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GRE
Arithmetic

By:
Darshan Kapadia
darshankapadia11@gmail
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3
Division Rule
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5
Absolute Value
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6
Consecutive Integers
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8
Factors
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8
Prime Factorization
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9
Greatest Common Factor (GCF)/ Highest Common Factor (HCF)
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10
Even and Odd
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11
Equivalent Fractions
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13
Operations on Fractions
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15
Multiply or dividing by Powers of Ten
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15
Exponents
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17

darshankapadia11@gmail
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18
Sequence
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19
Geometric Sequence
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21
Answers of Practice Questions
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33
Bibliography
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2

GRE - Arithmetic

Classification of Numbers
The numbers are classified into the following ways:

Numbers are classified to real numbers and imaginary numbers
...
Few of examples of imaginary numbers are shown
...

Real numbers are further classified to rational numbers and irrational numbers
...
√6 is an irrational number because it can’t
be written in form of ratio
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22/7 is an approximate value of 𝜋
...
Integers don’t have fractional
component
...
Negative integers
are the integers which less than 0
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Positive integers are the
integers which are more than 0
...
Neutral
integer is integer which is neither positive nor negative
...

Fractions are the numbers which are represented in form of ratio of numerator and denominator
...
Some examples
are shown
...

Some examples of improper fractions are as shown
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Even integers are the integers which are
multiples of 2
...
Odd integers are the
integers which are divided by 2 and left 1 as a reminder
...
are odd integers
...
No negative
numbers are prime
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2 is only even prime and it is the smallest prime
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Composite numbers are the numbers which have factors other
than one and number itself
...
Coprime numbers are the numbers that have only one factor is common to them,
namely 1
...
A perfect number is a positive integer that, excluding the number itself, is
equal to the sum of its positive factors
...
By adding factors
of 6 other than number itself, sum is equal to 6
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GRE - Arithmetic
Dividend is the which to be divided by some other number
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Quotient is a number which an answer of division, and reminder is the number
left after division
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From
this it is written as:
𝐷 =𝑑×𝑞+𝑟
Where,
D = Dividend, q = Quotient, d = Divisor, and r = Remainder
...
What is the remainder, when same
number is divided by 1000?
 10
 100
 1000
 10000
 None of the above
Solution:
D = 10000q + 100, D = 1000(10q) + 100
...


Basic Properties of Numbers
•

Addition and multiplication are commutative
...

Example: 4 + 5 = 5 + 4, and 4 x 5 = 5 x 4
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It means if order is changed then final
answer will changed as well
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•

Every number has an opposite number
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Example: Opposite of 9 is -9
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•

Every non-zero number has a reciprocal
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If they are multiplied, 5 × 5, then product is 1
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Example: Product of 5 and 1 is 5
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Example: Product of 10 and 0 is 0
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Example: a × b = 0, a = 0 or b = 0
...

Example: |3| = 3, and |-3| = 3
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Order of Operations
There is a specified sequence in which numerous operations must be applied while conducting
them
...
The bracket has the highest priority of solving
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Regardless of the type of brackets in the expression, one must begin with the most inner
bracket
...

The exponent has the 2nd highest priority while solving expression
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GRE - Arithmetic

•

Multiplication and division: The multiplication and division have the same priority, but in
left to right direction whichever comes first, that should be solved first
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•

Addition and subtraction: The addition and subtraction have the same priority, but in left
to right direction whichever comes first, that should be solved first
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Example: Solve [6 x 3 + 9 – (42 x 3) ÷ 4] x 2
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5
Answer = 7
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GRE - Arithmetic

Consecutive Integers
A sequence of integers increasing (or decreasing) by 1 is called consecutive integers
...

Consecutive increasing integers are written x, x + 1, x + 2, x + 3, x + 4, … in form of variables
...

Example: The sum of five consecutive numbers is 55
...
So, sum is x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 55
...
Numbers are 9, 10, 11, 12, and 13
...
The answer
is 13
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Example: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120
...

Factors of each number are finite
...

That is, no leftovers are created as a result of this technique
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GRE - Arithmetic
Example: Multiples of 120 are 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, …
Similarly, multiples of 100 are 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, …
Multiples of each number are infinite
...
There are two
methods to perform prime factorization, and they are repeated division method and factor tree
method
...

2
2
2
3
5

120
60
30
15
5
1

Prime factorization of 120 is 2 x 2 x 2 x 3 x 5
...


Prime Factors
The factor of a given number that is a prime number is called a prime factor
...
Similarly, prime factors of 100 are 2 and 5
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GRE - Arithmetic

Greatest Common Factor (GCF)/ Highest Common Factor (HCF)
A greatest common factor is the biggest factor that all of the numbers have in common
...
There are multiple methods to
find greatest common factor, but using prime factorization is the best to get it
...

Solution:
Prime factorization of 100 = 2 x 2 x 5 x 5, and 120 = 2 x 2 x 2 x 3 x 5
...
So, prime factorization of 100 and 120 are 2 x 2 x 5 = 20
...

Minimum two numbers are required to find the least common multiple of them
...

Example: Find the LCM of 100 and 120
...


120
60
30
15
5
1
1

Note:
GCF (a, b) x LCM (a, b) = a x b
Example: GCF (100, 120) = 20, LCM (100, 120) = 600
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Example: 0, 2, 4, 6, 8, -2, -4, -6, -8, -10 are all even
numbers
...
Example: 1,
3, 5, 7, 9, -1, -3, -5, -7, -9 are all odd numbers
...
Example: 6 + 4 = 10, and 16 – 12 = 4,

•

Odd ± Odd = Even
...
Example: 9 + 12 = 21, and 23 – 16 = 7,

•

Odd x Odd = Odd
...
Example: 6 x 10 = 60,

•

Even x Odd = Even
...


Example: If p and q are odd primes, which of the following could be a prime? [1]
 pq
 p2 + p
 p+q
 p+q+1
 2p + 4q
Solution:
p and q are odd primes
...
pq is not a prime number,
Option p2 + p = p(p + 1) has four factors 1, p, p + 1, p(p + 1)
...
p + q is not a prime number,
Option p + q + 1 remains odd because p + q is even and even + 1 is odd
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2p + 4q is not a prime number
...


Divisibility Rules
In arithmetic, divisibility rules are a collection of precise rules that apply to a number to
determine whether it is divisible by a specified number or not
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Example: A number 66528 is divided by 2 because unit digit of number is even
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Rule of 3 Example: 66528 is divided by 3 because sum of digits of 66528 is 27, and 27 is a
multiple of 3
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Rule of 4 Example: A number 66528 is divided by 4 because last two-digits of number are
divided by 4
...

Example: A number 332640 is divided by 5 because unit digit of number is 0
...

Example: A number 332640 has unit-digit equals to 0 and sum of digits 18
...

Subtracting twice the unit digit of the number from the remaining digits gives a

Rule of 7

multiple of 7
...
84 is multiple of 7, a number 987 is divided by 7
...


Rule of 8 Example: A number 66528 is divided by 8 because last two-digits of number are
divided by 4
...

Rule of 9 Example: 66528 is divided by 9 because sum of digits of 66528 is 27, and 27 is a
multiple of 9
...

Example: A number 332640 is divided by 10 because unit digit of number is 0
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Difference is 0, so number is divided by 11
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Example: A number 332640 has last two-digits divided by 4 and sum of digits
equals to 18
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Example: If d represents a single digit from 0 to 9 and 956d330452 is divisible by 9, what is d?
 0
 4
 5
 7
 None of the above
Solution:
Sum of digits of number must be divided by 9
...
The next number after 37
which is divisible of 9 is 45
...
Answer is 8
...

3

3×2

6

9

15

Example: 4 = 4×2 = 8 = 12 = 20 = ⋯
3

Here, 4 is the lowest term of equivalent fraction
...

An improper fraction can be converted to mixed fraction
...
It is 9 + 4, and it is read as 9 and 1 by 4
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Then their
numerators are added or subtracted
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GRE - Arithmetic
7

6

7×5

6×4

35

24

Example: 4 + 5 = (4×5) + (5×4) = 20 + 20 =

(35+24)
20

59

= 20

To multiply two fractions, multiply numerator with numerator and denominator with
denominator
...

Example:

𝑎/𝑏
𝑐

=

𝑎

,

𝑎

𝑏𝑐 𝑏/𝑐

=

𝑎𝑐
𝑏

, 𝑎𝑛𝑑

𝑎/𝑏
𝑐/𝑑

=

𝑎𝑑
𝑏𝑐

Example: At the first stop on Leroy Street, half the people get off the bus
...
At the third stop on Leroy Street, threefifths leave the bus
...
How many people were on
the bus before arriving at Leroy Street? [2]
 0
 1 – Driver
 4
 20
 24
Solution:
Suppose, there are T people on the bus before arriving on Leroy Steet
...
There

𝑇
2

people get off the bus and

𝑇
2

people remaining on the bus
...
There are
2 𝑇

𝑇

𝑇

𝑇

( ) = 3 new people get onto the bus and now there are 2 + 3 =

3 2

5𝑇
6

people on the bus
...
There 5 ( 6 ) = 2 left the bus and now there
are

5𝑇
6

𝑇

𝑇

− 2 = 3 people on the bus
...
There 2 (3) = 6 left the bus and now there 3 − 6 =
𝑇
6

= 4 are left
...


Answer is 24
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GRE - Arithmetic

Decimals
Any number can be expressed as combination of powers of 10 and powers of 1/10
...
5, it is called terminating decimals
...
3333… = 0
...
Here, the process is not terminated after 3
...
982 is a decimal where the period is called decimal point and it separates the power
of 10, left of the decimal point, from the powers of 1/10, right of decimal point
...
982 is written
as 4 x 102 + 5 x 101 + 7 x 100 + 9 x 10-1 + 8 x 10-2 + 2 x 10-3 = 400 + 50 + 7 + 0
...
08 + 0
...
982
...

9 is on tenth place, 8 is on hundredth place, 2 is on thousandth place, and so on
...

To multiply a number by 10n, just move the decimal place n-places to the right
...
869 × 102 = 54386
...

543
...
43869

Rounding of Decimals
The following rules need to remember while rounding of decimals:
1
...
If the next number on which rounding takes place is 0, 1, 2, 3, or 4, the current number
should remain the same,
3
...

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5865 on thousandth place
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The next number after 6 is
5 and if the next number on which rounding takes place is 5, 6, 7, 8, or 9 the current number
should increase by one
...
5865 on thousandth place is 567
...


Exponents
When a number is written in bn form, a number is called an exponent, where b is a base and n is
exponent or power of that number
...

There are few rules GRE aspirants need to remember to simplify exponents:
1
...
(bm )n = bmn
3
...

5
...

7
...
b0 = 1, b ≠ 0
n

9
...
[3]

 20
 40

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Roots
n

When a number is written a √b, a number is called a root, where b is a radicand, n is an index
...
When n = 3, it is known as cube root
...

Similar to exponents, there are few rules in roots as well
...
√𝑎 × √𝑏 = √𝑎𝑏
2
...
√𝑎 ± √𝑏 ≠ √𝑎 ± √𝑏
One important rule is to remember here
...
To remove
roots from the denominator is called rationalization of numbers
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GRE - Arithmetic


√10
2
2

 √5
 √2 + √5
Solution:
10√12b = 4√30a
a 10√12 5
12 5
2 √5 √5 √2 1
=
= ×√ = ×√ =
=
×
= √10
b
2
30 2
5 √2 √2 √2 2
4√30
Answer is

√10

...
When two-quantities are compared,
they must be in same unit
...
Few of the basic unit
conversion an aspirants must know
...
78 liters,

•

1 pound (lb
...


When a common number is multiplied or divided to ratio, it will generate new ratio
...

When two ratios are compared, a proportion is generated
...
Speed and distance are in direct proportion when
time is constant
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GRE - Arithmetic
Inverse proportion: When one quantity increases and the second quantity decreases, or vice
versa, both quantities are in inverse proportion
...

𝑎 3
=
𝑏 4
Quant
...
B

𝑎+1
𝑏+1

4
5

Solution:
𝑎

3

𝑎

6

𝑎

3+1

4

4

Suppose, 𝑏 = 4
...
A equals to 𝑏 = 4+1 = 5, and Quant
...
Both are equal and answer is
c
...
Quant
...
B equals to
4


...
Final answer is d
...
There are two types of sequence
...

Example: 1, 5, 9, 13, 17, 19, 23, … are in arithmetic sequence because difference between
consecutive number is constant
...

For above given sequence, 101th term of sequence = 1 + (101 – 1) x 4 = 401
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Example: 2, 4, 8, 16, 32, 64, 128, … are in geometric sequence because ratio between consecutive
number is constant
...

For above given sequence, 101th term of sequence = 2 x 2(101 – 1) = 2 x 2100 = 2101
...


For above given sequence, sum of first 101 terms =

2(2101 −1)
2−1

= 2102 − 2
...
What is the 4 th number in the sequence? [4]
 15
 19
 35
 43
 51
Solution:
As given in the question, sequence is in arithmetic sequence and common difference is (-4)
...


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K is a non-zero number [5]
Quant
...
B

The product of the opposite of K and the

The product of K and the reciprocal of K

reciprocal of K
2
...
A

Quant
...


4
...
A

Quant
...
After three
pennies are removed, the ratio of pennies to nickels is 3:2

5
...
A

Quant
...


If the sum of the positive factors of N is N + 1, then N must be [9]
 Odd
 Even
 A perfect square
 Prime
 Not prime

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Northern Lights College has only three majors – music, education, and math
...
Half of the students are education majors
...
Three-quarters of the music majors are female
...


The chief of police for Santa Monica USA notices that, not including himself, 3/5 of the
police force carries firearms
...

How many people on his force do not carry firearms? [11]
 5
 6
 11
 16
 24

9
...


For each positive integer n, Nth term of the sequence S is 1 + (-1)n [12]
Quant
...
B

The sum of the first 39 terms of S

39

Quant
...
B [13]

The number of integers between 100 and

36

500 that are multiples of 11
11
...
A

Quant
...

Quant
...
B

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A rectangular game board is composed of identical squares arranged in a rectangular
array of r rows and r + 1 columns
...
If r > 10, which of the following
represents the number of squares on the board that are neither in the 4th row nor in
the 7th column? [16]
 r2 – r
 r2 – 1
 r2
 r2 + 1
 r2 + r
14
...
Which of the following is equal to 𝟔𝟏𝟒 ? [18]
𝟐𝟓 ×𝟑𝟕
 22 x 32
 27 x 37
 29 x 32
 29 x 37
 29 x 39
16
...
What is the sum of 100 terms of the sequence? [19]
 1/10100
 1/100

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When the positive integer n is divided by 45, the remainder is 18
...
For each integer n > 1, let A(n) denote the sum of the integers from 1 to n
...
What is the value of A(200)? [21]
 10,100
 15,050
 15,150
 20,100
 21,500
19
...
The value of (𝟏
...
𝟖𝟑𝟑𝟑𝟑)
 1/2
 2/3
 3/2

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A certain theater has 100 balcony seats
...
If all the balcony seats are sold when the
price of each seat is $10, which of the following could be the price of a balcony seat if
the revenue from the sale of balcony seats is $1,360? [24]
 $12
 $14
 $16
 $17
 $18
22
...
Carla has 1/4 more sweaters than cardigans, and 2/5 fewer cardigans than turtle necks
...
The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all
integers n ≥ 3, the nth term in the sequence is the average (arithmetic mean) of the first
n – 1 term in the sequence
...
What is the remainder when 1317 +1713 is divided by 10? [28]

26
...

 x=y
 y=z

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Which of the following could be the units digit of 57N, where N is a positive integer?
[30]
Indicate all such statements
...
Which two of the following numbers have a product that is between −1 and 0? [31]
Indicate both of the numbers
...
Which of the following operations carried out on both the numerator and the
denominator of a fraction will always produce an equivalent fraction? [32]
Indicate all such operations
...


np < 0 [33]
Quant
...
B

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32
...
A

Quant
...
The
number x is greater than 60 percent of the numbers in T, and the number y is greater
than 40 percent of the numbers in T [35]
Quant
...
B

x–y

20

33
...


N is a positive integer [36]
Quant
...
B

The remainder when N is divided by 5

The remainder when N + 10 is divided by 5

Quant
...
B [37]

The number of two-digit positive integers

80

for which the unit digit is not equal to the
tens digit
35
...
A
𝑎
𝑏

36
...
A

Quant
...


38
...
B

x is a positive, odd integer [40]
Quant
...
B

(-3)x

-22x
n is an integer, and |2n+7| ≤ 10 [41]

Quant
...
B

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...


A set has exactly five consecutive positive integers [42]
Quant
...
B

The percentage decrease in the average of
the numbers when one of the numbers is

20%

dropped from the set
40
...
A

Quant
...
822 × 0
...
826

41
...
A

Quant
...


ab > 0; |c| > |a + b| [45]
Quant
...
B

|a + b - c|

|a| + |b| - |c|

43
...
A
2

3

Quant
...


4

(−1)𝑥 + (−1)2𝑥 + (−1)3𝑥 + (−1)4𝑥
x > z; y > z [47]

Quant
...
B

x+y

z

45
...
A

Quant
...
If 0 < y < x, then which of the following is a possible value of 𝟐𝟕𝒙+𝟐𝟑𝒚 ? [49]
𝟑𝒙+𝟐𝒚
I
...
7

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...


9
...


10
...
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime
...
If n = 4p, where p is a prime number greater than 2, how many different positive even
divisors does n have, including n? [51]
 2
 3
 4
 6
 8
49
...
If the greatest common divisor of x and 3y is 9, and the
least common multiple of 3x and 9y is 81, then what is the value of 81xy? [52]
 35
 36
 37
 38

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...
How many pairs of natural numbers whose HCF is 12 add up to 216? [53]
 3
 6
 9
 17
 18
51
...
98 + 100, and K = 1 + 3 + 5 + 7 +
...
+ 972 – 982 + 992 – 1002 = [54]
 J2 – K2
 -50(J2 – K2)
 -K – J
 K2 – J2
 (-J – K)2
52
...


𝒑𝟐 < 𝟐𝒑

II
...


𝒑𝟐 > 𝟐𝒑
 I
 II
 III
 I and II only
 I, II, and III

53
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GRE - Arithmetic
 None of these
54
...

The digits are used only once in each of the number and the sum of these two numbers
is 555
...
One side of a parking stall is defined by a straight stripe that consists of n painted
sections of equal length with an unpainted section 1/2 as long between each pair of
consecutive painted sections
...
If n is an integer
and the length, in inches, of each unpainted section is an integer greater than 2, what
is the value of n? [58]
 5
 9
 10
 14
 29
56
...
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31

GRE - Arithmetic

Answers of Practice Questions
1
...


B

3
...


C

5
...


D

7
...


B

9
...


C

11
...


C

13
...


C

15
...


D

17
...


D

19
...


D

21
...


160

23
...


1
...


0

26
...


1, 3, 7, 9

28
...


B, C

30
...


C

32
...


C

34
...


D

36
...


A

38
...


B

40
...


A

42
...


B

44
...


C

46
...


D

48
...


D

50
...


C

52
...


C

54
...


C

56
...
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32

GRE - Arithmetic

Solution
1

Let’s take K = 2,
Quantity – A: (-2) * 1/2 = -1
Quantity – B: 2 * 1/2 = 1
Answer is B
...

Hence, the answer is D
...

If we assume r = 9, 9/3 = 3 not possible because q = p
...
This is possible and the maximum value of r = 8
...


3

Let’s assume c = 8
Quantity – A: Divisors of 8 are 1, 2, 4, 8
...
of positive divisors of 2 * 8 = 16 are 1, 2, 4, 8, 16, and they are 5
...

Let’s assume c = 15
Quantity – A: Divisors of 15 are 1, 3, 5, 15
...
of positive divisors of 2 * 15 = 30 are 1, 2, 3, 5, 6, 10, 15, 30 and they
are 8
...

Hence, the answer is D
...
P/N = 7/4,
After three pennies removed, new ratio is 3:2, (P – 3)/N = 3/2
Solving for Nickel, N = 12
...


5

p2 ≤ 1; - 1 ≤ p ≤ 1

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...

Hence, the answer is E
...

Hence, the answer is D
...

Education major = T/2,
Math major = T/3,
Music major = T – T/2 – T/3 = T/6
Three-quarters of the music majors are female
...

Hence, the answer is E
...
Total police men are F + N
...

Hence, the answer is B
...

Sum of first 39 terms = 0 + 2 + 0 + 2 + 0 + 2 + up to 39 terms
...
com

34

GRE - Arithmetic
Here, we have 19 even terms and sum are 19 * 2 = 38
...

10

Easiest way to do this is to find the smallest multiple of 11 over hundred and the largest
below 500
...
0910011 = 9
...
So, the 10th multiple of 11
must be greater than 100
...

Similarly we do 500/11 = 45
...
45
...
We know that 45th multiple of 11 is 495
...
Remember to add 1 as both 10th multiple and
45th multiple is counted
...
Thus, C is the correct answer
...

Put a = -1 and b = 1, then we have Quantity A is (−1)10 = 1
...

Now put a = -2 and b = 1, Quantity A is (−2)10 = 1024
...
Now Quantity
A is greater
...

The largest perfect square less than 39 is 36
...
Solving for n we get
n = (+6) and (−6)
...

Hence both quantities are equal
...
[62]

13

If we were just counting all of the squares in the board game, we could use multiplication:
r rows times r + 1 columns
...

If we take one row out (doesn't matter if it’s the first, second, third, etc
...

If we also then take a column out, we would have r – 1 rows times r columns
...

So option A is correct
...
com

35

GRE - Arithmetic
14

Construct the following table and remember:
EVEN + ODD = ODD
EVEN + EVEN = EVEN
ODD + ODD = EVEN
EVEN * EVEN = EVEN
EVEN * ODD = EVEN
ODD * ODD = ODD
Now check the answer choices
...
So, let's test another pair of values
...
com

36

GRE - Arithmetic
Now check the remaining answer choices
...

By the process of elimination, the correct answer is C
...
[65]

16

1

1

𝑘

𝑘+1

Given 𝑎𝑘 = −
a1 = 1/1 – 1/2;
a2 = 1/2 – 1/3;

a3 = 1/3 – 1/4; …
a100 = 1/100 – 1/101
a1 + a2 + a3 + … + a100 = 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + … + 1/100 – 1/101 = 1 – 1/101
Sum is 100/101
...

17

We are given that when the positive integer n is divided by 45, the remainder is 18
...
Thus, 9 is the correct answer
...
[66]

18

In the question, you are given that A(n) is equal to the sum of the integers from 1 to n, so
A(200) = 1 + 2 + 3 + … + 100 + 101 + 102 + 103 + … + 200
...
+ 200
= A(100) + (100 + 1) + (100 + 2) + (100 + 3)
...
+ 100) + 100 ∗ 100
= 5050 + 5050 + 10000

darshankapadia11@gmail
...
[67]
19

One approach is to look for a pattern
...


...

In general, we can see that 10n – 74 will feature n – 2 9's followed by 26
...

This means the sum of its digits = 48(9) + 2 + 6 = 432 + 2 + 6 = 440
...
[68]

20

Here,
1
...
6666 = 2/3,
1
...
125 = 1 + (1/8) = 9/8,
0
...
8 = 4/5,
0
...
166666 = 5*(1/6) = 5/6
...
33333)(0
...
125) (4/3)(2/3)(9/8) 4 × 2 × 9 × 4 × 5 × 6
=
=
=2
(0
...
8)(0
...
[69]

21

Equation should be (10 + 2*x) * (100 – 5x) = 1,360, where x is the number of times, we
increased the price by $2
...
com

38

GRE - Arithmetic
Price = 10 + 2*3 = 16 or 10 + 2*12 = 34
Thus, the correct answer is Choice C
...

NOTE: Yes, I have started at 000 and ended at 299, even though the question asks us to
look at the numbers from 1 to 300
...
Okay, there are 300 integers from 000 to 299
...
, 9) appears the same number of times in the UNITS
position
...
So, the digit 1 must
appear (1/10)(300) times, which equals 30 times
...
, 9) appears the same number of times in the TENS
position
...
So, the digit 1 must
appear (1/10)(300) times, which equals 30 times
...
So, the digit 1
appears 100 times
...
[71]

23

Given:
S = (1/4 + 1) ∗ C = (5/4) ∗ C
and C = (1−2/5) ∗ T = (3/5) ∗ T
or T = (5/3) ∗ C
Now,
Let C = 12 (since it is a factor of 4 and 3
...
[72]

darshankapadia11@gmail
...
The AVERAGE = 3
...

The same applies to this question:
term1 = 1
term2 = 2
term3 = (1+2)/2 = 1
...

Notice that the AVERAGE of terms 1 and 2 is 1
...

So, to find term4, we take terms 1 and 2 (which we already know has an average of 1
...
5 (which is term3), then the average won't change
...
5 And so on
...
5 and term7 = 1
...
5, and so on
...
[73]

25

The remainder when dividing an integer by 10 always equals the units digit
...
Every fourth term is the same
...
Thus, 317 must end in 3
...
Every fourth term is the same
...
Thus, 713 must end in 7
...
Thus, the units digit is 0
...
Will it work with a larger number?
If x = 100, y = 100, 3x < 2y or (3)(100) < (2)(100) or 300 < 200 also incorrect
...


darshankapadia11@gmail
...

y > z:
If y = 1
...
1) < (4)(1) or 2
...

x > z:
If x = 1
...
1) < (4)(1) or 3
...

Hence option B, C and D are correct
...

Of course, 7 raised to a power has a repeating pattern
71 = 7
72 = 49, unit digit is 9
73 = 343, unit digit is 3

...
[30]

28

To having a negative product, you have to have one negative number and one positive
AND at the same time between -1 and zero
...
You must go through the process of calculation
...

B and C are the choices
...

Multiplying by 5
If we start with: x/y
And multiply the numerator and the denominator by 5, we get: 5x/5y

darshankapadia11@gmail
...

Dividing by 100
If we start with: x/y
And divide the numerator and the denominator by 100, we get: (x/100)/(y/100)
(x/100)/(y/100) = (x/100)(100/y) = 100x/100y
Since 100x/100y and x/y are equivalent fractions, statement C is TRUE
...
[75]
30

This is a very popular theorem of mathematics known as the Triangle inequality
...

Now looking at our problem: np < 0
...

By triangle equality we know that |n + p| < |n| + |p|
...

Hence clearly quantity B is greater
...

Now prime factors of 180 are 2, 3, and 5
...

Greatest prime factor of both the quantities is 5
...
[77]

32

Say that x = 2
...
If you
consider there are an infinite number of numbers between 0 and 2 when you use
decimals
...
1, 0
...
1579, 0
...
29,etc)
...
com

42

GRE - Arithmetic
Say that y = 1
...
So x – y = 2 – 1 = 1
...

But what if x were at the other extreme of the range, such as x = 48? If we keep y = 1,
that would mean that 40% of the numbers were between 0 and 1 and the next 20% were
between 1 and 48 (and the remaining 40% were between 48 and 50)
...
In this case, Quantity A is greater
...

Hence, D is correct
...

Quantity A becomes 5k + r
Quantity B becomes 5k + r + 10 or 5(k + 2) + r
Dividing each by 5 Quantity by 5 and checking remainder
Quantity A: k + r/5
Quantity B: (k + 2) + r/5
Quantity A has remainder r
...

Hence both quantities are equal
...
[78]

34

Take the task of creating 2-digit numbers and break it into stages
...

We can choose any digit from 1, 2, 3, 4, 5, 6, 7, 8, or 9
...

[Aside: we cannot choose 0 for the tens position, because numbers like 03 and 07 are not
considered 2-digit numbers]
Stage 2: Select a digit for the UNITS position
...

HOWEVER, for this question, the units digit must be DIFFERENT from the tens digit we
selected in stage 1
...
So,
we can complete stage 2 in 9 ways
...
com

43

GRE - Arithmetic
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus
create a 2-digit number) in (9)(9) ways (= 81 ways)
So, we have:
Quantity A: 81
Quantity B: 80
Hence the answer is A
...

Let a = 1 and b = 2
Quantity A: ½
Quantity B: (1 + 3)/(2 + 3) = 4/5
Quantity B is greater
...

Hence a relationship cannot be determined
...
[80]

36

We have x is an integer greater than 1
...
3333x
Now we can see that for some values of x such as 2 and 3 Quantity A is bigger for every
other value of x Quantity B is greater
...
[39]

37

-3 raised to odd integers always is negative
...


darshankapadia11@gmail
...

As you can see A is always greater than B
...
[81]
38

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to
know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
Given: |2n + 7| ≤ 10
In this case, we'll apply rule #1 to get: -10 ≤ 2n + 7 ≤ 10
Subtract 7 from all three parts: -17 ≤ 2n ≤ 3
Divide all three parts by 2 to get: -8
...
5
Since n is an INTEGER, the possible values of n are: -8, -7, -6, -5,
...
[82]

39

Choose numbers 1, 2, 3, 4, and 5
Original avg = 15/5 = 3
If 1 is dropped, avg = -16
...
67%
Quant - A: 16
...
com

45

GRE - Arithmetic
Hence, the answer is B
...
825
Quant - B: 0
...

Hence, the answer is A
...

If you pick a number, you will see the pattern
1 and 2, follow that for x/4 x = 2 which means 2/4 = 1/2 = 0
...
5 > 0 (zero is the hundredths digit),
2 and 3, follow that for x/4 you do have 3/4 = 0
...
50 and 5 > 0
and so on and so forth this pattern
...

Hence, the answer is A
...
(1)
|c| > |a + b|
=> |c| > |a|+|b| (from 1)
=> |a|+|b| - |c| < 0
=> Quantity B < 0
If you look at Quantity A, it is always greater than zero
...

Hence, the answer is A
...

Also, if x is ODD, then 2x is even, 3x is odd and 4x is even

darshankapadia11@gmail
...

Case ii: x is EVEN
If x is even, then x^2 is even, x^3 is even, and x^4 is even
...

So, we get:
Quantity – A: 1 + 1 + 1 = 3
Quantity – B: (-1) + 1 + (-1) + 1 = 0
In this case, Quantity B is greater
...

Hence, the answer is B
...

Case i: Since x > z and y > z, one possible set of values is x = 1, y = 1, and z = 0
We get:
Quantity A: x + y = 1 + 1 = 2
Quantity B: 0
In this case, Quantity A is greater
...
[88]

45

If you put the sequence as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, you can see that it conforms to the
condition that each term after the first is the average of the preceding term and the
following term:
a10 – a8 = 10 – 8 = 2

darshankapadia11@gmail
...

The sequence can also contain not consecutive numbers: try 1, 3, 5, 7, 9, 11, 13, 15, 17
etc
...

Hence, the answer is C
...


It is 9 + something, so min value is slightly more than 9
...

II) Max value
...

Now, x > y so 3x > 3y thus 3x + 2y > 3y + 2y
This means (3y + 2y)/(3x + 2y) < 1
...

III) is also out
ONLY 9
...
[90]
47

A prime number greater than 5 can have only the following four-unit digits: 1, 3, 7, or 9
...
For example, consider p = 11 = prime --> 2p + 1 = 23 = prime;
If the units digit of p is 3 then the units digit of 2p + 1 would be 7, which is a possible unit
digit for a prime
...
For example, consider p = 29 = prime --> 2p + 1 = 59 = prime
...
com

48

GRE - Arithmetic
The product of all the possible unit digits of Sophie Germain primes greater than 5 is 1 *
3 * 9 = 27
...
[91]
48

When p = 3, n = 4*3 = 12, positive even divisor of n = {2, 4, 6, 12} i
...
, 4 Divisors,
When p = 5, n = 4*5 = 20, positive even divisor of n = {2, 4, 10, 20} i
...
, 4 Divisors,
When p = 7, n = 4*7 = 28, positive even divisor of n = {2, 4, 14, 28} i
...
, 4 Divisors,
When p = 11, n = 4*11 = 44, positive even divisor of n = {2, 4, 22, 44} i
...
, 4
Divisors,
When p = 13, n = 4*13 = 52, positive even divisor of n = {2, 4, 26, 52} i
...
, 4
Divisors
...
[92]
49

If the greatest common divisor (GCD) of x and 3y is 9, then the GCD of 3x and 9y is 27
...

So, take (3^3)(3^4) = 27xy and multiply both sides by 3 to get: (3)(3^3)(3^4) = (3)(27xy)
Simplify: 3^8 = 81xy
Hence, the answer is D
...

We can have three such pairs:
1 + 17 = 18
5 + 13 = 18
7 + 11 = 18

darshankapadia11@gmail
...
[94]
51

We have several differences of squares hiding in the expression 1² - 2² + 3² - 4² + 5² - 6² +
…
...
+ 97² - 98² + 99² - 100² = 1² - 2² + 3² - 4² + 5² - 6² +
...
+ (97 - 98)(97 + 98) + (99 - 100)(99 +
100)
= (-1)(1 + 2) + (-1)(3 + 4) + (-1)(5 + 6) +
...
+ (97 + 98) + (99 + 100)]
= (-1)(1 + 2 + 3 + 4 +
...
97 + 98 + 99 + 100 = K + J
So, we're replace 1 + 2 + 3 + 4 +
...

We get: (-1)(1 + 2 + 3 + 4 +
...

Hence, the answer is C
...
p2 < 2p
...
1
1
...
1
1
...
2
...
p2 = 2p
...
True
III
...
Let's consider P=2
...
52 > 2∗2
...
25 > 5
...
[96]

53

1

Option – A: (−𝑎)−2𝑏 = (−𝑎)2𝑏 = 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒,
Option – B: (−𝑎)−3𝑏 , may be positive (consider a = 1 and b = 2) as well as negative
(consider a = 1 and b = -1),
1

1

Option – C: −(𝑎−2𝑏 ) = − 𝑎2𝑏 = − 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 = 𝑁𝑒𝑔𝑎𝑡𝑎𝑖𝑣𝑒,

darshankapadia11@gmail
...

Hence, the answer is C
...

This is possible with 8 and 7 only
...
Therefore, the sum of
the 2 digits in the 10's place should end with 4, so that with the carry over, we will have
5 in the 10's place
...

So, we now have 98 + 57 or 58 + 97 with 1 digit left as 4
...


498 + 57

ii
...


458 + 97

iv
...
[98]
55

One side of a parking stall is defined by a straight stripe that consists of n painted
sections of equal length with an unpainted section 1/2 as long between each pair of
consecutive painted sections
...


If we let x = the length of 1 painted section, then 0
...

The total length of the stripe from the beginning of the first painted section to the end
of the last painted section is 203 inches
...
com

51

GRE - Arithmetic
Important: If we examine the above diagram, we can see that, IF the entire stripe
consisted

of 3

painted

sections,

then

there

would

be 2

spaces

In general: (the number of spaces) = (the number of painted sections) - 1
So, if there are n painted sections, then there must be (n-1) spaces
...
Likewise, if there are n - 1 spaces, and each space has
a length of 0
...
5x(n - 1)
...
5x(n - 1) = 203
Simplify to get: nx + 0
...
5x = 203
Simplify: 1
...
5x = 203
To get integer coefficients, we'll multiply both sides of the equation by 2 to get: 3nx - x =
406
Factor both sides to get: x(3n - 1) = (2)(7)(29)
Since we're told that n and x are both positive integers, we know that 3n is a multiple of
3, which means 3n - 1 is 1 less than some of multiple of 3
When we examine the three prime factors of 406 (2, 7, and 29), we see that 2 and 29 are
both 1 less than some of multiple of 3
If 3n - 1 = 2, then n = 1, and 1 is not among the answer choices (Also, if we have just 1
painted section, then we have 0 spaces, which breaks the condition that each unpainted
section is an integer greater than 2)
If 3n - 1 = 29, then n = 10
...

Hence, the answer is C
...
com

52

GRE - Arithmetic
^5 - 2 and the pattern repeats, every 4 powers
we are looking for the 28th power, 28/4 = 7 R0, therefore we use the 4th place in the
pattern --> 6
33^47
for powers of 33, the units digit follows the pattern (^power - units digit):
^1 – 3
^2 – 9
^3 – 7
^4 – 1
^5 - 3 and the pattern repeats, every 4 powers
we are looking for the 47th power, 47/4 = 11 R3, therefore we use the 3rd place in the
pattern --> 7
37^19
for powers of 37, the units digit follows the pattern (^power - units digit):
^1 – 7
^2 – 9
^3 – 3
^4 – 1
^5 - 7 and the pattern repeats, every 4 powers
we are looking for the 19th power, 19/4 = 4 R3, therefore we use the 3rd place in the
pattern --> 3
6 x 7 x 3 = 126
...
[100]

darshankapadia11@gmail
...
F
...
, 2012, p
...


[2]

D
...
Blair Madore, "Barron's GRE Math Workbook," Barrons Educational Series, New Age
International (P) Limited, 2012, p
...


[3]

D
...
Blair Madore, "Barron's GRE Math Workbook," Barrons Educational Series, New Age
International (P) Limited, 2012, p
...


[4]

D
...
Jeff Kolby, "GRE Math Bible," Nova Press, 2008, p
...


[5]

D
...
Blair Madore, "Barron's GRE Math Workbook," Barrons Educational Series, New Age
International (P
...
, 2012, p
...


[6]

D
...
Blair Madore, "Barron's GRE Math Workbook," Barrons Educational Series, New Age
International (P) Ltd
...
41
...
F
...
, 2012, p
...


[8]

D
...
Blair Madore, "Barron's GRE Math Workbook," Barrons Educational Series, New Age
International (P) Ltd
...
43
...
F
...
, 2012, p
...


[10] D
...
Blair Madore, "Barron's GRE Math Workbook," Barrons Educational Series, New Age
International (P) Ltd
...
68
...
F
...
, 2012, p
...


darshankapadia11@gmail
...
Available: https://greprepclub
...
html
...

[13] Carcass, "The number of integers between 100 and 500 that are multi," 14 Feb 2017
...
Available: https://greprepclub
...
html
...

[14] Carcass, "a < 0 < b," 15 Feb 2017
...
Available: https://greprepclub
...
html
...

[15] Carcass, "n is an integer, and n^2 < 39," 05 Mar 2017
...
Available:
https://greprepclub
...
html
...

[16] Carcass, "A rectangular game board is composed of identical squares ar," 17 Feb 2017
...


Available:

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html
...

[17] Carcass, "If x and y are integers and x = 50y + 69, which of the follo," 05 Mar 2017
...

Available:

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...
html
...

[18] Carcass, "Which of the following is equal to," 25 Feb 2017
...
Available:
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...
html
...

[19] greMS15, "In the sequence a1, a2, a3,
...

[Online]
...
com/forum/in-the-sequence-a1-a2-a3-a100-thekth-term-is-defined-1983
...
[Accessed 17 May 2022]
...
com

55

GRE - Arithmetic
[20] sandy, "When the positive integer n is divided by 45, the remainder," 12 May 2016
...


Available:

https://greprepclub
...
html
...

[21] sandy, "For each integer n > 1, let A(n) denote the sum," 12 May 2016
...
Available:
https://greprepclub
...
html
...

[22] Carcass, "If 10^50 – 74 is written as an integer in base 10 notation what is the," 25 Nov
2021
...
Available: https://greprepclub
...
html
...

[23] Bunuel, "The value of (1
...
6666)(1
...
75)(0
...
8333) is closest to," 23 Oct
2018
...
Available: https://gmatclub
...
html
...

[24] GeminiHeat, "A certain theater has 100 balcony seats
...
[Online]
...
com/forum/a-certain-theater-has-100balcony-seats-for-every-2-increase-in-the-25129
...
[Accessed 17 May 2022]
...

[Online]
...
com/forum/gre-math-challenge-306
...


[Accessed 17 May 2022]
...
[Online]
...
com/forum/carla-has-1-4-more-sweaters-than-cardigansand-5941
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/qotd-8-the-first-term-in-a-certain-sequenceis-1-the-2nd-2645
...
[Accessed 17 May 2022]
...
com

56

GRE - Arithmetic
[28] sandy, "What is the remainder when 13^17 + 17^13 is divided by 10?," 13 Aug 2018
...
Available: https://greprepclub
...
html
...

[29] Carcass, "If x, y, and z are positive numbers such that 3x < 2y < 4z,," 06 Mar 2017
...

Available: https://greprepclub
...
html
...

[30] Carcass, "Which of the following could be the units digit of where n i," 12 Sep 2017
...
Available: https://greprepclub
...
html
...

[31] Carcass, "Which two of the following numbers have a product that is be," 11 Sep 2017
...


Available:

https://greprepclub
...
html
...

[32] sandy, "Which of the following operations carried out on both," 16 May 2016
...

Available:

https://greprepclub
...
html
...

[33] Carcass, "np < 0," 14 Feb 2017
...
Available: https://greprepclub
...
html
...

[34] Carcass,

"x

>

0

and

x^4

=

625,"

05

Mar

2017
...


Available:

https://greprepclub
...
html
...

[35] Carcass, "T is a list of 100 different numbers that are greater than 0," 27 Nov 2017
...
Available: https://greprepclub
...
html
...


darshankapadia11@gmail
...
,"

24

Feb

2017
...


Available:

https://greprepclub
...
html
...

[37] sandy, "Number of two digit positive integers for which the unit," 14 Jun 2016
...

Available:

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...
html
...

[38] sandy, "GRE Math Challenge #71- (a/b) or (a+3)/(b+3)," 03 May 2015
...
Available:
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...
html
...

[39] sandy, "x is an integer greater than 1
...
[Online]
...
com/forum/x-is-an-integer-greater-than-1724
...
[Accessed 17
May 2022]
...
," 10 Aug 2017
...
Available:
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...
html
...

[41] Carcass, "The difference between the greatest and least possible value," 22 Jun 2017
...


Available:

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...
html
...

[42] Carcass, "A set has exactly five consecutive positive integers
...
[Online]
...
com/forum/a-set-has-exactly-five-consecutive-positive-

integers-15120
...
[Accessed 17 May 2022]
...
82)^2

(0
...


[Online]
...
com/forum/topic-8721
...
[Accessed 17 May 2022]
...
com

58

GRE - Arithmetic
[44] Carcass, "The integers x and (x - 1) are not divisible by 4
...
[Online]
...
com/forum/the-integers-x-and-x-1-are-not-divisible-by-5797
...

[Accessed 17 May 2022]
...
[Online]
...
com/forum/ab18126
...
[Accessed 17 May 2022]
...
,"

15

Sep

2017
...


Available:

https://greprepclub
...
html
...

[47] Carcass,

"x

>

z

and

y

>

z,"

09

Oct

2019
...


Available:

https://greprepclub
...
html
...

[48] Carcass, "In the sequence above, each term after the first is equal to," 17 Jan 2020
...
Available: https://greprepclub
...
html
...

[49] BrentGMATPrepNow, "If 0 < y < x, then which of the following is," 31 Jan 2017
...

Available:

https://gmatclub
...
html
...

[50] alchemist009, "A “Sophie Germain” prime is any positive prime number p for," 15 May
2012
...
Available: https://gmatclub
...
html
...

[51] Walkabout, "If n = 4p, where p is a prime number greater than 2, how many differen," 27
Dec 2012
...
Available: https://gmatclub
...
html
...

[52] BrentGMATPrepNow, "x and y are positive integers
...
[Online]
...
com/forum/x-and-y-are-positiveintegers-if-the-greatest-common-divisor-of-x-and-233373
...
[Accessed 17 May 2022]
...
com

59

GRE - Arithmetic
[53] Carcass, "How many pairs of natural numbers whose HCF is 12 add up to 216? 6 3," 25
Mar 2021
...
Available: https://greprepclub
...
html
...

[54] BrentGMATPrepNow, "If J = 2 + 4 + 6 + 8 +
...
+," 08
May 2017
...
Available: https://gmatclub
...
html
...

[55] Bunuel, "If 1 < p < 3, then which of the following could be true?," 14 Jan 2020
...

Available:

https://gmatclub
...
html
...

[56] kingflo, "If a and b are nonzero integers, which of the following must be," 20 Jul 2013
...
Available: https://gmatclub
...
html
...

[57] KarunMendiratta, "A two digit number and a three digit number is formed using digits:
4,," 08 Mar 2021
...
Available: https://greprepclub
...
html
...

[58] parkhydel, "One side of a parking stall is defined by a straight stripe that consi," 27 Apr
2020
...
Available: https://gmatclub
...
html
...

[59] BrentGMATPrepNow, "What is the units digit of the product (32^28) (33^47) (37^19)?,"
09 Apr 2017
...
Available: https://gmatclub
...
html
...

[60] sandy, "Re: The number of integers between 36 100 and 500 that are multi," 15 Feb 2017
...
Available: https://greprepclub
...
html
...


darshankapadia11@gmail
...
[Online]
...
com/forum/a0-b-3264
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/n-is-an-integer-and-n-3382
...
[Accessed 17 May
2022]
...

[Online]
...
com/forum/a-rectangular-game-board-is-

composed-of-identical-squares-ar-3268
...
[Accessed 17 May 2022]
...

[Online]
...
com/forum/if-x-and-y-are-integers-and-x-50y69-which-of-the-follo-3388
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/which-of-the-following-is-equal-to-3319
...
[Accessed
17 May 2022]
...
[Online]
...
com/forum/when-the-positiveinteger-n-is-divided-by-45-the-remainder-2133
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/for-each-integer-n-1-let-a-n-denote-the-sum2131
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/if-10-50-74-iswritten-as-an-integer-in-base-10-notation-what-is-the-25559
...
[Accessed 17 May
2022]
...
com

61

GRE - Arithmetic
[69] GMATinsight, "The value of (1
...
6666)(1
...
75)(0
...
8333) is closest to," 23
Oct 2018
...
Available: https://gmatclub
...
html
...

[70] Carcass, "Re: A certain theater has 100 balcony seats
...
[Online]
...
com/forum/a-certain-theater-has-100balcony-seats-for-every-2-increase-in-the-25129
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/gre-math-challenge-306
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/carla-has-1-4-more-sweaters-than-cardigansand-5941
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/qotd-8-the-first-term-in-acertain-sequence-is-1-the-2nd-2645
...
[Accessed 17 May 2022]
...

[Online]
...
com/forum/if-x-y-and-z-are-positive-numberssuch-that-3x-2y-4z-3398
...
[Accessed 17 May 2022]
...


[Online]
...
com/forum/which-of-the-following-

operations-carried-out-on-both-2145
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/np3260
...
[Accessed 17 May 2022]
...
[Online]
...
com/forum/x-0-and-x-3380
...
[Accessed 17 May 2022]
...
com

62

GRE - Arithmetic
[78] sandy, "Re: n is a positive integer
...
[Online]
...
com/forum/n-is-a-postive-integer-8148
...
[Accessed 17 May
2022]
...
[Online]
...
com/forum/number-of-two-digit-positiveintegers-for-which-the-unit-2249
...
[Accessed 22 May 2022]
...
[Online]
...
com/forum/a-and-b-are-positive-integers-3261
...
[Accessed 17
May 2022]
...
," 22 Aug 2017
...
Available:
https://greprepclub
...
html
...

[82] GreenlightTestPrep, "The difference between the greatest and least possible value," 28
Jun 2017
...
Available: https://greprepclub
...
html
...

[83] bellavarghese, "Re: A set has exactly five consecutive positive integers
...

[Online]
...
com/forum/a-set-has-exactly-five-consecutivepositive-integers-15120
...
[Accessed 17 May 2022]
...
82)^2

(0
...


[Online]
...
com/forum/topic-8721
...
[Accessed 17 May 2022]
...
," 13 Aug 2017
...

Available:

https://greprepclub
...
html
...


darshankapadia11@gmail
...


[Online]
...
com/forum/ab-18126
...
[Accessed 17 May 2022]
...
,"

01

Nov

2021
...


Available:

https://greprepclub
...
html
...

[88] GreenlightTestPrep, "Re: x > z and y > z," 09 Oct 2019
...
Available:
https://greprepclub
...
html
...

[89] Roccoporco555, "Re: In the sequence above, each term after the first is equal to," 11 Feb
2020
...
Available: https://greprepclub
...
html
...

[90] chetan2u, "Re: If 0 < y < x, then which of the following is," 31 Jan 2017
...
Available:
https://gmatclub
...
html
...

[91] Bunuel, "Re: A “Sophie Germain” prime is any positive prime number p for," 15 May 2012
...


Available:

https://gmatclub
...
html
...

[92] GMATinsight, "Re: If n = 4p, where p is a prime number greater than 2, how many
differen," 27 Jul 2015
...
Available: https://gmatclub
...
html
...

[93] BrentGMATPrepNow, "Re: x and y are positive integers
...
[Online]
...
com/forum/x-and-y-arepositive-integers-if-the-greatest-common-divisor-of-x-and-233373
...
[Accessed 17
May 2022]
...
com

64

GRE - Arithmetic
[94] KarunMendiratta, "How many pairs of natural numbers whose HCF is 12 add up to 216? 6
3," 25 Mar 2021
...
Available: https://greprepclub
...
html
...

[95] BrentGMATPrepNow, "Re: If J = 2 + 4 + 6 + 8 +
...
+,"
10 May 2017
...
Available: https://gmatclub
...
html
...

[96] Leadership, "Re: If 1 < p < 3, then which of the following could be true?," 15 Jan 2020
...
Available: https://gmatclub
...
html
...

[97] Bunuel, "Re: If a and b are nonzero integers, which of the following must be," 20 Jul 2013
...
Available: https://gmatclub
...
html
...

[98] kvarunkumar1975, "Re: A two digit number and a three digit number is formed using
digits: 4,," 08 Mar 2021
...
Available: https://greprepclub
...
html
...

[99] BrentGMATPrepNow, "Re: One side of a parking stall is defined by a straight stripe that
consi," 27 Apr 2020
...
Available: https://gmatclub
...
html
...

[100] amynicole, "Re: What is the units digit of the product (32^28) (33^47) (37^19)?," 09 Apr
2017
...
Available: https://gmatclub
...
html
...

************************* End of Unit *************************

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