
...
Approach 2: You could ask yourself what would happen if the least of the
three consecutive integers was −28
...
But you were given that
the sum of the three consecutive integers is −84, which is less than −81
...
In the xy-plane, the equation of line k is 3x − 2y = 0
...
Quantity B
The x-intercept of line k
The y-intercept of line k
A
B
C
D
Explanation
Two approaches you could use to solve this problem are:
1: Reason algebraically
...
Approach 1: To solve this problem algebraically, note that given the equation
of a line in the xy-plane, the x-intercept of the line is the value of x when y
equals 0, and the y-intercept of the line is the value of y when x equals 0
...
If y = 0, then x = 0; and if x = 0, then y = 0
...
The correct answer is Choice C
...
Since two points determine a straight line, you can
do this by plotting two points on the line and drawing the line they determine
...
415
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...
GRE Practice Test 1
y
(2, 3)
x
(0, 0)
As you can see, the line passes through the origin, and so it crosses both the
x-axis and the y-axis at (0,0)
...
n is a positive integer that is divisible by 6
...
Quantity B
The remainder when n is
divided by 12
The remainder when n is
divided by 18
A
B
C
D
Explanation
One way to compare the two quantities is to plug in a few values of n
...
However, if you plug in n = 18, you find that the remainder when n
is divided by 12 is 6 and the remainder when n is divided by 18 is 0, so Quantity
B is greater than Quantity A
...
Another way to compare the two quantities is to find all of the possible
values of Quantity A and Quantity B
...
When dividing each of these integers by 12, you get
a remainder of either 0 or 6, so Quantity A is either 0 or 6
...
Note that when the value of Quantity B is 12, the value of
Quantity A, 0 or 6, is less than the value of Quantity B; but when the value of
Quantity B is 0, the value of Quantity A is greater than or equal to the value of
Quantity B
...
1−x 1
=
x−1 x
Quantity A
8
...
Since fractions are defined only when the denominator is not
x−1 x
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...
D
Answers and Explanations
equal to 0, the denominators of both of the fractions in the equation are
nonzero
...
To solve the equation for x, begin by multiplying both sides of the equation
by the common denominator x(x + 1) to get x(1 − x) = (x − 1)(1)
...
x(1 − x) = (x − 1)(1)
x − x2 = x − 1
x2 = 1
Since x2 = 1 and x ≠ 1, it follows that x = −1
...
Therefore, Quantity
2
B is greater, and the correct answer is Choice B
...
You can try plugging in a few numbers for x to see that this is true
...
1 − 7 −6
1−x
You can also show that for all values of x ≠ 1, the value of
is equal to
x−1
1 − x −(x − 1)
−1 algebraically by rewriting 1 − x as −(x − 1)
...
x−1
(x − 1)
1−x 1
Because the left side of the equation
= is equal to −1, it follows that
x−1 x
1
−1 = , and so x = −1
...
2
In a set of 24 positive integers, 12 of the integers are
less than 50
...
Quantity A
9
...
For this set of 24 integers,
you do not know the values of the two middle integers; you know only that half
of the integers are less than 50 and the other half are greater than 50
...
Thus the relationship cannot be
determined from the information given, and the correct answer is Choice D
...
Unlawful distribution of this ebook is prohibited
...
The fabric needed to make 3 curtains sells for $8
...
If the length of fabric required for each
curtain is 1
...
00
$38
...
00
$16
...
80
Explanation
Since 1
...
6), or
4
...
The fabric can be
purchased only by the full yard, so 5 yards of fabric would need to be purchased
...
00 per yard, the total cost of the fabric is $40
...
The
correct answer is Choice A
...
11
...
Which of the following statements individually provide(s) sufficient additional
information to determine whether the slope of line k is negative?
Indicate all such statements
...
The product of the x-intercept and the y-intercept of line k is positive
...
Explanation
For questions involving a coordinate system, it is often helpful to draw a figure
to visualize the problem situation
...
Conversely, you can see that if the x- and y-intercepts of a line
have the same sign then the slope of the line is negative
...
Unlawful distribution of this ebook is prohibited
...
Remember that you need to evaluate each statement by itself
...
So the information in Choice A is sufficient to determine that the slope
of line k is negative
...
You know that the product of two numbers is positive if both factors
have the same sign
...
To evaluate Choice C, it is helpful to recall the definition of the slope of a
line passing through two given points
...
”
b−s
...
Note that these are the denominator and the numerator, respectively, of
b−s
, the slope of line k
...
The information in Choice C is
sufficient to determine that the slope of line k is negative
...
The correct answer consists
of Choices A, B, and C
...
Unlawful distribution of this ebook is prohibited
...
−10t + 115
−20t + 150
The expressions in the table above give the distance from Centerville to
each of two trains t hours after 12:00 noon
...
The distance between the passenger train and Centerville at t hours
past noon is −20t + 150
...
−10t + 115 = −20t + 150
10t + 115 = 150
10t = 35
t = 3
...
5 hours
past noon, or at 3:30
...
13
...
Mark’s salary of $43,700 is the second-highest salary
in the first quartile of the 80 salaries
...
From this you can conclude that the word quartile refers to one of the
four groups that are created by listing the data in increasing order and then
dividing the data into four groups of equal size
...
Since Mark’s salary is the
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...
Answers and Explanations
second-highest in the first quartile, 18 salaries in that quartile are lower than his,
and one salary in that quartile is higher than his
...
The lowest
22 of those would be in the first quartile of the 88 salaries, and the remaining 4
(salaries 23 to 26) would be in the second quartile, followed by Mark’s salary
...
The correct
answer is Choice E
...
There are 20 positions in each
quartile, and Mark’s salary is at position 19
...
Note that position 19,
where Mark’s salary appears, is second-highest in the first quartile
...
...
Second quartile
...
8
9
20
21
22
Third quartile
Fourth quartile
23
24
25
26
27
45
46
47
48
49
67
68
69
70
71
...
1
2
Second quartile
New
salaries
Salary at
position 1 of
original list
...
To see what Mark’s position is with respect to the quartiles of the 88 salaries,
you need add the 8 new salaries to the list, renumber the list from 1 to 88, and
put 22 salaries in each quartile
...
In
particular, Mark’s salary moves from position 19 to position 27
...
Note that Mark’s salary is in position 27, the
fifth position in the second quartile
...
The correct answer is Choice E
...
Unlawful distribution of this ebook is prohibited
...
14
...
The point with coordinates (−6, 5) lies inside C, and the point with
coordinates (8, −7) lies outside C
...
In this question you are given that the point with coordinates (−6, −7) is the
center of circle C, the point with coordinates (−6, 5) lies inside circle C, and the
point with coordinates (8, −7) lies outside circle C, so you could draw the
following figure
...
You can also see
that the distance between (−6, −7) and (8, −7) is 6 + 8, or 14, and the radius of
C must be less than 14
...
The correct answer is 13
...
If −
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
m
is an even integer, which of the following must be true?
19
m is a negative number
...
m is a prime number
...
m is an even integer
...
Unlawful distribution of this ebook is prohibited
...
This means that − = 2k, or m = −19(2k) = 2(−19k),
19
which is a multiple of 2
...
You can see that none of the other choices can be the correct
answer by evaluating them as follows
...
If −
m
to be even
...
19
m
m does not have to be a positive number for −
to be even
...
19
example, if m = 38, then −
C
ɕ
The number used in (A), m = 38, shows that m does not have to be a
prime number
...
D
ɕ
Since m must be an even integer, m cannot be an odd integer
...
16
...
If v is the square of an integer, which of the
following numbers must also be the square of an integer?
Indicate all such numbers
...
You can use this fact,
together with the fact that the product and the sum of integers are also integers,
to examine the first two choices
...
So 81v is the
square of an integer
...
So
25v + 10Ίv + 1 is the square of an integer
...
To show that a given
statement is not true, it is sufficient to find one counterexample
...
If v = 4, then
4v2 + 4Ίv + 1 = 64 + 8 + 1 = 73, which is not the square of an integer
...
The correct answer consists of Choices A and B
...
Unlawful distribution of this ebook is prohibited
...
DISTANCE TRAVELED BY A CAR ACCORDING TO THE CAR’S SPEED
WHEN THE DRIVER IS SIGNALED TO STOP
110
100
90
80
70
60
50
40
30
20
10
0
Distance (feet)
Distance (feet)
Distance Traveled
During Reaction Time*
0 10 20 30 40 50 60 70 80 90 100
Speed (miles per hour)
Distance Traveled After Brakes
Have Been Applied
550
550
500
450
445
400
350
352
300
250
269
200
198
150
137
100
88
50
22
49
9
0
0 10 20 30 40 50 60 70 80 90 100
Speed (miles per hour)
*Reaction time is the time period that begins when the driver is signaled to stop
and ends when the driver applies the brakes
...
17
...
It is a good
idea to look at the graphs before you try to answer the questions, so you can
become familiar with the information contained in the graphs
...
It could be that all the information
you need to solve the problem is contained in one of the graphs, or it could be
that you need to get information from both of the graphs
...
Therefore, the
answer to this question is found using this graph by reading the speed, in miles
per hour, corresponding to a distance of 52 feet
...
On the graph, the
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...
Answers and Explanations
speed corresponding to a distance of 52 feet is a little less than 50 miles per
hour
...
18
...
At a speed of 40
miles per hour, the distance traveled during reaction time is a little less than 45
feet, and the distance traveled after the brakes have been applied is 88 feet
...
19
...
A good strategy for
solving this problem is to calculate the total stopping distance for the speeds
given in the options
...
For a speed of 55 miles per hour, the distance traveled
during reaction time is about 60 feet, and the distance traveled after the brakes
have been applied is about 170 feet; therefore, the total stopping distance is
about 60 + 170, or 230 feet
...
The correct answer is Choice A
...
Unlawful distribution of this ebook is prohibited
...
The total stopping distance for the car traveling at 60 miles per hour is
approximately what percent greater than the total stopping distance for the
car traveling at 50 miles per hour?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
22%
30%
38%
45%
52%
Explanation
To solve this problem you need to find the total stopping distance at 50 miles per
hour and at 60 miles per hour, find their difference, and then express the
difference as a percent of the shorter total stopping distance
...
At 50 miles per hour, the total
stopping distance is approximately 55 + 137 = 192 feet; and at 60 miles per hour
it is approximately 66 + 198 = 264 feet
...
375, or approximately 38%
...
192
21
...
Thus, every positive integer less than or equal to 25 is a factor of 25!
...
In view of this, it’s
reasonable to consider the next few integers greater than 25, including answer
choices A and B
...
Both 2 and 13 are factors of 25!, so 26 is
also a factor of 25!
...
However, the next integer, 29, is a prime number greater than 25, and as
such, it has no positive factors (other than 1) that are less than or equal to 25
...
However, the
question asks for an integer that is not a prime number, so 29 is not the answer
...
, but it is quicker to look at
the rest of the choices
...
Both 4 and 9 are factors
of 25!, so 36 is also a factor of 25!
...
Both 4 and
14 are factors of 25!, so 56 is also a factor of 25!
...
Although 2 is a factor of 25!, the prime number 29, as noted earlier, is
not a factor of 25!, and therefore 58 is not a factor of 25!
...
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...
Answers and Explanations
The explanation above uses a process of elimination to arrive at Choice E,
which is sometimes the most efficient way to find the correct answer
...
For if a positive integer
n is not a factor of 25!, then one of the following must be true:
(i) n is a prime number greater than 25, like 29 or 31, or a multiple of
such a prime number, like 58 or 62;
(ii) n is so great a multiple of some prime number less than 25, that it
must be greater than 58
...
The
prime factors of 25! are 2, 3, 5, 7, 11, 13, 17, 19, and 23, some of which occur
more than once in the product 25!
...
The prime number 3 occurs
once in each of these multiples, except for 9 and 18, in which it occurs twice
...
The same
reasoning can be used to find the number of times that each of the prime factors
occur, yielding the prime factorization 25! = (222)(310)(56)(73)(112)(13)(17)(19)(23)
...
Equivalently, if the positive integer n is not a factor of 25!, then,
restating (i) and (ii) above, the prime factorization of n must
(i) include a prime number greater than 25; or
(ii) have a greater exponent for one of the prime numbers in the prime
factorization of 25!
...
Clearly, all of these are greater than 58
...
22
...
Note that all
1 1
of the choices are possible orderings of the quantities , , and 1 from least to
a b
greatest
...
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...
The inequality 0 < a < 1 < b tells you that 0 < a < 1 and
1
that b > 1
...
Since b is greater than 1, the value of must be less than 1
...
O
23
...
If each circle
has radius r, what is the area of the shaded region?
A
ɕ
B
ɕ
Ί2
2
Ί3
2
r2
r2
C
ɕ
Ί2r2
D
ɕ
Ί3r2
E
ɕ
2Ί3r2
Explanation
If a geometric problem contains a figure, it can be helpful to draw additional
lines and add information given in the text of the problem to the figure
...
In this case,
drawing radius OP will divide the shaded region into two triangles, as shown in
the figure below
...
Therefore, in each of the triangles,
all three sides have length r, and each of the triangles is equilateral
...
However,
length r is
2
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...
Answers and Explanations
if you do not remember what the height is, you can use the following figure to
help you find the height
...
2
2
2
4
Since the shaded region consists of 2 equilateral triangles with sides of length r,
the area of the shaded region is (2)
Ί3
4
r2 =
Ί3
2
r2, and the correct answer is
Choice B
...
24
...
An inspector will select 2
lightbulbs simultaneously and at random from the box
...
Explanation
The desired probability corresponds to the fraction
the number of ways that 2 lightbulbs, both of which are not defective, can be chosen
the number of ways that 2 lightbulbs can be chosen
In order to calculate the desired probability, you need to calculate the values
of the numerator and the denominator of this fraction
...
Unlawful distribution of this ebook is prohibited
...
The
numerator of the fraction is the number of ways that 2 lightbulbs can be chosen
from the 18 that are not defective, also known as the number of combinations of
18 objects taken 2 at a time
...
2
2!(18−2)!
Simplifying, you get
18!
(18)(17)(16!) (18)(17)
=
=
= 153
2!16!
(2)(16!)
2
Similarly, the denominator of the fraction is the number of ways
that 2 lightbulbs can be chosen from the 20 in the box, which is
20
20!
(20)(19)(18!) (20)(19)
=
=
=
= 190
...
The correct answer
190
153
is
(or any equivalent fraction)
...
The problem states that lightbulbs are selected simultaneously
...
This is equivalent to choosing one lightbulb first and then choosing a second
lightbulb without replacing the first
...
If the first lightbulb selected is not defective,
selected will not be defective is
20
there will be 19 lightbulbs left to choose from, 17 of which are not defective
...
The probability that both lightbulbs selected will not be defective is the
19
product of these two probabilities
...
=
...
What is the perimeter, in meters, of a rectangular playground 24 meters
wide that has the same area as a rectangular playground 64 meters long
and 48 meters wide?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
112
152
224
256
304
Explanation
The area of the rectangular playground that is 64 meters long and 48 meters
wide is (64)(48) = 3,072 square meters
...
Therefore, the
same area, is 24 meters wide and
24
perimeter of the second playground is (2)(24) + (2)(128) = 304 meters
...
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...
9
GRE ®
Practice Test 2
Your goals
for this
chapter
g Take the second full-length authentic GRE®
revised General Test under actual test time limits
...
g Use your results to identify your strengths and
weaknesses
...
Practice Test 2 begins on the
following pages
...
The time allotted for each section appears at
the beginning of that section
...
Find a quiet place to work, and
set aside enough time to complete the test without being disturbed
...
Use your watch or a timer to keep track of the time limit for each section
...
However, when you take the real GRE revised
General Test on computer, you will click on your answer choices
...
If you plan to take the actual test on computer, you should type your
responses
...
You will need a supply of lined paper for this task
...
As
a result, the number of questions and time allowed per section are not the same as in the
computer-based test
...
Following this practice test you will find an answer key
...
You will also find explanations for each test question
...
Once you have worked your way through Practice Test 2, you will have a good idea
of how ready you are to take the actual test
...
For additional
test-preparation materials and suggestions, visit the GRE website at www
...
org/gre/
prepare
...
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...
You will then have 30 minutes to plan and compose
a response according to the specific instructions
...
Make sure that you respond according to the specific instructions and support your position on the
issue with reasons and examples drawn from such areas as your reading, experience, observations,
and/or academic studies
...
Be sure to develop your position fully and organize
it coherently, but leave time to reread what you have written and make any revisions you think are
necessary
...
Unlawful distribution of this ebook is prohibited
...
Analytical Writing
Issue Topic
Some people believe that corporations have a responsibility to promote the wellbeing of the societies and environments in which they operate
...
Write a response in which you discuss which view more closely aligns with your
own position and explain your reasoning for the position you take
...
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...
GRE Practice Test 2
The Graduate Record
Examinations®
SECTION 2
Analytical Writing
ANALYZE AN ARGUMENT
30 minutes
You will be given a short passage that presents an argument and specific instructions on how to
respond to that passage
...
A response to any other argument will
receive a score of zero
...
Make sure that
you respond according to the specific instructions and support your evaluation with relevant
reasons and/or examples
...
Be sure to develop your response
fully and organize it coherently, but leave time to reread what you have written and make any
revisions you think are necessary
...
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...
Analytical Writing
Argument Topic
The following appeared in a memorandum from the owner of Movies Galore, a chain of
video rental stores
...
Since we are famous for our special bargains, raising
our rental prices is not a viable way to improve profits
...
M
...
M
...
Therefore, in order to increase profits without jeopardizing our reputation for offering
great movies at low prices, we recommend implementing similar changes in our other nine
Movies Galore stores
...
Be sure to explain
how the answers to these questions would help to evaluate the recommendation
...
Unlawful distribution of this ebook is prohibited
...
Unlawful distribution of this ebook is prohibited
...
Verbal Reasoning
SECTION 3
Verbal Reasoning
Time — 35 minutes
25 Questions
For questions 1 to 8, select one entry for each blank from the corresponding column
of choices
...
1
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
2
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
3
...
Indeed it makes several longer
treatments of the effects of lost biodiversity seem (ii)________
...
Blank (ii)
D
ɕ redundant
E
ɕ pithy
F
ɕ premature
The government has no choice but to (i)________ the incessant demands for land
reform, and yet any governmental action that initiated land reform without
requisite attention to agrarian reform would (ii)________ the overall goal of
economic modernization
...
Unlawful distribution of this ebook is prohibited
...
Certain music lovers yearn for (i)________, but when it is achieved, there is
something missing; perhaps they feel uncomfortable in a world where nothing
discernible is (ii)________
...
A
ɕ dispassionate
B
ɕ problematic
C
ɕ straightforward
Blank (ii)
D
ɕ redundant
E
ɕ unsound
F
ɕ understated
Blank (iii)
G
ɕ ignored
H
ɕ discredited
I
ɕ confirmed
Only with the discovery of an ozone hole over Antarctica in 1985 did chemical
companies finally relinquish their opposition to a ban on chlorofluorocarbons
(CFCs), which destroy ozone
...
Blank (i)
A
ɕ imminent
B
ɕ imprudent
C
ɕ premature
8
...
Early attempts at such valuation resulted in
impressive but (ii)________ figures that were seized on by environmental
advocates and then, when these figures were later (iii)________, they were used by
opponents to tar the whole idea
...
Blank (ii)
Blank (ii)
D
ɕ corroborated
E
ɕ publicized
F
ɕ curtailed
Blank (iii)
G
ɕ encouraging
H
ɕ inconclusive
I
ɕ unsurprising
The incipient (i)________ regarding taxes could affect trade between the two
countries much more than the (ii)________ banana imports, which has been
going on for years
...
Blank (i)
A
ɕ row
B
ɕ accord
C
ɕ investigation
Blank (ii)
D
ɕ profitable dealing in
E
ɕ predicament regarding
F
ɕ festering dispute over
438
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...
Section 3
...
Questions 9 and 10 are based on the following reading passage
...
The shape of sauropod teeth suggested what they ate
...
Because no
modern land animals even approach sauropod size, scientists have also lacked a living
analogue to use as a guide to possible sauropod behavior
...
For the following question, consider each of the choices separately and select all that
apply
...
Which of the following can be inferred from the passage regarding the evidence
provided by sauropod teeth?
A
Ȟ The teeth allow inferences to be made about sauropod social behavior
...
C
Ȟ The teeth have no resemblance to those of any modern land animal
...
10
...
They confirm the evidence provided by trackways about sauropod
behavior
...
GO ON TO NEXT PAGE g
439
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...
GRE Practice Test 2
Questions 11 to 14 are based on the following reading passage
...
e
...
These researchers note that people with impairments in rapid eye movement (REM) sleep continue to lead normal
lives, and they argue that if sleep were crucial for memory, then these individuals
would have apparent memory deficits
...
Even if such studies were done, they could only clarify our understanding of the role of REM sleep, not sleep in general
...
But recent studies of memory performance after sleep — including one demonstrating that sleep
stabilizes declarative memories from future interference caused by mental activity
during wakefulness — make this claim unsustainable
...
But when sleep is compared with wakefulness, and performance is better after sleep, then some benefit of sleep for memory
must be acknowledged
...
The primary purpose of the passage is to
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
present the evidence that supports a particular claim regarding REM sleep
and memory
describe how various factors contribute to the effect of sleep on memory
argue against a particular position regarding sleep’s role in memory
summarize the most prevalent theory regarding sleep and memory
defend the importance of the consolidation of declarative memory
12
...
Sleep is more important to the consolidation of declarative memory than
to the consolidation of other types of memory
...
There are significant variations in the amount of sleep that people require
for the successful consolidation of memory
...
13
...
sleep”)?
A
ɕ
It provides the reasoning behind a claim about the role of sleep in
memory consolidation
...
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...
Section 3
...
D
ɕ It emphasizes the limited role sleep plays in the process of declarative
memory consolidation
...
14
...
15
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
eliminated
reinforced
put to rest
intensified
recognized
established
16
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
accord
indecision
consensus
disagreement
divergence
enthusiasm
GO ON TO NEXT PAGE g
441
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...
GRE Practice Test 2
17
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
reined in
bolstered
indemnified
propped up
manacled
lionized
18
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
bridling
exciting
forbidding
inhibiting
provoking
reversing
19
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
disaffection with
dislocation of
disentanglement from
subversion of
displacement of
estrangement from
442
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...
Section 3
...
Question 20 is based on the following reading passage
...
The
standard theory of planet formation holds that no planet that large could be formed so
close to a star, leading to the suggestion that the body is a companion star
...
20
...
If a planet’s orbit is disturbed, the planet can be drawn by gravity toward
the star it is orbiting
...
It is likely that there are many stars, in addition to Upsilon Andromedae
and the Sun, that are orbited by more than one smaller body
...
Question 21 is based on the following reading passage
...
However, perhaps part of the decline results from injuries going unreported: many employers have introduced safety-incentive programs, such as prize
drawings for which only employees who have a perfect work-safety record are eligible
...
21
...
Employers generally have to pay financial compensation to employees who
suffer work-related injuries
...
A continuing shift in employment patterns has led to a decline in the
percentage of the workforce that is employed in the dangerous occupations
in which workplace injuries are likely
...
GO ON TO NEXT PAGE g
443
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...
GRE Practice Test 2
Questions 22 and 23 are based on the following reading passage
...
Fewer than half of new novels published in Britain between 1800 and 1829 had the
author’s true name printed on the title page
...
One important tool available to researchers is the list of earlier works “by the author” often found
on title pages
...
Title pages were generally prepared last in the publication process, often
without full authorial assent, and in the last-minute rush to press, mistakes were frequently made
...
22
...
23
...
B
Ȟ Material on the title page was included without the author’s knowledge or
approval
...
444
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...
Section 3
...
line
5
The more definitions a given noun has, the more valuable is each one
...
They expand the uses of the word; language is enriched, thought is widened, and interpretations increase or dilate to fill the potentialities of association
...
The inner life of a writer often says more than most readers can know; the mind of a reader can discover truths that go beyond the intent or
perhaps even the comprehension of the writer
...
24
...
The passage suggests that a writer’s use of nouns that have multiple definitions
can have which of the following effects on the relationship between writer and
reader?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
It can encourage the reader to consider how the writer’s life might have
influenced the work
...
It can allow the reader to discern in a work certain meanings that the
writer did not foresee
...
It allows the writer to present unfamiliar ideas to the reader more
efficiently
...
This is the end of Section 3
...
Unlawful distribution of this ebook is prohibited
...
Fill all blanks in the way that best completes the text
...
The unexplained digressions into the finer points of quantum electrodynamics
are so ________ that even readers with a physics degree would be wise to keep a
textbook handy to make sense of them
...
The belief that politicians might become ________ after their election to office led
to the appointment of ethics officers at various levels of government
...
Even the charisma and technical prowess of two fine actors are not ________ the
task of fully invigorating a gray domestic drama with a tired tale to tell
...
There may be a threshold below which blood pressure reductions become
________ given that a long-running study showed no decreased heart risk for
drops in blood pressure below a certain point
...
Unlawful distribution of this ebook is prohibited
...
Verbal Reasoning
5
...
Blank (i)
A
ɕ sham
B
ɕ unpremeditated
C
ɕ justifiable
6
...
” Yet true
forgetting is (i)________ than the phenomenon of repressed memory
...
Blank (i)
A
ɕ less controlled
B
ɕ different in its effect
C
ɕ far more common
8
...
The myth is that artists are
somehow different, that they reject (i)________, but of course that’s not true: most
artists work as the rest of us do, (ii) ________, day by day, according to their own
customs
...
Blank (ii)
Blank (ii)
D
ɕ eases
E
ɕ conveys
F
ɕ entails
Blank (iii)
G
ɕ permanent
H
ɕ arduous
I
ɕ immediate
Rather than viewing the Massachusetts Bay Colony’s antinomian controversy as
the inevitable (i)________ of the intransigent opposing forces of radical and
(ii)________ beliefs, male and female piety, (iii)________ and secular power, and
the like, as other critics have, Winship argues that the crisis was not “fixed and
structural
...
Unlawful distribution of this ebook is prohibited
...
Questions 9 to 12 are based on the following reading passage
...
Building on this assumption, archaeologists asserted that adverse environmental conditions and droughts were responsible for the disappearances and
migrations of southwestern populations from many sites they once inhabited
...
To
examine the relationship between environmental variation and sociocultural change in
the Western Pueblo region of central Arizona, which indigenous tribes have occupied
continuously for at least 800 years, a research team recently reconstructed the climatic,
vegetational, and erosional cycles of past centuries
...
Rather, they found that local areas experienced different patterns
of rainfall, wind, and erosion, and that such conditions had prevailed in the Southwest
for the last 1,400 years
...
The researchers characterized episodes of variation in southwestern environments
by frequency: low-frequency environmental processes occur in cycles longer than one
human generation, which generally is considered to last about 25 years, and highfrequency processes have shorter cycles
...
In contrast, high-frequency fluctuations such
as seasonal temperature variations are observable and somewhat predictable, so that
groups could have adapted their behaviors accordingly
...
Although early Pueblo peoples did protect themselves against environmental risk
and uncertainty, they responded variously on different occasions to similar patterns of
high-frequency climatic and environmental change
...
These findings suggest that groups’ adaptive choices depended on cultural and social
as well as environmental factors and were flexible strategies rather than uncomplicated
reactions to environmental change
...
Group size
and composition, culture, contact with other groups, and individual choices and
actions were — barring catastrophes such as floods or earthquakes — more significant
for a population’s survival than were climate and environment
...
Unlawful distribution of this ebook is prohibited
...
Verbal Reasoning
9
...
Which of the following findings would most strongly support the assertion made
by the archaeologists mentioned in line 3?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
A population remained in a certain region at least a century after erosion
wore away much of the topsoil that sustained grass for their grazing
animals
...
As winters grew increasingly mild in a certain region, the nomadic
residents of the region continued to move between their summer and
winter encampments
...
A half century of drought and falling groundwater levels caused a certain
population to abandon their settlements along a riverbank
...
The fact that “adjacent agricultural fields can produce significantly different
yields” (lines 16–17) is offered as evidence of the
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
unpredictability of the climate and environment of the southwestern
United States
difficulty of producing a consistent food supply for a large population in
the Western Pueblo region
lack of water and land suitable for cultivation in central Arizona
local climatic variation in the environment of the southwestern United
States
high-frequency environmental processes at work in the southwestern
United States
GO ON TO NEXT PAGE g
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...
GRE Practice Test 2
12
...
line
5
Arctic sea ice comes in two varieties
...
To the untrained eye, all sea ice looks
similar, but by licking it, one can estimate how long a particular piece has been floating around
...
As the ice gets thicker, the rejected salt collects in tiny pockets
of brine too highly concentrated to freeze
...
Eventually, if the ice survives, these pockets of brine drain out through fine, veinlike channels, and the ice becomes fresher; multiyear ice can even be melted and drunk
...
13
...
B
Ȟ It is typically filled with fine, veinlike channels
...
14
...
Unlawful distribution of this ebook is prohibited
...
Verbal Reasoning
For questions 15 to 18, select the two answer choices that, when used to complete
the sentence, fit the meaning of the sentence as a whole and produce completed
sentences that are alike in meaning
...
It would have been disingenuous of the candidate to appear ________ when her
opponent won the election, but she congratulated the victor nonetheless
...
As market forces penetrate firms and bid up the value of attributes of labor that
are more measurable than is the knowledge born of experience, it can be
expected that trends in wages will not ________ those whose main value lies in
such experiential knowledge
...
The point we might still take from the First World War is the old one that wars
are always, as one historian aptly put it, ________: they produce unforeseeable
results
...
This is the kind of movie — stuffed with intimations of faraway strife and
people in suits talking frantically on cell phones and walkie-talkies — that is
conventionally described as a political thriller, but the film is as apolitical as it
is ________
...
Unlawful distribution of this ebook is prohibited
...
Questions 19 and 20 are based on the following reading passage
...
Admonished by government
entomologists, farmers began to diversify
...
In 1873, just before the locusts’
most withering offensive, nearly two-thirds of Minnesota farmland was producing
wheat; by the invasions’ last year, that fraction had dropped to less than one-sixth
...
In addition to planting alternative crops, many
farmers turned to dairy and beef production
...
For the following question, consider each of the choices separately and select all that
apply
...
According to the passage, before the recommendations by the government
entomologists, which of the following was true about farming west of the
Mississippi River?
A
Ȟ Farmers focused primarily on growing wheat
...
C
Ȟ A relatively small portion of farmland was devoted to crops other than
wheat
...
In the context in which it appears, “robust” (line 8) most nearly means
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
crude
demanding
productive
vigorous
rich
452
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...
Section 4
...
In 1998 the United States Department of Transportation received nearly 10,000 consumer complaints about airlines; in 1999 it received over 20,000
...
In both years the
vast majority of complaints concerned flight delays, cancellations, mishandled baggage, and customer service
...
21
...
The number of passengers flying on United States airlines was
significantly higher in 1999 than in 1998
...
The appearance in 1999 of many new Internet sites that relay complaints
directly to the Department of Transportation has made filing a complaint
about airlines much easier for consumers than ever before
...
GO ON TO NEXT PAGE g
453
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...
GRE Practice Test 2
Questions 22 to 24 are based on the following reading passage
...
Other commentators insist, however, that Notre-Dame did not have flying buttresses
until the thirteenth or fourteenth century, when they were added to update the building aesthetically and correct its structural flaws
...
It is clear, now that
nineteenth-century paint and plaster have been removed, that the nave’s lower buttresses date from the twelfth century
...
Chevron decoration, which was characteristic of the second half of
the twelfth century and was out of favor by the fourteenth century, is entirely absent
from modifications to the building that can be dated with confidence to the thirteenth
century
...
The passage is primarily concerned with
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
tracing the development of a controversy
discussing obstacles to resolving a controversy
arguing in support of one side in a controversy
analyzing the assumptions underlying the claims made in a controversy
explaining why evidence relevant to a controversy has been overlooked
23
...
Its design flaws were not apparent until flying buttresses were added in
the thirteenth or fourteenth century
...
It had been modified in some respects before flying buttresses were added
in the thirteenth or fourteenth century
...
454
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...
Section 4
...
The author’s argument concerning Notre-Dame’s flying buttresses depends on
which of the following assumptions about the choir’s lower flyers?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
They accurately reproduce the decoration on the choir’s original lower
flyers
...
They were the models for the choir’s original upper flyers
...
They were constructed after the nave’s flyers were constructed
...
The average temperature of the lobster-rich waters off the coast of Foerkland has been
increasing for some years
...
In particular, lobster
larvae take less time to reach the size at which they are no longer vulnerable to predation by young cod, the chief threat to their survival
...
25
...
The increase in water temperatures off Foerkland has not been as
pronounced as the increase in average soil temperatures in Foerkland
...
Even though lobsters grow faster in warmer waters, warmer waters have
no effect on the maximum size to which a lobster can eventually grow
...
STOP
...
455
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...
GRE Practice Test 2
SECTION 5
Quantitative Reasoning
Time—40 minutes
25 Questions
For each question, indicate the best answer, using the directions given
...
All figures are assumed to lie in a plane unless otherwise indicated
...
That is, you should not assume that quantities
such as lengths and angle measures are as they appear in a figure
...
For questions with geometric figures, you should base your answers on geometric reasoning, not on estimating or comparing quantities by sight or by measurement
...
Graphical data presentations, such as bar graphs, circle graphs, and line
graphs, are drawn to scale; therefore, you can read, estimate, or compare
data values by sight or by measurement
...
Select one of the following four answer choices and fill in the
corresponding oval to the right of the question
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity A
Quantity B
Correct Answer
A
B
C
D
Example 1:
(2)(6)
2+6
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
Q
P
S
R
Quantity A
Example 2:
Quantity B
PS
SR
Correct Answer
A
B
C
D
(since equal lengths cannot
be assumed, even though
PS and SR appear equal)
456
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...
Section 5
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity B
3−1
4−1
4
3
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
x < 1 and x ≠ 0
Quantity A
2
...
Quantity B
0
...
Quantity A
4
...
Unlawful distribution of this ebook is prohibited
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity B
Quantity A
5
...
The area of triangle PQR
Quantity A
7
...
Quantity A
8
...
Unlawful distribution of this ebook is prohibited
...
Quantitative Reasoning
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
In a quality-control test, 50 boxes—each containing 30
machine parts—were examined for defective parts
...
12
...
Quantity A
9
...
94
A
B
C
D
Questions 10 to 25 have several different formats
...
For Numeric Entry questions, follow the
instructions below
...
¼
¼
¼
¼
Your answer may be an integer, a decimal, or a fraction, and it may be
negative
...
Equivalent forms of the correct answer, such as 2
...
50, are all correct
...
Enter the exact answer unless the question asks you to round your answer
...
In year Y, the population of Colorado was approximately half that of New
Jersey, and the land area of Colorado was approximately 14 times that of
New Jersey
...
Unlawful distribution of this ebook is prohibited
...
(2y)°
35°
11
...
What is the value of y ?
y=
12
...
If a new data set is
formed by adding 3 to each number in S, what is the standard deviation of the
numbers in the new data set?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
13
...
14
...
Which of the following
lists of numbers have the same range as the numbers in list K ?
Indicate all such lists
...
Unlawful distribution of this ebook is prohibited
...
Quantitative Reasoning
15
...
What is the ratio of Aisha’s income in 2004 to her income in 2003 ?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
16
...
At those rates, how many weeks will it take
Jacob to save $500, in terms of n ?
Jacob’s weekly take-home pay is n dollars
...
LENGTH OF UNEMPLOYMENT FOR WORKERS IN REGION X FOR TWO INDUSTRIES, 2003
Manufacturing Industry
Total: 10 million
20%
1 to 4
weeks
40%
10%
18%
12%
5 to 10 weeks
11 to 14 weeks
15 to 25 weeks
26 weeks or more
Service Industry
Total: 8 million
5%
16%
14%
1 to 4
weeks
56%
9%
Note: The circle graphs show the distributions of workers who were unemployed for at
least 1 week in 2003, by length of unemployment, rounded to the nearest week
...
In the circle graphs, the degree measure of the central angle of the sector
representing the number of workers unemployed for 11 to 14 weeks is how
much greater in the manufacturing industry graph than in the service
industry graph?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
5Њ
10Њ
15Њ
18Њ
20Њ
GO ON TO THE NEXT PAGE b
461
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...
GRE Practice Test 2
18
...
8
12
16
20
If one of the workers in the manufacturing and service industries who were
unemployed for at least 1 week will be randomly selected, what is the
probability that the person selected will be a service industry worker who
was unemployed for 26 weeks or more?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
20
...
04
0
...
21
0
...
90
The ratio of the number of manufacturing industry workers who were
unemployed for 5 to 10 weeks to the number of service industry workers
who were unemployed for 5 to 10 weeks is closest to which of the
following?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
5 to 4
6 to 5
3 to 2
5 to 2
7 to 6
For the following question, select all the answer choices that apply
...
If ⎪ t+3 ⎪ > 5, which of the following could be the value of t ?
Indicate all such values
...
Unlawful distribution of this ebook is prohibited
...
Quantitative Reasoning
22
...
If x and
y are positive integers, which of the following CANNOT be zero?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
23
...
Which of the following is true about the set of all points in the plane that
are the same distance from all three points?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
24
...
It contains one point
...
It is a line
...
If x < y < 0, which of the following inequalities must be true?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
y+1
xy < y2
xy < x2
For the following question, enter your answer in the box
...
What is the length of a diagonal of a rectangle that has width 5 and
perimeter 34 ?
STOP
...
463
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 2
SECTION 6
Quantitative Reasoning
Time—40 minutes
25 Questions
For each question, indicate the best answer, using the directions given
...
All figures are assumed to lie in a plane unless otherwise indicated
...
That is, you should not assume that quantities
such as lengths and angle measures are as they appear in a figure
...
For questions with geometric figures, you should base your answers on geometric reasoning, not on estimating or comparing quantities by sight or by measurement
...
Graphical data presentations, such as bar graphs, circle graphs, and line
graphs, are drawn to scale; therefore, you can read, estimate, or compare
data values by sight or by measurement
...
Select one of the following four answer choices and fill in the
corresponding oval to the right of the question
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity A
Quantity B
Correct Answer
A
B
C
D
Example 1:
(2)(6)
2+6
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
Q
P
S
R
Quantity A
Example 2:
Quantity B
PS
SR
Correct Answer
A
B
C
D
(since equal lengths cannot
be assumed, even though
PS and SR appear equal)
464
This ebook was issued to Diane Massey, order #11560922926
...
Section 6
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity B
Quantity A
1
...
u
v
Quantity A
2
...
The number of integers that are in both set A
and set B is 20
...
The total number of integers
that are in set A or set B,
or both
Quantity B
170
GO ON TO THE NEXT PAGE b
465
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...
GRE Practice Test 2
A
ɕ
B
ɕ
C
ɕ
D
ɕ
Quantity A is greater
...
The two quantities are equal
...
x is a negative integer
...
Quantity B
2x
3x+1
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
(x + 3)( y − 4) = 0
Quantity A
6
...
This amount was
15 percent of his earnings last summer
...
The amount of Geoff’s
earnings last summer not
used to buy the new guitar
Quantity B
$3,570
Set S consists of 5 objects
...
The number of subsets
of set S that consist of
1 object
Quantity B
The number of subsets
of set S that consist of
4 objects
466
This ebook was issued to Diane Massey, order #11560922926
...
Section 6
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
The length of line segment
AC
3
A
B
C
D
Questions 10 to 25 have several different formats
...
For Numeric Entry questions, follow the
instructions below
...
¼
¼
¼
¼
Your answer may be an integer, a decimal, or a fraction, and it may be
negative
...
Equivalent forms of the correct answer, such as 2
...
50, are all correct
...
Enter the exact answer unless the question asks you to round your answer
...
What is the slope of line k in the xy-plane above?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
−5
−1
0
1
5
GO ON TO THE NEXT PAGE b
467
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 2
b − 3, b − 1, b + 2, b + 3, b + 4
11
...
What
is the average (arithmetic mean) of the five terms?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
3
4
5
6
7
For the following question, enter your answer in the box
...
What is the area of the region shown above?
13
...
At the beginning of
the year, there were 300 fish in the pond, of which 15 percent were catfish;
and at the end of the year, there were 400 fish in the pond, of which 10
percent were catfish
...
14
...
If both lights flash together at a certain time, how many
seconds later will both lights flash together the next time?
seconds
468
This ebook was issued to Diane Massey, order #11560922926
...
Section 6
...
15
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
a−b
a2 − b2
ab
a2b
a2b + ab2
x
x
16
...
The frame is 1 inch wide on all sides
...
Unlawful distribution of this ebook is prohibited
...
PERCENT OF THE 300 PEOPLE IN GROUP 1 AND THE 400 PEOPLE
IN GROUP 2 WHO HAVE SELECTED AILMENTS
Respiratory Ailment
Percent of People
in Group 1 Who
Have Ailment
Percent of People
in Group 2 Who
Have Ailment
Allergic sensitivity to endotoxins
14%
21%
Asthma (allergic)
3%
4%
Asthma (nonallergic)
2%
3%
Hay fever
4%
10%
Sneezing and itchy eyes
8%
11%
Wheezing (allergic)
5%
6%
Wheezing (nonallergic)
2%
5%
17
...
35
32
28
24
For the seven ailments, what is the median of the numbers of people in
group 2 who have the ailments?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
19
...
Unlawful distribution of this ebook is prohibited
...
Quantitative Reasoning
For the following question, enter your answer in the boxes
...
What is the ratio of the number of people in group 2 with the ailment
sneezing and itchy eyes to the total number of people in both groups with
the ailment sneezing and itchy eyes?
Give your answer as a fraction
...
Of the people in a certain survey, 58 percent were at most 40 years old and
70 percent were at most 60 years old
...
If x > 0, which of the following is equal to 1
...
Alice earns d dollars and has t percent of what she earns deducted for taxes
...
1t) dollars
d(1 − 0
...
Unlawful distribution of this ebook is prohibited
...
24
...
Which of the following values of n could be used to disprove the
student’s conjecture?
Indicate all such values
...
1
3
4
6
7
Eight points are equally spaced on a circle
...
This is the end of Section 6
...
Unlawful distribution of this ebook is prohibited
...
Analytical Writing Measure
One way to evaluate your performance on the Issue and Argument topics you answered
on this practice test is to compare your essay responses with the scored sample essay
responses for these topics and review the rater commentary
...
The Issue and Argument scoring guides start on page 37
...
Verbal Reasoning and Quantitative Reasoning Measures
The tables that follow contain information to help you evaluate your performance on
the Verbal Reasoning and Quantitative Reasoning measures of Practice Test 2
...
Compare your
answers with the correct answers given in the table, crossing out questions you
answered incorrectly or omitted
...
Knowing which questions you answered incorrectly or omitted can help you identify content areas in which you need more practice or review
...
With each answer, the key provides a number, the P+
...
P+ is used to gauge the relative
difficulty of a test question
...
You can use
the P+ to compare your performance on each test question to the performance of other
test takers on that same question
...
Alternatively, if the P+ for a question is 14, that means that 14 percent of GRE
test takers who received this question answered it correctly
...
To calculate your scores on Practice Test 2:
b
b
b
Add the number of correct answers in Sections 3 and 4 to obtain your raw Verbal Reasoning score
...
Once you have calculated your raw scores, refer to the Practice Test 2 score
conversion table on pages 479–480
...
Note the scaled scores provided
...
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...
To get a sense of how test takers are scoring on the Verbal Reasoning and Quantitative Reasoning measures of the actual test, you can review Verbal Reasoning and
Quantitative Reasoning percentile ranks on the GRE website at www
...
org/gre
/percentile (PDF)
...
Updated annually in July, this table
includes the Verbal Reasoning and Quantitative Reasoning scores on the 130–170 scale
in one-point increments and the corresponding percentile ranks
...
This is a reasonable indication of your rank among GRE revised General Test examinees if you took Practice Test 2 under standard timed conditions
...
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...
Verbal Reasoning
Question
Number P+
1
2
3
4
5
6
7
8
9
10
71
68
41
74
71
55
28
38
74
54
11
66
12
60
13
73
14
60
15
16
17
18
19
20
74
41
27
45
56
42
21
35
22
51
23
83
24
25
37
78
Correct Answer
Choice A: innocuous
Choice C: banished from
Choice C: comprehensive; Choice D: redundant
Choice B: heed; Choice F: compromise
Choice C: flawlessness; Choice D: wrong
Choice B: problematic; Choice E: unsound; Choice H: discredited
Choice A: imminent; Choice F: curtailed; Choice G: encouraging
Choice A: row; Choice F: festering dispute over
Choice B: The shape of the teeth indicates that sauropods were herbivorous
...
Choice C: argue against a particular position regarding sleep’s role in
memory
Choice A: There are some memory-consolidation processes that have
nothing to do with sleep
...
Choice B: identifies a specific function that sleep plays in the memoryconsolidation process
Choice A: eliminated AND Choice C: put to rest
Choice D: disagreement AND Choice E: divergence
Choice A: reined in AND Choice E: manacled
Choice A: bridling AND Choice D: inhibiting
Choice A: disaffection with AND Choice F: estrangement from
Choice B: If a planet’s orbit is disturbed, the planet can be drawn by gravity
toward the star it is orbiting
...
Choice B: The possibility that the title page of a work may attribute works
written by other authors to the author of that work
AND
Choice C: The possibility that the author’s name printed on a title page is
fictitious
Choice A: The title page was prepared for printing in a hurried manner
...
Choice B: nuances
Choice C: It can allow the reader to discern in a work certain meanings that
the writer did not foresee
...
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...
Verbal Reasoning
Question
Number P+
1
2
3
4
5
6
7
8
9
72
50
80
59
48
61
41
40
74
10
84
11
68
12
48
13
69
14
15
16
17
18
19
93
56
75
53
59
66
20
21
44
55
22
23
46
42
24
40
25
57
Correct Answer
Choice D: frustrating
Choice C: venal
Choice D: adequate to
Choice E: superfluous
Choice A: sham; Choice D: cloak
Choice B: habit; Choice E: ploddingly
Choice B: different in its effect; Choice F: entails; Choice G: permanent
Choice C: collision; Choice E: orthodox; Choice G: clerical
Choice C: presenting evidence to challenge an explanation and offering an
alternative explanation
Choice E: A half century of drought and falling groundwater levels caused a
certain population to abandon their settlements along a riverbank
...
AND
Choice C: It tastes saltier than perennial ice
...
AND
Choice C: A relatively small portion of farmland was devoted to crops other
than wheat
...
Choice C: arguing in support of one side in a controversy
Choice E: It was originally constructed in an architectural style that was
considered outmoded by the thirteenth or fourteenth century
...
Choice C: Because of their speeded-up growth, lobsters now get large
enough to be legal catch before they reach reproductive maturity
...
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...
Quantitative Reasoning
Question
Number P+
Correct Answer
1
2
3
4
63
80
63
45
5
6
7
8
9
67
73
48
59
35
10
60
11
12
13
14
84
54
76
65
15
66
Choice C: The two quantities are equal
...
Choice B: Quantity B is greater
...
Choice B: Quantity B is greater
...
Choice A: Quantity A is greater
...
Choice C: The two quantities are equal
...
5
Choice C: 5
Choice D: – 3
Choice B: – 7, – 4, – 2, 1, 13
AND
Choice D: 2, 3, 5, 15, 19, 22
AND
Choice E: 4, 5, 6, 24
Choice C: 6 to 5
16
51
Choice B:
17
18
19
20
21
51
49
51
45
69
22
23
24
25
42
41
40
62
2,500
n
Choice D: 18°
Choice B: 8
Choice A: 0
...
Choice E: xy x2
13
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GRE Practice Test 2
Answer Key
Section 6
...
Choice D: The relationship cannot be determined from the information
given
...
Choice C: The two quantities are equal
...
Choice D: The relationship cannot be determined from the information
given
...
Choice C: The two quantities are equal
...
Choice D: 1
Choice B: 4
156
Choice A: decreased by more than 5%
30
Choice B: a2
b2
AND
Choice C: ab
Choice C: 6
Choice D: 28
Choice C: 24
Choice C: 150%
44
(or any equivalent fraction)
68
Choice B: 2,100
x
Choice A:
80
Choice E: d (1 – 0
...
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...
Unlawful distribution of this ebook is prohibited
...
Unlawful distribution of this ebook is prohibited
...
Others believe that the only responsibility
of corporations, provided they operate within the law, is to make as much money as possible
...
In developing and supporting
your position, you should address both of the views presented
...
Proponents of this view would argue that major environmental catastrophes (e
...
,
the oil spill in the Gulf) are key examples of the damage that can be wrought when
corporations are allowed to operate unchecked
...
In fact, the expectation is simply that corporations will follow
the law, and in the course of doing so, engage in every possible tactic to their advantage in the pursuit of more and greater profit
...
The corporation arose as a model of business in which capital could be raised
through the contributions of stockholders; investors purchases shares in a company,
and their money is then used as the operating capital for the company
...
The company may itself have generally
altruistic goals (perhaps it is a think tank that advises the government on how to
improve relations with the Middle East, or perhaps it is a company built around finding
alternative forms of energy), but the immediate expectation of the investor is that he
himself will see dividends, or profits, from the investment he has made
...
, if
any
...
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...
Is it a bad thing to have a corporation negatively affect the environment (and by
extentsion, its inhabitants)? To pump noxious fumes into the atmosphere as a
by-product of its manufacturing processes? Of course, and this is why agencies such
as the EPA were established and why governments — federal, state, and local — are
expected to monitor such companies to ensure that such practices fall within the
boundaries of legal expectations
...
But the assumption that corporations have an inherent
obligation or responsibility to go above and beyond that to actively PROMOTE the
environment and the well-being of society is absurd
...
If the very purpose of a corporation is to
generate profits, and the obligation to adhere to safety expectations established by law
cuts into those profits, then to expect corporations to embrace such practices beyond
what is required is to presume that they willingly engage in an inherently selfdestructive process: the unnecessary lowering of profits
...
Treehuggers everywhere should be pleased that
environmental protections exist, but to expect corporations to “make the world a better
place” is to embrace altruism to the point that it becomes delusion
...
In
fact, the opposite is true — we should be vigilant with the business world and maintain
our expectations that corporations do not make their profits at the EXPENSE of the
well-being of society
...
Reader Commentary
This response receives a 6 for developing an insightful position on the issue in accordance with the assigned task, skillfully weaving a position that takes into consideration
both of the statements in the prompt
...
” In the second paragraph, the writer offers compelling reasons for this rejection by discussing the purpose
and structure of corporations
...
A cogent statement of the writer’s position appears at the conclusion of the
response: “we should be vigilant with the business world and maintain our expectations that corporations do not make their profits at the EXPENSE of the well-being of
society
...
” The
response as a whole is logically organized, with each paragraph serving as a stepping
stone in the development of the writer’s position
...
This sentence demonstrates the level of language facility seen throughout the
response: “If the very purpose of a corporation is to generate profits, and the obligation
to adhere to safety expectations established by law cuts into those profits, then to
expect corporations to embrace such practices beyond what is required is to presume
that they willingly engage in an inherently self-destructive process: the unnecessary
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Analytical Writing Sample Responses
lowering of profits
...
The sentence demonstrates
the outstanding nature of this response
...
Successful corporations try and
make as much money as possible
...
Corporations
have a duty and a responsability to ensure the well being of the society in which they
are a part
...
One of these is making sure that workers are well taken care of
...
One way that corporations can attract these workers is by offering them
generous benefits
...
Health care plans provided by employers mean
that these people have at their disposal health coverage, which means that they have
the care they need if they get sick
...
Another area where corporations providing support for themselves and society is
in the creation of human capital
...
One way that employers
can contribute to this is by sponsoring worker training programs, or paying for their
employees to return to school
...
An employee who
received an education sponsored by an employer may be thankful for receiving that
education, and may work harder for that employer
...
The main reason that corporations have a duty to contribute to the well being of
society is that they are a part of the society
...
A good example of this is BP, after the recent oil spill
in the gulf
...
This cost them huge amounts of money to clean up, as well as the fines
they had to pay for causing this
...
As the spill was happening, many people boycotted the company, resulting in lost
potential revenue
...
Another reason corporations have to ensure the well-being of a society is that by
makign a society better off, a company may have more consumers
...
If a
corporation tries to bring people up and increase the overall economic well being of
society, they may find that more and more people have to ability to afford their goods
...
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...
Concentrating on the long term here means that
corporations can increase their pool of potential consumers
...
While in the short term it may work
for a corporation to ignore their societal responsability, it is advantageous in the long
term for the entire corporation to make sure society is getting better
...
This is something that corportions should be
ready and willing to take advantage of, and something that society should hold them
accountable for
...
In this case, the writer argues that corporations do indeed have a responsibility
to promote the well-being of the societies and environments in which they operate,
offering several reasons and well-chosen examples to explain why it is in the interests
of corporations to fulfill these responsibilities
...
While the writer clearly
signals at the beginning his or her alignment with the first position (“Corporations
have a duty and a responsability to ensure the well being of the society of which they
are a part”), the paragraphs that follow in fact acknowledge the writer’s opening statement (“In order to survive, corporations must make money”)
...
The various reasons and examples offered are
brought together to support a thoughtful position that implicitly suggests that the two
views are not as mutually exclusive as they might first appear
...
There are some minor errors, but
overall the writer’s control of language is strong, demonstrating sentence variety and
appropriate use of vocabulary
...
Discernibly stronger than the
adequate level of analysis in a 4, the response has thoughtful, nuanced analysis of the
issue that earns it a score of 5
...
I agree
that making profits is important
...
Their customers are how they
make their money
...
Consider light bulbs
...
It is basically just a glass globe with electricity running through it! If a bulb
gets too hot, it could potentially start a fire
...
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...
Makers of light bulbs know and understand all these
dangers
...
If everyone who used light bulbs was afraid of getting
zapped profits would obviously go down and light bulbs would not be a very profitable
enterprise
...
The automobile is one of the most
dangerous tools man uses
...
Insuring that the vehicles contain designs and parts that promote customer
safety is a main focus of car manufacturers
...
For instance, air bags, anti-lock braking
systems, online crash reporting
...
These features were not cheap
to develop, but car manufacturers improved their profits anyway because they
developed products with public safety in mind, which is what customers expect
...
Worrying about the safety and actually improving it for customers is
not just a basic responsibility of corporations, but it drives their profits, too
...
Increasing the focus on
consumers, worrying about taking care of them and the environment, can only lead
to bigger profits and success for corporations in the long run
...
It supports and develops its position competently, using relevant examples
...
Specifically, its position and the examples it develops argue that businesses can
care about both profits and ethical responsibility through the ways they develop products
...
For instance, both of the examples the response uses are about product safety; the discussion of automobile design
does not advance the position much more than the prior discussion of lightbulb production
...
It demonstrates sufficient
control of the conventions of standard written English, and its main points are made
with acceptable clarity
...
g
...
” and “symbiosis relationship”) and some awkward sentences
...
Overall, then, this response demonstrates adequate development and control of language,
making the score of 4 appropriate
...
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...
This statement addresses
both views that many people have about corporations
...
Half of this argument deals with people that like the idea of corporations
...
These people are ones that have never encountered a corupt corporation
...
It isn’t until they are being faced with a problem within a
particular corporation where they either work for them or have just dealt with them
...
The other side of this argument is that many people believe corporations are just
money hungry
...
Many
small business owners will side with this argument
...
As Mark Twain once said, “The vast amount of money is only in a couple of
hands”
...
In addition, corporations are large and with
that being said they lead to more lines of coruption
...
Can these corporation owners really oversee everything that is going on? Ask any employee at a corporate office if they believe their
workplace is being ran how they think the corporation would want it
...
Just like any other issue there are two sides to the story
...
They don’t care
about the people that are helping them make money
...
Reader Commentary
This response receives a score of 3 primarily because it is limited in focus
...
” The writer
proceeds to develop an explanation of these two positions, citing the various qualities
that lead each group of people to their beliefs, but the response concludes by declaring
that “there are two sides to the story” without adopting any position of its own
...
Although the response does discuss the two opposing positions, it never discusses which view more closely aligns with the writer’s own
...
Sentences such as “Just like in any other aspects of life,
people can get images of something as being good if they only brush the outside” are
typical of the writing in this response and, despite the presence of some errors, demonstrate a sufficient control of the conventions of standard written English
...
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Analytical Writing Sample Responses
Score 2 Response
I think corporations have a responsibility to not only follow the law but also work with
the societies and enviroments they are in
...
An example of this is BP’s accident in the Gulf
of Mexico — they might have been following the law and regulations, but once an
accident happens, our societies and environments are affected
...
Now BP faces so many
liabilities and needs to pay money
...
It is also important that corporations makes as much as money possible
...
However, there are always choices that corporations can take and they can make
money by promoting the well-being of the societies and environments
...
Reader Commentary
This seriously flawed response attempts to address the task directions by considering
both of the views presented in the prompt
...
work with the societies and environments they are in
...
Instead, the writer moves on to a discussion of the financial implications of the oil spill
for BP
...
” This position is
supported with a single relevant but undeveloped reason
...
” Overall, then, this response provides few
examples in support of its claims
...
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GRE Practice Test 2
Score 1 Response
It is certainly true that some people believe that corporations have a responsibility to
promote the well being of societies and environments
...
It is easy to see why it would be
difficult for some people to decide between these two positions
...
It takes little more than
examining the recent United States financial crisis to see the ill effects suffered by
society at large when corporations focus on maximizing profits
...
The first paragraph begins with a nearly word-for-word
restatement of the prompt, which increases the length of the response but does not
demonstrate the ability to develop a position on the issue in relation to the specific task
instructions
...
The writer does nothing to relate that sentence to this specific prompt
...
Although it does demonstrate understanding of the issue, it fits the “extremely
brief” description from the scoring guide description of a 1
...
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Analytical Writing Sample Responses
SECTION 2
Analytical Writing
ANALYZE AN ARGUMENT
The following appeared in a memorandum from the owner of Movies Galore, a chain of
video rental stores
...
Since we are famous for our special bargains, raising
our rental prices is not a viable way to improve profits
...
M
...
M
...
Therefore, in order to increase profits without jeopardizing our reputation for offering
great movies at low prices, we recommend implementing similar changes in our other nine
Movies Galore stores
...
Score 6 Response
One question which needs to be addressed before implementing the recommendation
is whether there are not other ways to improve profits besides cutting operating
expenses
...
He rules out the first course, and hence claims the second option must be
chosen
...
Even if it is granted that there are only two options for increasing profitability —
cutting costs, and raising rental prices — one might wonder why raising rental prices
is so unthinkable
...
However, in making this conclusion, he makes several
assumptions without considering questions that need to be addressed
...
One would need to ask if prices could be increased slightly, while
keeping them cheap
...
Perhaps such a reputation would be widespread enough to persist
despite a slight increase in prices
...
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...
Perhaps it could instead become
known as the store with the friendliest employees
...
The author needs to answer these questions to convince us that profits are
caused by bargains, and not by the other factors that may be involved
...
The author seems to
assume that because the cost-cutting measures worked at the Marston location, it will
work at the others, but this is far from clear
...
Perhaps the most important question that needs to be asked is whether the Marston
location’s changes truly increased profitability
...
It is quite possible that the Marston location’s profits
decreased as a result of their cost cutting, and this is a question that needs to be
addressed
...
Even if the cost-cutting measures increased profitability at the Marston store last
month (and a causal relationship, though presumably assumed, is still far from
evident), there is no guarantee that such measures would continue to increase
profitability over time
...
As word gets around that the Marston store
has cut their hours and their selection, they may in fact jeopardize their reputation for
offering “great movies at low prices
...
If, as mentioned above, Movies Galore is famous for more than its
great bargains — if customers prefer Movies Galore because of its selections, as well —
then such a move may drastically reduce profits over time
...
Reader Commentary
This outstanding response clearly addresses the specific task directions and presents a
cogent, insightful analysis by discussing specific questions that need to be addressed in
order to analyze the argument presented
...
The
response articulately discusses the information needed to evaluate whether the recommendation is likely to have the predicted result and demonstrates how this information
would help to evaluate the recommendation
...
g
...
One would need to ask
...
Throughout this response, the writer provides the
cogent development typical of a 6 response
...
g
...
Unlawful distribution of this ebook is prohibited
...
Perhaps it already is
...
Transitions are natural, and the paragraphs build on one another,
succinctly and completely developing the writer’s points
...
Score 5 Response
Management’s prediction that declining profits could be reversed by reducing
operating hours and reducing stock seems to be rash since there is little evidence that
proper research has been conducted
...
The management states that the downtown Marston store “significantly decreased
its operating expenses by closing at 6:00pm rather than 9:00pm
...
Could it be that most people renting movies have
normal working hours and have leisure time at night and to fill that time they turn to
renting movies? If management researches its daily rental history, it may discover that
its peak rental hours are between 6:00pm and 9:00pm
...
If management
wants to reverse a decline in profits by cutting hours of operation and thereby reducing
expenses, it would be adventageous to determine through research which block of
time during the day is the least profitable and then cut those hours of operation
...
The management then states that operating expenses will also be cut “by
eliminating all movies released ore than five years ago
...
Is it possible that the success of a movie rental
business is based on its ability to provide customers with a wide array of movie
selections, both new and old? It could be dangerous for this business to eliminate its
stock of older movies without first determining the percentages of income that come
from each product
...
Even if little profit does come from older movies, it may still be unwise to
eliminate the stock of older movies
...
This may be especially relevent in the case of a new movie that is a sequal to an older
movie or part of a trilogy
...
The management states that Movie Galore already has a “reputation for
offering great movies
...
Overall, the management makes a prediction that is untrustworthy and potentially
damaging
...
If the proper
investigation is implemented by the management, Movies Galore stores may reverse
the recent decline of profits
...
Unlawful distribution of this ebook is prohibited
...
The response approaches
the task by asking questions that seek to understand whether the management of
Movies Galore truly understands where its greatest profits are generated
...
” In both cases, the writer indicates the specific
kinds of information that management would need to gather (e
...
, “If management
researches its daily rental history, it may discover that its peak rental hours are
between 6:00pm and 9:00pm”) in order to determine whether its prediction is valid
...
g
...
In general, then, development of
the points the writer makes is thorough, but it is not as compelling as that required for
a 6
...
In general, writing skills, in
spite of a few spelling errors and some repetitious sentence structuring (several sentences in both the second and third paragraphs depend upon an “if
...
” In terms of writing skill and analysis, then, this
response earns a score of 5
...
This reduction would consist of closing the stores 3 hours early and
reducing its stock to include movies released only within the last 5 years
...
First, it is necessary to ask if the Marston store is similar to the other Movies Galore
stores
...
The performance of the other stores would be a critical piece to this
proposition since what works for one store, may not work for another
...
It is
possible that only a brief period of low profits, consistent with variablity in the market,
spurred the reduction and this actually caused a greater decrease in profits
...
Data regarding profits from several months before and several
months after the reduction in operating expenses would be necessary to determine if
this reduction was at all helpful
...
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...
Perhaps closing early resulted in such a decline in the operating
costs as employees did not have to be paid, that the reduction in their stock was
unnecessary
...
A more in depth analysis of
the variables involved is necessary
...
Specifically, the necessity of the reduction in
other stores shoudl be determined, data regarding the effectiveness of the reduction in
operating expenses in the Marston store should be analyzed, and an analysis of the
components of this reduction should be completed
...
In accordance with the task directions, the
response raises appropriate questions that could help to evaluate the recommendation
and its predicted result
...
e
...
For example, the relatively brief second paragraph supports the assertion that the downtown Marston store may not be comparable
to the chain’s other stores, but it does so with minimal reasoning
...
A basic organizational structure, aided by the use of
simple transitions between paragraphs and sufficient sentence variety within paragraphs, are other qualities of this response that underscore its adequacy
...
There are some minor grammatical errors and typos (e
...
,
there is a tense error in paragraph 3: “what effect did the reduction in operating
expenses had on store profits in Marston?”; there is also vague diction in the same
paragraph: “Because the declines in profit are termed to be ‘recent’ and that the reduction of operating expenses happened within the last month, this is unclear”), but the
response manages to convey ideas with acceptable clarity overall
...
Score 3 Response
It is imperative that “Movies Galore” must find a way to reduce operating expenses
without jepardizing its popularity with the customer
...
The reduction of hours needs to be reversed
...
People go to the video store to rent movies more frequently in the evening
hours than in the morning
...
The
adjustment in hours can be structured so that the store opens later in the morning, and
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...
GRE Practice Test 2
costomers can simply return the movies in a drop box, allowing the store to remain
open later in the evening for people who want to rent movies
...
Unlike food moves don’t
go bad after a certain amount of time
...
It would be bad business to assume that people will not want to rent
movies over five years old, and “Movies Galore” might actually lose customers if they
do so
...
The basic ideas of cutting stock and reducing operating hours do indicate saving
money, however only if it is done correctly with both the business and the consumer in
mind
...
” So they
need to consider exactly how their proposals are going to impact the consumer and
whether or not they will actually lose business by putting these policies in place
...
Reader Commentary
While this response conveys ideas with acceptable clarity, despite an occasional error,
it earns a score in the lower half because it mainly discusses tangential matters
...
” And that is what paragraphs 2 and 4 do: they avoid relevant
analysis and instead engage in analyzing tangential matters and generally agreeing
with the prompt
...
Paragraph 4 agrees with the overall recommendation
and concludes that Movies Galore is generally going in the right business direction
...
So, although the response exhibits competent control of the conventions of standard written English, it does not manage to exhibit adequate development of relevant
analysis
...
Thus, it merits a score of 3
...
Thus to increase
the profits, offering movies at low prices can be one of the ways
...
Raising the rental prices of the videos
would not be a better option because this will not lead to an increase in the profits
made by the company
...
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Analytical Writing Sample Responses
The increase in the profits can also be brought about by giving various exciting
offers at different occassions, for example- buy three and get one free video at the time
of Christmas , New Year etc can attract more and more customers towards the stores
and also bring about an increase in the profits earned by the stores
...
Thus, in order to increase
the profits without jeopardizing the reputation of the stores , it is recommended to
implement the similar changes as mentioned above in all the other nine Movies Galore
stores
...
It
does not follow the directions of the assigned task
...
The
response also develops ideas poorly and contains serious errors in grammar, usage, and
mechanics, such as in this sentence: “If the customers will get videos in lower price in
comparsion to the rent, they will prefer to purchase more videos then taking them on
the rent
...
Score 1 Response
Yes reducing the price of the movies would attract more coustmers
...
Watching a movie in the theater would be lesser than renting the movie
...
They had to shut down their store at 6:00pm instead of 9:00pm
Reader Commentary
This response is fundamentally deficient
...
The “Yes” that begins the first sentence makes it seem as if the writer is responding to a claim made in the prompt, but
the fact that the remainder of the sentence makes a claim that never appears in the
prompt (i
...
, “reducing the price of the movies would attract more coustmers”) suggests, at best, a very limited understanding of the argument
...
The second paragraph consists almost entirely of verbatim or poorly
paraphrased material from the prompt and, as such, provides no additional evidence
either that the writer understands the argument or that the writer has the ability to
develop an organized response
...
495
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...
GRE Practice Test 2
Answers and Explanations
SECTION 3
Verbal Reasoning
25 Questions with Explanations
For questions 1 to 8, select one entry for each blank from the corresponding column
of choices
...
1
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
innocuous
conspicuous
robust
menacing
distinctive
Explanation
The sentence begins with “Although,” indicating that the correct answer will contrast
in tone with the “alarming term ‘invasive species
...
” All the other choices are consistent with
being alarming
...
2
...
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
lured to
enchanted with
banished from
protected by
immured in
Explanation
The words “Far from being” and the mention of “cutbacks” imply that the correct
answer will create a contrast with the idea that “serious researchers are playing a growing role in innovation
...
Choices A, B, D, and E do not create any such
contrast
...
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Answers and Explanations
3
...
Indeed it makes several longer
treatments of the effects of lost biodiversity seem (ii)________
...
The “brief
survey,” like any survey, could in fact be surprisingly “distorted,” “objective,” or “comprehensive
...
Of the three choices, only “comprehensive”
is particularly unexpected of a brief survey
...
If the short survey is surprisingly comprehensive, then longer treatments may
not convey any useful additional information, making them “redundant
...
Reading the sentence again with “comprehensive” and “redundant” filling the
blanks confirms that these two choices result in a coherent whole
...
4
...
Blank (i)
A
ɕ anticipate
B
ɕ heed
C
ɕ silence
Blank (ii)
D
ɕ delineate
E
ɕ condone
F
ɕ compromise
Explanation
The sentence informs us that the government has an “overall goal,” and the use of “and
yet” indicates that initiating land reform without attending to agrarian reform would
have some negative consequence for that goal
...
” The use of “and yet” also implies that the government’s response to the demands for land reform must be in line with initiating such
reform, so Choice C, “silence,” is incorrect
...
Only “heed”
describes an appropriate response
...
497
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...
GRE Practice Test 2
5
...
Blank (i)
A
ɕ novelty
B
ɕ beauty
C
ɕ flawlessness
Blank (ii)
D
ɕ wrong
E
ɕ visionary
F
ɕ changed
Explanation
The structure of the sentence alerts us that it will describe a kind of contradiction or
paradox: music lovers want something, but when they get what they want, they discover some cause for dissatisfaction
...
Thus, the correct answer is flawlessness (Choice C) and wrong (Choice D)
...
Putting a cash value on the ecological services provided by nature — such as the
water filtration “service” provided by a forested watershed — has, historically,
been a (i)________ process
...
Blank (i)
A
ɕ dispassionate
B
ɕ problematic
C
ɕ straightforward
Blank (ii)
D
ɕ redundant
E
ɕ unsound
F
ɕ understated
Blank (iii)
G
ɕ ignored
H
ɕ discredited
I
ɕ confirmed
Explanation
The correct response for the first blank cannot be determined without considering the
second sentence
...
Neither Choice D, “redundant,” nor Choice F, “understated,” makes sense
when coupled with the preceding “impressive but
...
Once “unsound” is selected for the second blank, it follows that “confirmed” cannot
be correct for the third blank
...
” Since the figures were unsound, it is natural that they
would later be “discredited
...
From the second sentence it is
clear that the process of putting a cash value on the ecological services provided by
nature is neither “dispassionate” nor “straightforward
...
”
Thus, the correct answer is problematic (Choice B); unsound (Choice E); and discredited (Choice H)
...
Unlawful distribution of this ebook is prohibited
...
Only with the discovery of an ozone hole over Antarctica in 1985 did chemical
companies finally relinquish their opposition to a ban on chlorofluorocarbons
(CFCs), which destroy ozone
...
Blank (i)
A
ɕ imminent
B
ɕ imprudent
C
ɕ premature
Blank (ii)
D
ɕ corroborated
E
ɕ publicized
F
ɕ curtailed
Blank (iii)
G
ɕ encouraging
H
ɕ inconclusive
I
ɕ unsurprising
Explanation
According to the first sentence, chemical companies opposed a ban on CFCs and then
changed their stance in 1985 with the discovery of an ozone hole
...
”
What follows the colon in the second sentence explains why the chemical industry
“no longer felt compelled to oppose” a ban on CFCs
...
Among the choices for the third blank, only “encouraging” has a sufficiently positive
connotation
...
Since the completed third blank now indicates that studies of CFC substitutes have been successful, “curtailed” makes the most
sense in the second blank
...
Thus, the correct answer is imminent (Choice A); curtailed (Choice F); and
encouraging (Choice G)
...
The incipient (i)________ regarding taxes could affect trade between the two
countries much more than the (ii)________ banana imports, which has been
going on for years
...
Blank (i)
A
ɕ row
B
ɕ accord
C
ɕ investigation
Blank (ii)
D
ɕ profitable dealing in
E
ɕ predicament regarding
F
ɕ festering dispute over
Explanation
The words “both disagreements” at the end of the second sentence indicate that both
blanks should be filled with words or phrases that are synonyms for “disagreement
...
(Note that the word “row” has many meanings, one of which is “a quarrel
...
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...
GRE Practice Test 2
For each of questions 9 to 14, select one answer choice unless otherwise instructed
...
line
5
10
Fossil bones of the huge herbivorous dinosaurs known as sauropods were first discovered and studied between 1840 and 1880, providing evidence for the gargantuan
dimensions of the adults
...
But
aside from trackways, or series of fossilized footprints — which established that sauropods at least occasionally lived in herds — fossils incorporating direct evidence of other
behavior, such as reproductive behavior, have been almost nonexistent
...
Until the recent discovery of
fossilized sauropod nesting grounds, scientists were thus uncertain whether sauropods
laid eggs or gave birth to live young
...
For the following question, consider each of the choices separately and select all that
apply
...
Which of the following can be inferred from the passage regarding the evidence
provided by sauropod teeth?
A
Ȟ The teeth allow inferences to be made about sauropod social behavior
...
C
Ȟ The teeth have no resemblance to those of any modern land animal
...
Choice A is incorrect: the passage mentions that fossilized footprints permit the
inference that sauropods exhibited herd behavior, but there is no indication that this or
any other social behavior can be inferred from sauropod teeth
...
”
Choice C is incorrect: the passage says that there are no modern land animals similar in size to sauropods, not that there are no such animals with similar teeth
...
Unlawful distribution of this ebook is prohibited
...
10
...
They confirm the evidence provided by trackways about sauropod
behavior
...
Explanation
Choice A is the only correct answer
...
Until this discovery, except for the trackways that showed herd
behavior, “fossils incorporating direct evidence” of sauropod behavior were “almost
nonexistent” (lines 5–6)
...
There is no information in the passage to suggest that the nesting
grounds confirmed evidence provided by the trackways, or even that the trackway evidence needed confirming
...
Nothing in the passage suggests that there are theories of the nature of sauropod herd behavior that have been
reevaluated
...
Unlawful distribution of this ebook is prohibited
...
line
5
10
15
Some researchers contend that sleep plays no role in the consolidation of declarative
memory (i
...
, memory involving factual information)
...
Yet the same researchers acknowledge that the
cognitive capacities of these individuals have never been systematically examined, nor
have they been the subject of studies of tasks on which performance reportedly
depends on sleep
...
These researchers also claim that improvements of memory overnight can be
explained by the mere passage of time, rather than attributed to sleep
...
Certainly there are memory
consolidation processes that occur across periods of wakefulness, some of which
neither depend on nor are enhanced by sleep
...
Description
The passage presents and then rebuts two arguments made by researchers who question the contribution of sleep to the consolidation of declarative memory (memory
involving factual information)
...
In response, the passage says that these
researchers themselves acknowledge the absence of systematic study of such individuals’ cognitive abilities, study that would be necessary in order to fully support the
researchers’ claim
...
The second claim is that improvements
of memory that occur overnight might be explained merely by the passage of time
...
11
...
Therefore, Choice C is correct
...
Choice
B is incorrect: the passage is concerned with the effect of sleep on memory, but not
with any factors that contribute to that effect
...
Unlawful distribution of this ebook is prohibited
...
Instead, it cites a claim and then assesses and rejects that
claim
...
12
...
Sleep is more important to the consolidation of declarative memory than
to the consolidation of other types of memory
...
There are significant variations in the amount of sleep that people require
for the successful consolidation of memory
...
Explanation
The passage states that “there are memory-consolidation processes that occur across
periods of wakefulness
...
Choices B, C, and D are
incorrect: the passage does not discuss types of memory other than consolidative memory, the relative importance to consolidative memory of REM and non-REM sleep, or
differences among individuals in the amount of sleep they require
...
The last sentence of the passage indicates that performance on memory tasks
has been found to be better after sleep than after periods of wakefulness
...
Which of the following best describes the function of the sentence in lines 14–16
(“Certainly
...
It explains why a previous claim about sleep and memory is
unsustainable
...
It emphasizes the limited role sleep plays in the process of declarative
memory consolidation
...
Explanation
The cited sentence begins with the word “Certainly,” a clue that the sentence will concede that the researchers are not entirely wrong: in this instance, they are not wrong
about memory consolidation occurring during periods of wakefulness
...
Choice A is incorrect: the sentence deals with memory consolidation during
wakefulness, not with the role of sleep in memory consolidation
...
Choice C is incorrect: the sentence does not
demonstrate anything
...
Unlawful distribution of this ebook is prohibited
...
Choice D is
incorrect: while the sentence does acknowledge that some memory-consolidation
processes are not dependent on sleep, it does not go so far as to claim that sleep plays
a limited role in memory consolidation generally
...
The importance of the study mentioned in lines 12–14 is that it
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
reveals the mechanism by which declarative memory is stabilized during
sleep
identifies a specific function that sleep plays in the memory-consolidation
process
demonstrates that some kinds of mental activity can interfere with
memory consolidation
suggests that sleep and wakefulness are both important to memory
consolidation
explains how the passage of time contributes to memory consolidation
Explanation
The question asks what “the importance of the study mentioned in lines 12–14” is
...
This protection of
memory from interference is the “specific function” played by sleep mentioned in
Choice B
...
Choice A is incorrect: there is no description
of any mechanism, or specific process, by which declarative memory is stabilized
...
For questions 15 to 19, select the two answer choices that, when used to complete
the sentence, fit the meaning of the sentence as a whole and produce completed
sentences that are alike in meaning
...
In American Indian art, the supposed distinction between modern and traditional
was fabricated by critics, and when artists have control over interpretation of
their own work, the distinction appears, happily, to have been ________
...
Accordingly, when the sentence reports a
happy outcome, this must mean that the distinction has been abandoned or rejected
...
Thus, the correct answer is eliminated (Choice A) and put to rest (Choice C)
...
Unlawful distribution of this ebook is prohibited
...
Notwithstanding their ________ regarding other issues, township residents have
consistently passed the board of education’s annual budget
...
” “Accord” and “consensus” are similar in meaning but do not provide the required contrast
...
“Indecision” fits the context, but there is no other word among
the possible choices that matches it closely
...
17
...
A
Ȟ
B
Ȟ
C
Ȟ
D
Ȟ
E
Ȟ
F
Ȟ
reined in
bolstered
indemnified
propped up
manacled
lionized
Explanation
The “market rivals” would clearly like to see the company experience some negative
outcome
...
Thus, the correct answer is reined in (Choice A) and manacled (Choice E)
...
Unlawful distribution of this ebook is prohibited
...
Skeptics contend that any scheme for charging visitors to Web sites that rewards
the vendor adequately would require steep prices, ________ the kind of frequent,
casual use of Web sites that surfers now take for granted
...
To justify the skeptics’ reaction, the “steep prices” must be associated
with a decrease in visitor volume
...
“Forbidding” is too strong:
steep prices might dissuade a casual visitor, but they would not forbid one
...
Thus, the correct answer is bridling (Choice A) and inhibiting (Choice D)
...
It seems obvious that Miles Davis’ ________ the Juilliard School, which resulted
in his decision to drop out, was based on the school’s training of musicians for a
kind of music that he did not want to play
...
” Only “disaffection with” and
“estrangement from” are consistent with a decision to drop out and result in sentences
nearly alike in meaning
...
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...
Answers and Explanations
For each of questions 20 to 25, select one answer choice unless otherwise instructed
...
Astronomers found a large body orbiting close to the star Upsilon Andromedae
...
A subsequent discovery puts that suggestion in doubt: two other large bodies were found orbiting close to Upsilon Andromedae, and the standard theory of companion stars allows
for at most one companion star
...
Which of the following, if true, most helps to resolve the status of the orbiting
body without casting doubt on the two standard theories mentioned?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
The smaller a planet orbiting a star is, and the farther away it is from the
star, the less likely it is to be discovered
...
The largest of the bodies orbiting Upsilon Andromedae is the farthest
away from the star, and the smallest is the nearest
...
In most cases of companion stars, the smaller companion is much fainter
than the larger star
...
The question asks what would resolve this conflict without casting doubt on either one of the theories
...
This explanation also leaves the standard theory of companion stars
intact
...
Choice C is
incorrect as well, since whatever the relative size and position of the three bodies may be,
all three appear to be too close according to the standard theories
...
Choice E is similarly irrelevant and thus incorrect: information about the brightness of a star relative to its companion star does not help clarify the status of the large bodies discussed in the passage
...
Unlawful distribution of this ebook is prohibited
...
In Gilavia, the number of reported workplace injuries has declined 16 percent in the
last five years
...
Since a workplace injury would disqualify an employee from such programs, some
employees might be concealing injury, when it is feasible to do so
...
Which of the following, if true in Gilavia, most strongly supports the proposed
explanation?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
In the last five years, there has been no decline in the number of workplace
injuries leading to immediate admission to a hospital emergency room
...
Many injuries that happen on the job are injuries that would be impossible
to conceal and yet would not be severe enough to require any change to
either the employee’s work schedule or the employee’s job responsibilities
...
Employers who have instituted safety-incentive programs do not in general
have a lower proportion of reported workplace injuries among their
employees than do employers without such programs
...
If the number of injuries that cannot be concealed —
such as injuries requiring immediate emergency care — has not declined in the same
period, that could help bolster the claim that the decline in overall reported injuries
may be a result of concealable injuries going unreported rather than an actual decline
in workplace injuries in general, so Choice A is correct
...
More reported injuries
would not support the author’s argument, making Choice B incorrect
...
While a decline in dangerous occupations could well
result in a decrease in workplace injuries, this fact would challenge the author’s
argument, not support it, so Choice D is incorrect
...
508
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...
Answers and Explanations
Questions 22 and 23 are based on the following reading passage
...
Fewer than half of new novels published in Britain between 1800 and 1829 had the
author’s true name printed on the title page
...
One important tool available to researchers is the list of earlier works “by the author” often found
on title pages
...
Title pages were generally prepared last in the publication process, often
without full authorial assent, and in the last-minute rush to press, mistakes were frequently made
...
The passage explains that few
authors during this period used their real names and goes on to describe how title
pages can facilitate — but also hamper — efforts to attribute these works
...
22
...
Choice A is incorrect: the passage mentions that the attribution of early-nineteenthcentury fiction was sometimes achieved when the author came forward to acknowledge a previously anonymous work (lines 4–5), so Choice A can be eliminated
...
Since the mistake most likely to “create new confusion” would be the inclusion of works not written by the author, Choice B may be
inferred
...
had the author’s true name printed on the title page
...
Hence,
Choice C may be inferred
...
Unlawful distribution of this ebook is prohibited
...
23
...
B
Ȟ Material on the title page was included without the author’s knowledge or
C
Ȟ
approval
...
Explanation
Choices A and B are correct
...
This indicates
that title pages were often prepared for printing in a hurried manner; hence, Choice A
can be inferred
...
Choice C is incorrect: nowhere does the passage speculate about commercial
motives for falsifying information on title pages
...
Questions 24 and 25 are based on the following reading passage
...
Multiple definitions, each subtly different from all the others, convey multiple shades of meaning
...
The very impossibility of absoluteness in the definition of certain nouns adds to the levels of
connotation they may reach
...
And all of it finds expression because a
word can mean many things
...
The passage describes how this increases possibilities for interpretation and the expression of ideas, thus enriching the relationship
between readers and writers
...
In the context in which it appears, “shades” (line 2) most nearly means
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
reminders
nuances
obscurities
coverings
degrees
510
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...
Answers and Explanations
Explanation
In the context in which it appears, “shades” is used to refer to the subtle distinctions in
meaning that are made possible by “multiple definitions, each subtly different from all
the others
...
In deciding between Choice B and Choice E, one should bear in mind that the sentence
focuses on subtle differences in meaning as opposed to different degrees of emphasis
for the same meaning
...
25
...
It can cause the reader to become frustrated with the writer’s failure to
distinguish between subtle shades of meaning
...
It allows the writer to provide the reader with clues beyond the word itself
in order to avoid ambiguity
...
Explanation
Lines 7–8 clearly indicate that multiple meanings of words enable readers to “discover
truths that go beyond the intent or perhaps even the comprehension of the writer”;
hence, Choice C is the correct answer
...
511
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...
GRE Practice Test 2
SECTION 4
Verbal Reasoning
25 Questions with Explanations
For questions 1 to 8, select one entry for each blank from the corresponding column
of choices
...
1
...
A
ɕ uninteresting
B
ɕ controversial
C
ɕ unsophisticated
D
ɕ frustrating
E
ɕ humorless
Explanation
An initial reading of this sentence might suggest that the blank should be filled with a
word like “complex” that indicates how hard it is to “make sense of” the digressions
...
Focusing on the second
half of the sentence suggests a different interpretation
...
If the digressions are “uninteresting,” “unsophisticated,” or “humorless,” the
sentence provides no reason to think it would be wise to make sense of them, and if
they are “controversial,” it provides no reason to think that a textbook would help
...
Thus, the correct answer is frustrating (Choice D)
...
The belief that politicians might become ________ after their election to office led
to the appointment of ethics officers at various levels of government
...
Of the choices provided, only “venal” fits that context
...
Thus, the correct answer is venal (Choice C)
...
Unlawful distribution of this ebook is prohibited
...
Even the charisma and technical prowess of two fine actors are not ________ the
task of fully invigorating a gray domestic drama with a tired tale to tell
...
The “even the” followed by positive characteristics indicates that the actors
did not meet that challenge; “adequate to” is the only answer choice that conveys this
sense
...
4
...
A
ɕ worthwhile
B
ɕ indiscernible
C
ɕ arduous
D
ɕ significant
E
ɕ superfluous
Explanation
The portion of the sentence that begins with “given that” provides a reason for a conclusion reached in the first part of the sentence
...
”
Thus, the correct answer is superfluous (Choice E)
...
Unlawful distribution of this ebook is prohibited
...
Unlike the problems in recent financial scandals, issues raised by the regulators
in this case appear largely to pertain to unwieldy accounting rules that are open
to widely divergent interpretations — not to (i)________ transactions designed to
(ii)________ corporate malfeasance
...
” Clearly, these latter issues must have
involved wrongdoing
...
For the first blank, only “sham” fits; “unpremeditated” or “justifiable” transactions could not be designed to cloak malfeasance
...
6
...
The myth is that artists are
somehow different, that they reject (i)________, but of course that’s not true: most
artists work as the rest of us do, (ii) ________, day by day, according to their own
customs
...
” This view is contrasted with a myth that artists are
“somehow different
...
Rejecting “latitude” might well
match being governed by work routines, and though “materialism” is sometimes
rejected by artists, it is not relevant to having work routines
...
Thus, the correct answer is habit (Choice B) and ploddingly (Choice E)
...
Unlawful distribution of this ebook is prohibited
...
Repression of painful memories is sometimes called “willed forgetting
...
In spite of
the effort that it (ii)________, repressing unwanted memories is less (iii) ________
than truly forgetting them, for repressed memories are prone to come back
...
The third sentence sets up a comparison between repressing memories and forgetting them
...
Choice G,
“permanent,” is the only choice that is related to the tendency to come back
...
One would
ordinarily expect that something entailing effort would be more rather than less permanent
...
Filling the second and third blanks makes it possible to fill the first blank
...
Thus, Choice B, “different in its
effect,” is correct
...
8
...
”
Blank (i)
A
ɕ dissolution
B
ɕ melding
C
ɕ collision
Blank (ii)
D
ɕ revolutionary
E
ɕ orthodox
F
ɕ questionable
Blank (iii)
G
ɕ clerical
H
ɕ civil
I
ɕ cerebral
Explanation
The words “Rather than” indicate that the other critics, unlike Winship, think of the
controversy as “fixed and structural
...
The second and third blanks appear in a series of examples of such opposing forces; only “orthodox” contrasts with “radical” in the second
blank and only “clerical” contrasts with “secular” in the third blank
...
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...
GRE Practice Test 2
For each of questions 9 to 14, select one answer choice unless otherwise instructed
...
line
5
10
15
20
25
30
35
40
Until recently, many anthropologists assumed that the environment of what is now the
southwestern United States shaped the social history and culture of the region’s indigenous peoples
...
However, such deterministic arguments fail to acknowledge that local environmental variability in the Southwest makes generalizing about that environment difficult
...
The researchers found it impossible to provide a single, generally applicable characterization of environmental conditions for the region
...
Rainfall, for example, varied within and between local valley
systems, so that even adjacent agricultural fields can produce significantly different
yields
...
The researchers pointed out that low-frequency
processes, such as fluctuations in stream flow and groundwater levels, would not usually be apparent to human populations
...
When the researchers compared sequences of sociocultural change in the Western Pueblo region with episodes of
low- and high-frequency environmental variation, however, they found no simple correlation between environmental process and sociocultural change or persistence
...
The researchers identified seven major
adaptive responses, including increased mobility, relocation of permanent settlements,
changes in subsistence foods, and reliance on trade with other groups
...
Environmental conditions mattered, but they were rarely, if ever,
sufficient to account for sociocultural persistence and change
...
Description
The passage describes research that bears on a presumed historical relationship
between environmental variation and sociocultural change among indigenous people
of the southwestern United States
...
Unlawful distribution of this ebook is prohibited
...
The passage then goes on to point out
studies that show problems with this explanation, including the lack of generally applicable characterizations of the environment in the region and lack of correlation
between environmental changes and sociocultural changes
...
9
...
The passage does not mention the creation of controversy or discuss flaws in
research methodology; therefore, Choices A and B are incorrect
...
The passage presents recent research findings but not in defense
of a long-held interpretation; therefore, Choice E is incorrect
...
Which of the following findings would most strongly support the assertion made
by the archaeologists mentioned in line 3?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
A population remained in a certain region at least a century after erosion
wore away much of the topsoil that sustained grass for their grazing
animals
...
As winters grew increasingly mild in a certain region, the nomadic
residents of the region continued to move between their summer and
winter encampments
...
A half century of drought and falling groundwater levels caused a certain
population to abandon their settlements along a riverbank
...
The question asks which finding would support this assertion
...
Choice D is incorrect
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...
GRE Practice Test 2
because it does not mention a change in environmental conditions and therefore cannot support an assertion about the effects of changing environmental conditions
...
11
...
Choice A is incorrect: while such variability might
give rise to unpredictability, that is not how the difference in agricultural yields is being
used as evidence in the passage
...
Choice E is incorrect: a discussion of highand low-frequency processes occurs in the third paragraph, but the author does not
present geographic differences in rainfall and agricultural yield as either a high- or a
low-frequency environmental process
...
It can be inferred from the passage that which of the following activities is NOT
an example of a population responding to high-frequency environmental
processes?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
Developing watertight jars in which to collect and store water during the
rainy season
Building multistory dwellings in low-lying areas to avoid the flash
flooding that occurs each summer
Moving a village because groundwater levels have changed over the last
generation
Trading with other groups for furs from which to make winter clothes
...
You are
asked to choose the one answer choice that does not provide such an example
...
Unlawful distribution of this ebook is prohibited
...
Choice C is the best answer: the passage mentions fluctuations in ground water levels
as a low-frequency process (lines 21–22); moving a village because of a change that
takes place over the course of a generation is not a response to a high-frequency
process
...
line
5
Arctic sea ice comes in two varieties
...
To the untrained eye, all sea ice looks
similar, but by licking it, one can estimate how long a particular piece has been floating around
...
As the ice gets thicker, the rejected salt collects in tiny pockets
of brine too highly concentrated to freeze
...
Eventually, if the ice survives, these pockets of brine drain out through fine, veinlike channels, and the ice becomes fresher; multiyear ice can even be melted and drunk
...
For the following question, consider each of the choices separately and select all that
apply
...
The passage mentions which of the following as being a characteristic of seasonal
ice?
A
Ȟ It is similar in appearance to perennial ice
...
C
Ȟ It tastes saltier than perennial ice
...
Choice A is correct: the passage states that “to the untrained eye, all sea ice looks
similar” (lines 2–3)
...
Choice C is correct: in lines 6–8, the passage establishes that first-year ice tastes
salty but eventually gets fresher if the ice survives
...
Unlawful distribution of this ebook is prohibited
...
In the context in which it appears, “fine” (line 7) most nearly means
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
acceptable
elegant
precise
pure
small
Explanation
“Fine” appears in the context of an explanation of how the brine drains out; in such
a context, it must be being used to describe a physical characteristic of the channels
...
Only
Choice E, “small,” helps to explain why the process is slow and is therefore the best
choice
...
For questions 15 to 18, select the two answer choices that, when used to complete
the sentence, fit the meaning of the sentence as a whole and produce completed
sentences that are alike in meaning
...
It would have been disingenuous of the candidate to appear ________ when her
opponent won the election, but she congratulated the victor nonetheless
...
” Certainly “ecstatic” and “euphoric” reactions would be highly disingenuous or insincere
...
Thus, the correct answer is ecstatic (Choice B) and euphoric (Choice E)
...
As market forces penetrate firms and bid up the value of attributes of labor that
are more measurable than is the knowledge born of experience, it can be
expected that trends in wages will not ________ those whose main value lies in
such experiential knowledge
...
Unlawful distribution of this ebook is prohibited
...
” The blank
has to do with trends in wages for those whose main value in the labor force lies in
“experiential knowledge
...
Given the “not” that precedes the blank, “favor” and “aid” make for such an
outcome and result in sentences alike in meaning
...
The point we might still take from the First World War is the old one that wars
are always, as one historian aptly put it, ________: they produce unforeseeable
results
...
The two answer choices for which “they
produce unforeseeable results” would most clearly serve as a definition are “astounding” and “stunning
...
”
Thus, the correct answer is astounding (Choice B) and stunning (Choice E)
...
This is the kind of movie — stuffed with intimations of faraway strife and
people in suits talking frantically on cell phones and walkie-talkies — that is
conventionally described as a political thriller, but the film is as apolitical as
it is ________
...
” The film is not political but rather apolitical, and the phrase “as apolitical as it is
...
“Humdrum” and “dull” are the opposite of “thrilling” and are therefore the best choices
...
521
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...
GRE Practice Test 2
For each of questions 19 to 25, select one answer choice unless otherwise instructed
...
line
5
10
Historians credit repeated locust invasions in the nineteenth century with reshaping
United States agriculture west of the Mississippi River
...
Wheat had come to nearly monopolize the
region, but it was particularly vulnerable to the locusts
...
Farmers learned that peas and beans were far less vulnerable to the insects, and corn
was a more robust grain than wheat
...
Although pastures were often damaged
by the locusts, these lands were almost always left in better shape than the crops were
...
Since
wheat, the dominant crop in the region, was especially susceptible to damage from
locusts, it made sense for farmers to lower their wheat production and raise their production of other crops and animals less vulnerable to locust invasions
...
19
...
B
Ȟ Peas and beans had not yet been planted in the region
...
Explanation
Choices A and C are correct
...
Choice B is incorrect: although wheat was the dominant crop, there is no indication that peas and beans had not been planted in the region prior to the admonishments of government entomologists
...
522
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...
Answers and Explanations
20
...
” Of the choices presented, “vigorous” is most similar in meaning to “robust
...
Therefore, Choice D is the correct answer
...
In 1998 the United States Department of Transportation received nearly 10,000 consumer complaints about airlines; in 1999 it received over 20,000
...
In both years the
vast majority of complaints concerned flight delays, cancellations, mishandled baggage, and customer service
...
21
...
The number of passengers flying on United States airlines was
significantly higher in 1999 than in 1998
...
The appearance in 1999 of many new Internet sites that relay complaints
directly to the Department of Transportation has made filing a complaint
about airlines much easier for consumers than ever before
...
Explanation
The passage describes two different year-over-year increases in airline passenger complaints: both the absolute number of complaints and the rate of complaints more than
doubled from 1998 to 1999
...
Choice D is the correct answer: it weakens the argument because it presents a scenario in which the increase in complaints and in the rate of complaints could merely be
the result of an easier means of filing complaints, not an actual increase in passenger
dissatisfaction
...
Unlawful distribution of this ebook is prohibited
...
Choice E is incorrect: the fact that some airlines experienced a smaller increase than
others does not change the fact that all airlines experienced an increase and thus cannot weaken the argument
...
But the passage also
says that the rate of complaints increased, making Choice B incorrect
...
line
5
10
15
Nineteenth-century architect Eugène-Emmanuel Viollet-le-Duc contended that Paris’s
Notre-Dame cathedral, built primarily in the late twelfth century, was supported from
the very beginning by a system of flying buttresses — a series of exterior arches (flyers)
and their supports (buttresses) — which permitted the construction of taller vaulted
buildings with slimmer walls and interior supports than had been possible previously
...
Although post-twelfth-century modifications and renovations complicate efforts to resolve this controversy — all
pre-fifteenth-century flyers have been replaced, and the buttresses have been rebuilt
and/or resurfaced — it is nevertheless possible to tell that both the nave and the choir,
the church’s two major parts, have always had flying buttresses
...
Moreover, the choir’s lower flyers have chevron
(zigzag) decoration
...
Description
The passage describes a disagreement about when Notre-Dame cathedral was supported by flying buttresses, with Viollet-le-Duc arguing that buttresses were present
from the cathedral’s construction in the late twelfth century and others claiming the
buttresses were built later
...
22
...
Choice A is incorrect because while the passage describes a controversy, it makes no mention of how that controversy developed
...
Unlawful distribution of this ebook is prohibited
...
23
...
Its design flaws were not apparent until flying buttresses were added in
the thirteenth or fourteenth century
...
It had been modified in some respects before flying buttresses were added
in the thirteenth or fourteenth century
...
Explanation
The passage states that the “other commentators” claim that Notre-Dame first received
flying buttresses when it was updated for aesthetic and structural reasons in the thirteenth or fourteenth century
...
Choice A is incorrect
because the passage does not include any information about other cathedrals, let alone
attribute a view of them to the other commentators
...
Choice C is incorrect because the passage does not attribute any
views of the embellishments on the flying buttresses to the other commentators; similarly, Choice D is incorrect because the passage does not describe the other commentators as discussing any modifications prior to the thirteenth or fourteenth century
...
The author’s argument concerning Notre-Dame’s flying buttresses depends on
which of the following assumptions about the choir’s lower flyers?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
They accurately reproduce the decoration on the choir’s original lower
flyers
...
They were the models for the choir’s original upper flyers
...
They were constructed after the nave’s flyers were constructed
...
But since all flyers constructed prior to
the fifteenth century have been replaced, the chevron decorations can indicate only
that flyers were present in the twelfth century if those decorations accurately reproduce the decorations that existed on the original flyers
...
Choice B is incorrect: whether chevron decorations are used only on the exterior is
525
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 2
not a point of dispute in the passage
...
Question 25 is based on the following reading passage
...
In warmer water, lobsters grow faster
...
Consequently, the survival rate of
lobster larvae must be going up, and the lobster population in Foerkland’s coastal
waters is bound to increase
...
Which of the following, if true, most seriously weakens the argument?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
There are indications that in recent years the fishing fleet operating off the
coast of Foerkland has been taking cod at an unsustainably high rate
...
Because of their speeded-up growth, lobsters now get large enough to be
legal catch before they reach reproductive maturity
...
Cod are a cold-water species, and the increasing water temperatures have
caused a northward shift in Foerkland’s cod population
...
The basis for the conclusion is
that the change in the water temperature, by speeding the growth of lobster larvae, has
made them less vulnerable to predation by cod
...
Thus, Choice C
weakens the argument and is the correct answer
...
The other
choices have no clear bearing on the argument
...
Unlawful distribution of this ebook is prohibited
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity B
4
3
A
B
C
D
Explanation
In this question, you are asked to compare
nonzero number, then a−1 =
3−1
4
with
...
Using these rules of exponents, you
a
a
can see that
3−1
1
1
4
= (3−1) −1 =
(4) =
4−1
4
3
3
Thus,
3−1 4
= , and the correct answer is Choice C
...
A
B
C
D
Explanation
In this question, you are given that x < 1 and x ≠ 0, and you are asked to
compare x2 + 1 with x3 + 1
...
||
x2 + 1 ? x3 + 1
Then simplify the comparison
...
Unlawful distribution of this ebook is prohibited
...
Note that the
strategy of simplifying the comparison requires you to consider whether the
steps in the simplification are reversible
...
If you
follow the simplification steps in reverse, you can see that the placeholder in
each step remains unchanged: 1 > x implies x2 > x3 because multiplying by the
positive number x2 retains the inequality greater than (>)
...
Therefore, Quantity A is greater than Quantity B, and the correct
answer is Choice A
...
5% of x
1
x
2
3
...
5% of
1
1
x with x
...
2
2
1
Therefore, x is equal to 50% of x
...
5% of x
...
You could also make the comparison by rewriting 0
...
Rewrite 0
...
0
...
The correct answer is Choice B
...
Quantity A
4
...
The only
528
This ebook was issued to Diane Massey, order #11560922926
...
D
Answers and Explanations
Frequency
information you are given is that the median income of the group in Quantity A
is $3,000 greater than the median income of the group in Quantity B
...
The median is also equal to the 50th percentile
...
In particular,
for each group of incomes, you do not know how much greater than the median
the 75th percentile of the group of incomes is, nor do you know the relationship
between the 75th percentiles of the two groups
...
15
10
5
0
16
2
1
4
2
7
3
11
10
4
5
6
The graph above shows the frequency distribution of 50
integer values varying from 1 to 6
...
The average (arithmetic
mean) of the 50 values
Quantity B
The median of the 50
values
A
B
C
D
Explanation
In this question, you are given a graph of the frequency distribution of 50 integer
values and are asked to compare the average (arithmetic mean) with the median
of the distribution
...
So, for the 50 values shown in the
graph, the median is the average of the 25th and 26th values, both of which are
equal to 5
...
Once you know that the median of the 50 values is 5, the comparison
simplifies to comparing the average of the 50 values with 5
...
Since the part of the distribution that is below 5 contains 23 values—13 of
which are more than 1 unit below 5—and the part of the distribution that is
above 5 contains 11 values—none of which is more than 1 unit above 5—the
average (arithmetic mean) of the 50 values must be less than 5
...
Alternatively, you can calculate the average of the 50 values as follows
...
Unlawful distribution of this ebook is prohibited
...
34, is less than the median of the 50
50
values, 5
...
Thus the average of the 50 values,
Q
√5
R
2 5
3
P
S
Quantity A
6
...
Note that both triangles are right triangles and that line
segment PR is the hypotenuse of both triangles
...
Also, for any right triangle, the lengths of the two legs of the triangle are a
base and the corresponding height
...
Therefore, you can conclude that the area of
1
triangle PQR is (2Ί5)(Ί5), or 5
...
From the figure, you know that the
length of RS is 3, but you do not know the length of PS
...
So, to find the length of PS, you first need to find the length of hypotenuse
PR
...
The lengths of legs PQ
and QR of triangle PQR are 2Ί5 and Ί5, respectively
...
530
This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
Returning to triangle PSR, you now know that the length of hypotenuse PR
is 5 and the length of leg RS is 3
...
Since legs PS and RS have lengths 4 and 3, respectively, the area of triangle
1
PSR is (4)(3), or 6
...
So Quantity B, the area of triangle PSR, is greater than
Quantity A, the area of triangle PQR, and the correct answer is Choice B
...
The sum of the odd
integers from 1 to 199
The sum of the even
integers from 2 to 198
A
B
C
D
Explanation
In this question, you are asked to compare the sum of the odd integers from 1 to
199 with the sum of the even integers from 2 to 198
...
How many integers are in each sum? Note that there are 200
integers from 1 to 200, where 100 of them are even and 100 of them are odd
...
So Quantity A is the sum of 100 integers and Quantity B is the sum
of 99 integers
...
Therefore, it is reasonable to find a more efficient way to
calculate the sums or to find a way to compare the sums without actually
calculating them
...
You can begin by writing a few terms from the beginning
and the end of the sum
...
+ 195 + 197 + 199
You can pair the odd integers in the sum and add the two integers in each pair
as follows
...
+ 195 + 197 + 199
200
200
200
Note that the sum of the integers in each of the three pairs shown is 200
...
It follows that
1 + 3 + 5 +
...
+ (99 + 101)
= 50(200)
= 10,000
531
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...
GRE Practice Test 2
Now consider the sum of the 99 even integers from 2 to 198
...
+ 194 + 196 + 198
In this sum, note that
the sum of the 1st and 99th terms is 2 + 198 = 200
the sum of the 2nd and 98th terms is 4 + 196 = 200
You can continue pairing terms in this way until 98 of the 99 terms in the sum
have been rearranged into 49 pairs and the 50th term is unpaired
...
It follows that
2 + 4 +
...
+ 196 + 198 = (2 + 198) + (4 + 196) +
...
Alternatively, you can try to compare the two sums without actually
calculating them
...
Write
each sum with the terms in increasing order, as follows, pairing the nth term in
Quantity B with the nth term in Quantity A and noting that there is no term in
Quantity B that is paired with the 100th term, 199, in Quantity A
...
+ 193 + 195 + 197 + 199
Quantity B: 2 + 4 + 6 +
...
Consequently, Quantity A is 199 − 99 more than
Quantity B—that is, 100 more than Quantity B—and the correct answer is
Choice A
...
Quantity A
Quantity B
s
t
1
5
8
...
Since the expression involves the
t
5
t
variables s and t, you need to look for a relationship between s and t using the
equation 32s = 2t
...
However, one of the bases is 32 and the other is 2
...
In
fact, 32 = 25
...
In the rewritten equation, the bases are equal, so you can
conclude that 5s = t
...
Unlawful distribution of this ebook is prohibited
...
Quantity A is equal to Quantity B, and the
t 5
correct answer is Choice C
...
The
number of defective parts was recorded for each box,
and the average (arithmetic mean) of the 50 recorded
numbers of defective parts per box was 1
...
Only one
error was made in recording the 50 numbers: “1”
defective part in a certain box was incorrectly recorded
as “10”
...
The actual average number
of defective parts per box
Quantity B
0
...
12
...
Then you are
asked to compare the actual average number of defective parts per box with 0
...
To determine the actual average number of defective parts per box, first note
that the sum of the 50 recorded numbers equals the average of the 50 recorded
numbers times 50—that is, (1
...
Now you know that for 49 of the 50 boxes, the actual number of defective
parts is equal to the recorded number; and for one box, the actual number is 9
less than the recorded number
...
So
the sum of the actual numbers of defective parts is 56 − 9, or 47
...
94
...
10
...
The population density (number of persons per unit of land
area) of Colorado in year Y was approximately how many times the
population density of New Jersey?
1
A
ɕ 28
1
B
ɕ 14
1
C
ɕ 7
D
ɕ 1
4
E
ɕ 1
2
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This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 2
Explanation
The information given in the question can be rewritten algebraically as follows
...
population density of Colorado =
population of Colorado
land area of Colorado
2 ( ןpopulation of New Jersey)
1
Ϸ
(14) ( ןland area of New Jersey)
Ϸ
1
1
of New Jersey
2 ן 41 ןpopulationof New Jersey
land area
Ϸ
28 ( ןpopulation density of New Jersey)
1
1
times the
28
population density of New Jersey
...
Thus, the population density of Colorado was approximately
For the following question, enter your answer in the box
...
k
m
In the figure above, line k is parallel to line m
...
Therefore, you can conclude that these two angles are congruent
...
5
...
5
...
Unlawful distribution of this ebook is prohibited
...
The numbers in data set S have a standard deviation of 5
...
The new data set is
formed by adding the same number, 3, to each number in data set S
...
Because the standard deviation of the
numbers in S is 5, the standard deviation of the numbers in the new data set is
also 5
...
13
...
2(2y − 3) = y(3 − y)
4y − 6 = 3y − y2
2
y +y−6=0
(y + 3)(y − 2) = 0
Since a product equals 0 only if at least one of the factors equals 0,
y + 3 = 0 or y − 2 = 0
y = −3 or y = 2
Thus, there are two values of y that satisfy the equation, −3 and 2
...
The correct
answer is Choice D
...
Unlawful distribution of this ebook is prohibited
...
To do this, you can substitute the answer choice for y in the
2y − 3 3 − y
=
, replace the equals sign in the equation by the placeequation
y
2
?
holder symbol =, and then simplify to see whether the two expressions are in
fact equal
...
4
2
2(4) − 3 ? 3 − 4
=
4
2
8 − 3 ? −1
=
4
2
5 ? 1
=−
4
2
5
1
≠ − , you can conclude that the placeholder symbol does not represent
4
2
equality, and therefore the equation does not hold for y = 4
...
To see that the equation
is true when
y
2
y = −3, substitute y = −3 in the equation and replace the equals sign = with the
?
2(−3) − 3 ? 3 − (−3)
placeholder symbol =
...
This
−3
2
relationship can be simplified as follows
...
The correct answer is Choice D
...
14
...
Which of the following
lists of numbers have the same range as the numbers in list K ?
Indicate all such lists
...
Unlawful distribution of this ebook is prohibited
...
The greatest number in list K
is 10 and the least number is −10
...
So, to answer the question, you need to consider
each list of numbers given in the choices and determine whether that list of
numbers has a range of 20
...
Therefore, you need to look only at the first number and last number
in each list to determine which lists have a range of 20
...
Choice A: The greatest number is 15 and the least number is −15; therefore,
the range is 15 − (−15) = 15 + 15 = 30
...
Choice C: The greatest number is 10 and the least number is 0; therefore, the
range is 10 − 0 = 10
...
Choice E: The greatest number is 24 and the least number is 4; therefore, the
range is 24 − 4 = 20
...
The correct answer consists
of Choices B, D, and E
...
Aisha’s income in 2004 was 20 percent greater than her income in 2003
...
Therefore, the ratio of her income in 2004
to her income in 2003 is 120 to 100, which is equivalent to 6 to 5
...
Alternatively, to say that Aisha’s income in 2004 was 20% greater than her
1
income in 2003 is the same as saying that her income increased by
...
The correct answer is Choice C
...
Unlawful distribution of this ebook is prohibited
...
4n
dollars for
5
expenses and saves the rest
...
Each week he uses
E
ɕ
625n
Explanation
It may be helpful to consider how you would determine the number of weeks it
would take Jacob to save $500 if you knew how much he saved each week
...
At that rate, it is easy to see that it
would take him 500 ,52 נor 20, weeks to save $500
...
Now use the information given in the question to determine an algebraic
expression representing the amount Jacob saved each week
...
Therefore, the amount he
are given that Jacob’s weekly expenses are
5
saves each week is equal to his weekly take-home pay minus his weekly
4n 5n 4n 5n − 4n n
expenses, or n −
=
−
=
= dollars
...
So
the number of weeks it will take Jacob to save $500 is
n
5 2,500
500 = ן 005 = נ
...
5
n
n
Questions 17 to 20 are based on the following data
...
538
This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
17
...
The degree measure of the sector representing the number of workers
unemployed for 11 to 14 weeks is 10% of 360Њ, or 36Њ, for the manufacturing
industry graph and is 5% of 360Њ, or 18Њ, for the service industry graph
...
The correct
answer is Choice D
...
Which of the following could be the median length of unemployment, in
weeks, for manufacturing industry workers who were unemployed for at
least 1 week?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
4
8
12
16
20
Explanation
Note that the sectors in the manufacturing industry circle graph separate the
unemployed manufacturing industry workers into five groups by length of
unemployment; also, the percent of workers within each of the five groups is
given
...
Since the lengths are rounded to whole
numbers of weeks, most of the 10 million lengths must be repetitions
...
To find the median length, first note that the group with the shortest
unemployment lengths, 1 to 4 weeks, accounts for the first 40% of the lengths in
the ordered list
...
So the median length is in
the 5-to-10 week interval
...
The correct answer is Choice B
...
Unlawful distribution of this ebook is prohibited
...
If one of the workers in the manufacturing and service industries who were
unemployed for at least 1 week will be randomly selected, what is the
probability that the person selected will be a service industry worker who
was unemployed for 26 weeks or more?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
0
...
09
0
...
40
0
...
the number of service industry workers who were unemployed 26 weeks or more
the number of workers in the two industries who were unemployed at least 1 week
The number of workers in the two industries who were unemployed for at least
1 week is the sum of the total numbers of workers represented by the two
graphs, or 10 million + 8 million = 18 million
...
72 million
...
72 million
72
Therefore, the desired probability is
=
= 0
...
The correct
18 million
1,800
answer is Choice A
...
The ratio of the number of manufacturing industry workers who were
unemployed for 5 to 10 weeks to the number of service industry workers
who were unemployed for 5 to 10 weeks is closest to which of the
following?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
5 to 4
6 to 5
3 to 2
5 to 2
7 to 6
Explanation
According to the graphs, the number of manufacturing industry workers who
were unemployed for 5 to 10 weeks is 20% of 10 million, or 2 million; and the
number of service industry workers who were unemployed for 5 to 10 weeks is
16% of 8 million, or 1
...
Thus, the ratio of the two numbers is 2 to
1
...
To answer the question, you must now determine which of the answer
choices is closest to the ratio 2 to 1
...
A good way to compare ratios is to
express each ratio as a fraction and then as a decimal, and then to compare the
2
, which is
decimals
...
28 can be expressed as the fraction
1
...
5625
...
Unlawful distribution of this ebook is prohibited
...
As you go through the answer choices, keep
in mind that you are trying to determine which is closest to 1
...
5
Choice A: 5 to 4 can be expressed as , which is equal to 1
...
4
6
Choice B: 6 to 5 can be expressed as , which is equal to 1
...
5
3
Choice C: 3 to 2 can be expressed as , which is equal to 1
...
Note that this
2
ratio is close to 1
...
5
Choice D: 5 to 2 can be expressed as , which is equal to 2
...
2
7
Choice E: 7 to 6 can be expressed as , which is approximately equal to 1
...
6
Of the five choices, the ratio in Choice C is closest to 1
...
The correct
answer is Choice C
...
21
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
F
Ǣ
−9
−6
−2
0
2
3
Explanation
One way to approach this question is to substitute each of the answer choices
into the inequality and determine which ones satisfy the inequality
...
The correct answer consists of Choices A and F
...
Therefore, all values of t greater than 2 or less than −8 satisfy the
inequality ⎪ t + 3 ⎪ > 5
...
The correct answer consists of Choices A and F
...
Unlawful distribution of this ebook is prohibited
...
The operation is defined for all integers x and y as x y = xy − y
...
Here are two
examples
...
Are there positive integers x and y
for which the answer choice is equal to 0 ? If not, then that answer choice is the
correct answer
...
Using the formula, try to find positive integers x and y for
which x y = 0, that is, for which xy − y = 0
...
So now you must find positive integers x and y such that the
product of the two numbers x − 1 and y is 0
...
For example, if x = 1
and y = 2, then x y = 1 2 = (1)(2) − 2 = 0, and both x and y are positive
integers
...
Choice B: y x
...
Therefore, you might try the example in Choice A but with the
values of x and y interchanged: y = 1 and x = 2
...
Therefore, Choice B is not correct, since there are
positive integers x and y for which y x = 0
...
Using the formula, try to find positive integers x and y
for which (x − 1) y = 0, that is, for which (x − 1)y − y = 0
...
Here the product of the two numbers x − 2 and y is 0
...
For example, if x = 2 and y = 10, then
(x − 1) y = (2 − 1) 10 = 1 10 = (1)(10) − 10 = 0, and both x and y are positive
542
This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
integers
...
Choice D: (x + 1) y
...
Factoring y out of the
left-hand side of the equation (x + 1)y − y = 0 yields (x + 1 − 1)y = xy = 0
...
Since both x and y must be positive
but 0 is not positive, it follows that there are no positive integers x and y for
which (x + 1) y = 0
...
Choice E: x (y − 1) cannot be correct, since Choice D is correct, but Choice
E is considered here for completeness
...
Factoring y − 1 out of the left-hand side of the equation x(y − 1) − (y − 1) = 0
yields (x − 1)(y − 1) = 0
...
So the product will be 0 if x = 1 or y = 1, no matter what the value of the other
variable is
...
Therefore, Choice
E is not correct, since there are positive integers x and y for which x (y − 1) = 0
...
P, Q, and R are three points in a plane, and R does not lie on line PQ
...
It contains one point
...
It is a line
...
Explanation
First consider just two of the three points, say P and Q, and the set of points in
the plane that are the same distance from them
...
Are there others? You may recall from geometry
that the points on the line that bisects PQ and is perpendicular to PQ are all the
points that are equidistant from P and Q
...
Because R does not lie on line PQ, line segments PQ and PR do not lie on
the same line, and so their respective perpendicular bisectors are not parallel
...
The point of intersection is on both perpendicular bisectors, so it is
equidistant from P and Q as well as from P and R
...
Are there any other points that
are equidistant from P, Q, and R ? If there were, they would be on both
perpendicular bisectors, but in fact only one point lies on both lines
...
543
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 2
24
...
Keep this in mind as you evaluate each of
the inequalities in the answer choices, to see whether the inequality must be
true
...
According to the conditions given in the question, y is
greater than x
...
So it cannot be true that y + 1 < x
...
Choice B: y − 1 < x
...
Consider what happens if y = −2 and x = −7
...
Therefore,
Choice B is not the correct answer
...
Note that y2 is positive and x is negative, so xy2 is negative
...
Consider what happens if x = −4 and y = − , where
2
y2 < 1
...
Therefore, Choice C is not the correct answer
...
Since y is a negative number, multiplying both sides of the
inequality x < y by y reverses the inequality, resulting in the inequality xy > y2
...
Therefore, Choice D is not the correct answer
...
You can show that the inequality in Choice E, xy < x2, must be true as
follows: Multiply both sides of the given inequality x < y by x to obtain the
inequality x2 > xy, reversing the direction of the inequality because x is negative
...
For the following question, enter your answer in the box
...
What is the length of a diagonal of a rectangle that has width 5 and
perimeter 34 ?
Explanation
In this question, you are given that a rectangle has width 5 and perimeter 34,
and you are asked to find the length of a diagonal of the rectangle
...
Note that you are not given L but you are given that
544
This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
W = 5 and that the perimeter is 34
...
2(L + 5) = 34
L + 5 = 17
L = 12
The following figure shows a rectangle of length 12, width 5, and diagonal of
length D
...
Therefore, by the Pythagorean theorem,
52 + 122 = D2
25 + 144 = D2
169 = D2
13 = D
The length of the diagonal is 13, so the correct answer is 13
...
Unlawful distribution of this ebook is prohibited
...
Quantity B is greater
...
The relationship cannot be determined from the information given
...
Quantity B
Quantity A
1
...
Since
the circle is inscribed in the square, the diameter of the circle is equal to the
length of a side of the square, or 5
...
Because p is greater than 3, it follows that 5p is greater than 15
...
2u + v = 14
uv = 0
Quantity A
Quantity B
u
v
2
...
Consider the equation uv = 0
...
But
since you are also given that 2u + v = 14, it follows that u and v cannot both
equal 0
...
If u = 0, then
2u + v = 14 simplifies to v = 14
...
However, if v = 0,
then 2u + v = 14 simplifies to 2u = 14, or u = 7
...
In the first case, u < v, and in the second case, u > v
...
546
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...
Answers and Explanations
Quantity A
Quantity B
9502,000
106,000
3
...
Note that both quantities are written in the form “base to a power
...
Because powers of 10 are easier to work with than powers of 950, it is
reasonable to try to compare the quantities by rewriting the quantity 9502,000 as a
power of 10
...
However, if you
can approximate 950 by a power of 10, you may then be able to use the
approximation to compare the quantity 9502,000 with the quantity 106,000
...
Raising
both sides of the inequality 950 < 103 to the power 2,000 gives the inequality
9502,000 < (103)2,000
...
Thus, Quantity A is less than Quantity B, and the correct
answer is Choice B
...
The number of integers that are in both set A
and set B is 20
...
The total number of integers
that are in set A or set B,
or both
170
A
B
C
D
Explanation
In this question, you are given that the number of integers in set A is 40, the
number of integers in set B is 150, and the number of integers that are in both A
and B is 20
...
This is the type of question for which a Venn diagram is usually helpful to
represent the information given
...
A
40
B
150
Note that there is no number in the shaded region of the diagram—the region
representing the integers in both A and B
...
Unlawful distribution of this ebook is prohibited
...
It is a good idea, therefore, to redraw the Venn diagram so that the
numbers are separated into three categories: the integers in A only, the integers
in B only, and the integers in both A and B
...
A only
B only
20 130
20
A and B
Observe that summing the numbers of integers in set A only, set B only, and both
A and B yields the total number of integers that are in set A or set B, or both
...
Another approach is to realize that if you listed the integers in set A and the
integers in set B, you would have listed the integers that are in both A and B
twice and all of the other integers once
...
x is a negative integer
...
A
B
C
D
Explanation
In this question, you are asked to compare 2x with 3x+1, given that x is a negative
integer
...
You are given that x is a negative integer, so the greatest integer you can plug
in for x is −1
...
2
In this case, 2x is less than 3x+1
...
To
analyze this relationship further, plug in another value of x, for example, −2
...
2
4
3
Again, 2x is less than 3x+1, but note that these values are closer together than
the previous values of 2x and 3x+1
...
1 1
1 1
For x = −3, it follows that 2x = 2−3 = 3 = and 3x+1 = 3−3+1 = 3−2 = 2 =
...
Unlawful distribution of this ebook is prohibited
...
Since 2x is less than 3x+1 for x = −1 and 2x is greater than 3x+1 for x = −3,
the relationship between these two quantities cannot be determined from the
information given
...
Since both quantities are algebraic expressions, another way to approach the
comparison is to set up a placeholder relationship, denoted by ? , between the
||
two quantities and then to simplify to see what conclusions you can draw
...
||
|?| 3(3x)
2x ? 3x+1
x
2
2x
? 3
3x
||
x
2
3
|?| 3
For any value of x (including negative integer values of x), the value of 3x is
positive, so dividing by 3x does not affect any inequality that might be
represented by the placeholder
...
Note that
=
, where n = −x; so the
3
2
n
3
problem can be reduced further to comparing
with 3, given that n is a
2
positive integer
...
For small values of n,
is less than 3, but for large values of n,
is
2
2
greater than 3
...
(x + 3)( y − 4) = 0
Quantity A
Quantity B
xy
−12
6
...
Since (x + 3)(y − 4) = 0 and the product of two
numbers can equal 0 only if at least one of the numbers in the product equals 0,
you can conclude that x = −3 or y = 4, or both
...
When x = −3, you can choose any number as the
value of y and the equation (x + 3)(y − 4) = 0 will be satisfied
...
For example, if y = 1, then xy = −3 is greater than −12; and if
y = 10, then xy = −30 is less than −12
...
Unlawful distribution of this ebook is prohibited
...
The correct answer is Choice D
...
This amount was
15 percent of his earnings last summer
...
The amount of Geoff’s
earnings last summer not
used to buy the new guitar
Quantity B
$3,570
A
B
C
D
Explanation
In this question, you are asked to compare the amount of Geoff’s earnings last
summer not used to buy a new guitar with the amount $3,570
...
So the relationship between Geoff’s earnings last summer and the amount he
spent to buy the guitar can be expressed by the equation
(0
...
15
$4,200
...
Therefore, Quantity A is equal to Quantity B, and the correct answer
is Choice C
...
Quantity A
8
...
Recall that a set R is a subset of set
S if all of the members of R are also members of S
...
Therefore, the number of subsets of S with 1 object is
equal to the number of subsets of S with 4 objects
...
Another approach to solving this problem is to consider a particular set of 5
objects and determine all of the subsets consisting of 1 object and all of the
subsets consisting of 4 objects
...
There are 5
subsets of S consisting of 1 object: {a}, {b}, {c}, {d}, and {e}; there are 5 subsets of S
consisting of 4 objects: {a, b, c, d}, {a, b, c, e}, {a, b, d, e}, {a, c, d, e}, and {b, c, d, e}
...
Unlawful distribution of this ebook is prohibited
...
The correct answer is Choice C
...
The length of line segment AC
3
A
B
C
D
Explanation
In this question, you are asked to compare the length of line segment AC with 3
...
Based on the fact that the sum of the measures of the angles
in a triangle is 180Њ, you can conclude that the triangle to the left of the vertical
line is a 45Њ-45Њ-90Њ right triangle and the triangle to the right of the vertical line
is a 30Њ-60Њ-90Њ right triangle
...
B
45°
A
45°
30°
90° 90°
D
2
60°
C
Note that the length of AC is equal to the length of AD plus the length of DC
...
In the figure, you are given that the length of BC, the hypotenuse of the
30Њ-60Њ-90Њ triangle, is 2
...
Recall that if the length of
the hypotenuse of a 30Њ-60Њ-90Њ triangle is 2, then the length of the side opposite
the 30Њ angle is 1, and the length of the side opposite the 60Њ angle is Ί3
...
Now consider the 45Њ-45Њ-90Њ triangle ABD
...
Since the length of BD is Ί3, the
length of AD is also Ί3
...
Since the length of AD is Ί3 and the length of DC is 1, it follows that the
length of AC is equal to Ί3 + 1
...
Unlawful distribution of this ebook is prohibited
...
Because Ί3 is less than 2, it follows that the length of AC, which is equal to
Ί3 + 1, is less than 2 + 1, or 3
...
y
k
O
5
x
–5
10
...
Thus, the slope of line k is
−5 − 0 −5
=
=1
0−5
−5
The correct answer is Choice D
...
The median of the five terms listed above is 5, where b is a constant
...
Unlawful distribution of this ebook is prohibited
...
You are given that 5 is the median of the five terms b − 3, b − 1, b + 2, b + 3,
and b + 4, where b is a constant
...
Observe that the five
terms are already given in increasing order
...
Since b = 3, it follows that the values of the five terms are 0, 2, 5, 6, and 7,
0 + 2 + 5 + 6 + 7 20
=
= 4
...
For the following question, enter your answer in the box
...
What is the area of the region shown above?
Explanation
In this question, you are asked to determine the area of the given region
...
15
Rectangle R
8
12
Rectangle S
9
The area of the region is the sum of the areas of the two rectangles
...
Since the width of rectangle S is 12 − 8, or 4, the
area of rectangle S is (9)(4), or 36
...
The correct answer is 156
...
Unlawful distribution of this ebook is prohibited
...
15
8
12
Small rectangle
9
The area of the region is the area of the rectangle with length 15 and width 12
minus the area of the small rectangle
...
Since the length of the small rectangle is 15 − 9,
or 6, and the width of the small rectangle is 12 − 8, or 4, the area of the small
rectangle is (6)(4), or 24
...
The
correct answer is 156
...
During a one-year study, biologists observed the number of fish in a certain
pond as well as the percent of the fish that were catfish
...
From the beginning of the year to the end of the year,
the number of catfish in the pond
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
decreased by more than 5%
decreased by 5%
did not change
increased by 5%
increased by more than 5%
Explanation
The answer choices indicate that the question is asking about the percent change
in the number of catfish
...
15)(300), which is 45
...
10)(400), which is 40
...
The percent by which the number of catfish decreased from the beginning of
the year to the end of the year is
the decrease in the number of catfish over the year
5
= )%001( ן
(100%) Ϸ 11%
the number of catfish at the beginning of the year
45
Thus, the number of catfish decreased by about 11%
...
554
This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
For the following question, enter your answer in the box
...
On a radio tower, a red light flashes every 6 seconds and a blue light flashes
every 10 seconds
...
The following lists show the flash times
for both lights as the numbers of seconds after the time at which both lights
flashed together
...
Blue light: 10, 20, 30, 40, 50, 60, 70, 80, 90,
...
Therefore, if both
lights flash together, they will flash together again 30 seconds later
...
Alternatively, you may realize that if the lights flash together, the number of
seconds that will elapse before they flash together the next time is the least
common multiple of 6 and 10
...
6 = (2)(3)
10 = (2)(5)
Since 2 is a factor in both products, but 3 and 5 are factors of only one of the
products, the least common multiple of 6 and 10 is (2)(3)(5), or 30
...
The correct answer is 30
...
15
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
a−b
a2 − b2
ab
a2b
a2b + ab2
Explanation
In this question, you are given that a < b < 0 and are asked to determine which
of the answer choices must be positive
...
Choice A: a − b
...
Subtracting b from
both sides of the inequality a < b gives the inequality a − b < 0
...
555
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 2
Choice B: a2 − b2
...
Then you can subtract b2 from
both sides of the inequality a2 > b2 to conclude that a2 − b2 > 0
...
Alternatively, note that a2 − b2 can be factored as (a − b)(a + b)
...
Thus, a2 − b2 is the
product of two negative numbers, so it must be positive
...
Because a and b are negative, you can conclude that their
product ab must be positive
...
Because a2b can be written as (a)(a)(b), which is the product
of three negative numbers, you can conclude that a2b must be negative
...
By the reasoning in the explanation of Choice D, Choice
E is the sum of two negative numbers
...
Choices B and C must be positive, and Choices A, D, and E must be negative
...
x
x
16
...
The frame is 1 inch wide on all sides
...
To do this, you need to express both
the area of the frame and the area of the picture in terms of x and then find the
value of x for which the two expressions are equal
...
Since the area of a rectangle is the length times the width, you need to know the
length and width of the inner and outer rectangles
...
However, since you know that the width of the frame
556
This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
is 1 inch, it follows that the width of the inner rectangle is equal to the width of
the outer rectangle minus 2 inches, or x − 2 inches
...
In the figure, you are given that the width of the outer rectangle is x inches,
but the length is not given
...
Thus, the area of the outer
rectangle is x(x + 2) square inches
...
Now you are ready to set up the equation
...
x(x − 2) = 4x
x2 − 2x = 4x
x2 − 6x = 0
x(x − 6) = 0
There are two solutions to the equation, x = 0 and x = 6
...
Therefore, when x = 6, the area of the picture equals the area of the
frame
...
Questions 17 to 20 are based on the following data
...
Unlawful distribution of this ebook is prohibited
...
The number of people in group 2 who have hay fever is how much greater
than the number of people in group 1 who have hay fever?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
37
35
32
28
24
Explanation
In group 1, there are 300 people, 4% of whom have hay fever
...
04)(300) people, or 12 people, who have hay fever
...
Therefore, in group 2,
there are (0
...
Since
40 − 12 = 28, it follows that there are 28 more people in group 2 who have hay
fever than there are in group 1
...
18
...
To find the middle number
easily, first order from least to greatest the percents of people in group 2 who
have the seven ailments, then find the median of the percents, and finally
calculate the number of people corresponding to that percent
...
Respiratory Ailment
Percent of People in Group 2
Who Have Ailment
Asthma (nonallergic)
3%
Asthma (allergic)
4%
Wheezing (nonallergic)
5%
Wheezing (allergic)
6%
Hay fever
10%
Sneezing and itchy eyes
11%
Allergic sensitivity to endotoxins
21%
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This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
The median percent, which is the fourth number in the list, is 6%
...
06)(400), or 24,
and the correct answer is Choice C
...
The number of people in group 1 who have the ailment wheezing (allergic)
is what percent greater than the number of people in group 1 who have the
ailment wheezing (nonallergic)?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
50%
75%
150%
200%
300%
Explanation
In group 1, there are 300 people, 5% of whom have allergic wheezing and 2% of
whom have nonallergic wheezing
...
05)(300) people, or 15 people, have
allergic wheezing and (0
...
Therefore, in group 1, the number of people who have allergic wheezing exceeds
9
(100%) greater
the number who have nonallergic wheezing by 9, which is
6
than 6, or 150% greater than 6
...
For the following question, enter your answer in the boxes
...
What is the ratio of the number of people in group 2 with the ailment sneezing
and itchy eyes to the total number of people in both groups with the ailment
sneezing and itchy eyes?
Give your answer as a fraction
...
Therefore, in group 2, there are (0
...
In group 1, there are 300 people, 8% of whom have
sneezing and itchy eyes
...
08)(300) people, or 24
people, who have sneezing and itchy eyes
...
Thus, the ratio of the
number of people in group 2 who have sneezing and itchy eyes to the total
44
number of people in both groups who have sneezing and itchy eyes is
...
68
559
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 2
21
...
If 252 of the people in the survey
were more than 40 years old and at most 60 years old, what was the total
number of people in the survey?
A
ɕ
B
ɕ
C
ɕ
D
ɕ
E
ɕ
1,900
2,100
2,400
2,700
3,000
Explanation
In this question, it is given that of the people surveyed, 58% were at most 40
years old and 70% were at most 60 years old
...
Let x be the total number of
people in the survey
...
12x = 252, and so
252
x=
= 2,100
...
12
and the correct answer is Choice B
...
If x > 0, which of the following is equal to 1
...
25% of x to a fractional expression
...
25% is
equivalent to the decimal 0
...
Converting the decimal 0
...
0125 =
of x,
=
...
25% of x is equal to
10,000 80
80
x
or , and the correct answer is Choice A
...
Unlawful distribution of this ebook is prohibited
...
Alice earns d dollars and has t percent of what she earns deducted for taxes
...
1t) dollars
d(1 − 0
...
01t
...
01td dollars
...
01td dollars
...
01td is an algebraic expression with two terms,
each containing d as a factor
...
01t)
...
Recall that t percent can be expressed as
For the following question, select all the answer choices that apply
...
A student made a conjecture that for any integer n, the integer 4n + 3 is a
prime number
...
A
Ǣ
B
Ǣ
C
Ǣ
D
Ǣ
E
Ǣ
1
3
4
6
7
Explanation
Recall that a prime number is an integer greater than 1 that has no positive
divisors other than 1 and itself
...
Any of the
answer choices for which the integer 4n + 3 is not a prime number could be
used to disprove the conjecture that for any integer n, the integer 4n + 3 is a
prime number
...
The evaluations are as follows:
Choice A: For n = 1, the integer 4n + 3 is 4(1) + 3, or 7, which is a prime
number
...
Choice C: For n = 4, the integer 4n + 3 is 4(4) + 3, or 19, which is a prime
number
...
561
This ebook was issued to Diane Massey, order #11560922926
...
GRE Practice Test 2
Choice E: For n = 7, the integer 4n + 3 is 4(7) + 3, or 31, which is a prime
number
...
Thus, the correct
answer consists of Choices B and D
...
Eight points are equally spaced on a circle
...
The figure below shows
a circle with 8 equally spaced points, labeled A through H, and quadrilateral
BCDH, which is one of the many quadrilaterals that have 4 of the 8 equally
spaced points as vertices
...
the number of squares that can be drawn using 4 of the 8 points as vertices
the number of quadrilaterals that can be drawn using 4 of the 8 points as vertices
To calculate the desired probability, you need to determine the number of
squares and the number of quadrilaterals that can be drawn using 4 of the 8
points as vertices
...
Therefore, the number of quadrilaterals that can be drawn using 4
562
This ebook was issued to Diane Massey, order #11560922926
...
Answers and Explanations
of the 8 points as vertices is equal to the number of ways of choosing 4 points
from the 8 points shown
...
You can calculate the value of this expression as
time) is equal to
4!(8 − 4)!
follows
...
Because the points are equally spaced around the circle, there are only 2
squares that can be drawn using 4 of the 8 points as vertices, namely ACEG and
BDFH, as shown in the following figures
...
563
This ebook was issued to Diane Massey, order #11560922926
...
POWERPREP II
®
Version 2
...
Installation Procedures
Download the free software at www
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Minimum System Requirements
Microsoft® XP, Vista, or 7; Microsoft® Internet Explorer version
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Note: Internet connectivity (cable modem, DSL or better) is required to launch the
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It’s packed with everything you need to do your
best on the test—and move toward your graduate or business school degree
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No other guide to the GRE revised General Test gives you:
real tests—two in the book and two downloadable to your computer
measures plus valuable tips for answering each question type
responses and actual raters’ comments
Download Official POWERPREP II Software
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With two full-length, authentic, computer-based GRE revised General Tests
Compatible with PC systems
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