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Numerical Reasoning

11
...
) (25) ^0 - (-2) ^4 + (-3^4) - (-8) ^2 =?

a
...
50% c
...
52
...
51
...
2 b
...
+161 d
...
-160

12
...
) -2 ^2 - (-9) ^2 - (-3^2) + 15^0 =?

a
...
840 c
...
3360 e
...
-75 b
...
-85 d
...
0

13
...
The numbers
are 7, 8, 10, and 15
...
) 20% of 30% of X is 225 what is the value of X a
...
5 b
...
375
d
...
112
...
7 b
...
10 d
...
8

4
...
) The mean median and mode of seven numbers are equal
...
What is the seventh number?

a
...
b
...


a
...
22 c
...
10 e
...
the area is 6 times its original
...
the area is 8 times its original
...
) Number Series: 1, 2, 2, 3, 4, 4, 8, 5, __

5
...
What is the number?

a
...
7 c
...
20 e
...
100 b
...
10,000 d
...
) Number Series: 15, 7
...
5, 15, 60, ____

6
...
000225 = ____?

a
...
120 c
...
420 e
...
15 b
...
5 c
...
15 d
...
015 e
...
0015

17
...
) √0
...
2,833,300 b
...
2,833,000 d
...
none of the above

a
...
0
...
0
...
0
...
0
...
) The product of the ages of three sisters is 567
...
What is the age of
their younger sister?

8
...
645
...
645
...
651
...
688
...
none of the above
9
...
9,900 b
...
9,800 d
...
none of the above

a
...
10 c
...
8 e
...
) Number Series: [4÷4×2], [8÷4×2], [16÷4×2], ___
a
...
16 c
...
8 e
...
) Round off to the nearest hundreds place: 9,650

20
...
If 70% of the solution is
water, how many milliliters of pure milk are in 1 liter of this solution?

a
...
9,700 c
...
9,600 e
...
30 b
...
250 d
...
none of the above

21
...
0001 = ___

30
...
0
...
0
...
0
...
4
...
40
...
3/11 b
...
3/4 d
...
3/5

22
...
) 0
...
125 as to 1
...
0 b
...
−98 d
...
None of the above

a
...
625 b
...
125 c
...
625 d
...
125 e
...
250

23
...


32
...
2 is to _________

a
...
3996 less than 2, 836 c
...
1404 less than 2, 836 e
...
) If twice the value of a certain number is increased by 8 the result is
40
...
60 b
...
80 d
...
1
33
...
7 b
...
9 d
...
15
34
...
8 b
...
24 d
...
none of the above

a
...
31 c
...
39 e
...
) Genzy's dad is 5 times as old as Genzy and Genzy is twice as old
as her sister Zymie
...
How
old is Genzy now?

35
...
43 + 123
...
5544 + 444
...
4 b
...
8 d
...
none of the above

36
...
) In a group of 120 persons, there are 32 more women than men
...
5/12 b
...
52/80 d
...
50/70

a
...
88 c
...
56 e
...
50 b
...
54 d
...
70

27
...
) 18+ 3 × 3 + (54/3+ -68/-4) =

a
...
it decreases by 1/4 c
...
it
decreases by 1/2 e
...
) There are 3 numbers whose sum is 54; one number is double and triple
times greater than the other numbers, what are those numbers?

28
...
10, 20, 34 b
...
8, 16, 30 d
...
7, 14, 21

a
...
-27 c
...
81 e
...
) At 6:30 am, Jeany told Margarette that she found Blessy 15 and ¼
hours ago, at what time Jeany found Blessy ?

29
...
75 is to ¾ as 0
...
2/3 b
...
5/6 d
...
3/5

a
...
7184 d
...
7184 b
...
4468 e
...
7814 c
...
5678

37
...
62 b
...
26 d
...
330

a
...
6:30pm c
...
3:25pm e
...
) If three siomai cost P 15 pesos, how much if Kenneth buy 12
siomais
...
Four consecutive integers have a mean of 9
...
What is the largest of
these integers?

a
...
45 c
...
60 e
...
38 b
...
11 d
...
19

42
...
A baseball pitcher won 80% of the games he pitched
...
43 b
...
44 d
...
46

a
...
28 c
...
35 e
...
) What is the smallest positive number, which when you divided by
3, 4 or 5, will leave a remainder of 2?

52)
...
What percent
of the year did he work?

a
...
22 c
...
122 e
...
9% b
...
75% d
...
none of the above

44
...
There are 40 students in a class
...

What percent of the class are girls?

a
...
42 c
...
237 e
...
60% b
...
43% d
...
none of the above

45
...
Analie took a math test and got 48 correct and 12 incorrect answers
...
232 b
...
546 d
...
none of these
46
...
The ratio of girls to boys
is ___

a
...
75% c
...
80% e
...
120 is what percent of 48?

a
...
3 : 4 c
...
1 : 2

a
...
5% b
...
25% d
...
) A pet store has 8 cats, 12 dogs, and 3 rabbits
...
120% of what number is 72?

a
...
cats to dogs c
...
cats to all animals
48
...
3 : 7 b
...
2 : 7 d
...
The ratio of two sides of a parallelogram is 4 : 3
...

a
...
16cm, 12cm b
...
none of the above c
...
144 b
...
14,400 d
...
10% of 300 is what number?
a
...
0
...
30 d
...
Two and one-half percent of what number is 88?
a
...
35,200 c
...
2 d
...
95% of people in my street have a car
...
How many do not have a car?
a
...
92 c
...
75 e
...
If 300 students filled form for entrance test and 280 appeared in test
out of which only 70% have passed test then number of students who
failed test are
a
...
54 c
...
104 e
...
40 % of 5 is equal to

69)
...
35 b
...
625 d
...
4900
70)
...
12 b
...
-1 d
...
23

a
...
20 c
...
2 d
...
02 e
...
The population of a certain town is 5,000
...
In a shipment of computers, 2/25 of the computers are defective
...
7500 b
...
14250 d
...
5250

a
...
2/23 c
...
23/2 e
...
Gary decided to cycle to his friend’s house at a speed of 6kph and the
journey took 30 minutes
...
Which of the following is divisible (with no remainder) by 6di
a
...
625874 c
...
235465 e
...
18 km b
...
6 km d
...
none of these

64)
...
If 80% of the solution
is water, how many liters of pure orange are in 25 liters of this solution?

73)
...
If
the rate of the river is current, is 6 kph, what is the rate of the boat in still
water?

a
...
15 c
...
5 e
...
30 kph b
...
84 kph d
...
none of these

65)
...
If a car travels at 60 kph, what is the distance it travels in 30 minutes?

a
...
5/6 c
...
5/12 e
...
2 km b
...
120 km d
...
none of these

66)
...
A car travels 120 miles at a speed of 40 miles per hour and makes a
return trip at a speed of 60 miles per hour
...
-1/3 b
...
1/2 d
...
3
67)
...
The profit is
shared equally among the 4 owners of the company
...
125,000 b
...
500,000 d
...
375,000
68)
...
21/5 b
...
20 d
...
5

a
...
44 c
...
48 e
...
E
...
A
...
D
...
2 × 0
...
06X = 225
X = 225/0
...
B
...
Let n be the sides of the squire
perimeter
n × n = area
(n^2)/(n+n+n+n) = X/(n+n+n+n)^2
(n^2)(4n)^2 = X (4n)
[(n^2)(4n)^2]/(4n) = X
(n^2)(4n) = X
Therefore, if the perimeter of a squire is doubled, the area is 4
times its original
...
C
...

Q: what is a number?
NOTE:
of →”x”
Is → “=”

Let n be our number
Solution:
One forth percent → ¼%
Of a number → × n
Is 25 → = 25
Then combine for a new equation:
¼% × n = 25
Convert ¼% to plain fraction
¼% ÷ 100% =
¼% × 1/100 = 1/400 or 0
...
25% PERCENT
0
...
0025 n = 25
n = 25/0
...
0025 × 10,000 = 25
25 = 25

6
...
0
...
E
...
0009
8
...
645
...
The only choices is A and B
...
C
...

10
...
9,600
Round off to the nearest hundreds place: 9,650
*( Rule of 5 ) EVEN number before 5 is to keep the number
11
...
51
...
8×4 = 51
...
D
...
C
...
A
...
C
...
A
...
5, 7
...
5 = 7
...
5×1 = 7
...
5×2 = 15
15×4 = 60
60×8 = 480✔
17
...
2,800,000✔
18
...
7
The product of the ages of three sisters is 567
...
What is the
age of their younger sister?
567÷3 = 189
189÷3 = 63
63÷3 = 21
21÷3 = 7
Group those for 3s into two
(3×3) and (3×3)
(3×3) = 9
9 is 2 more than 7
Therefore, the age of their younger sister is 7byrs old ✔
19
...
16
A6
...
D
...
If 70% of the solution
is water, how many milliliter of pure milk are in
...
3 × 1000 = 300ml pure milk ✔
21
...
0
...
0001 = ___
Just move the decimal place to left four times
22
...
0
Review the RULE of exponents on negative
(−7)² + (−7²) =
49 + (−49) = zero✔
23
...
3996 more than 2,836
When the first and the last digits of 2, 836 are interchanged, the
new number is _____
...
B
...
What is the number?
Twice the value of a certain number
---> 2n increased by 8
---> +8 the result is 40
---> = 40
Then combine the equation
2n + 8 = 40
2n = 40 - 8
2n = 32
n = 32/2 = 16✔
25
...
8

Genzy's dad is 5 times as old as Genzy and Genzy is twice as old
as her sister Zymie
...
How old is Genzy now?
Now
...
5(2z) + 2
Genzy = 2z
...
z + 2
[5(2z)+2]+[2z+2]+[z+2] = 58
[10z)+2]+[2z+2]+[z+2] = 58
13z + 6 = 58
13z = 58 - 6
13z = 52
z = 52/13 = 4
Genzy 2z = 2(4) = 8✔
26
...
76
In a group of 120 persons, there are 32 more women than men
...
A
...
25n × ?n = n²

?n = n²/1
...
25 n
?n = 100/125 n
?n = 4/5 n
1 - 4/5 =
5/5 - 4/5 = 1/5
From 1n, now it is 4/5 n
...
B
...
B
...
75 is no doubt equals to 3/4
So, 0
...
75 : 3/4 = 0
...
8 = 0
...
6/0
...
8 or 4/5
30
...
3/10
Soln#1
75% is to 1/2 as 45% is to 0
...
5 = 0
...
75÷3)×2=0
...
45÷3)×2=0
...
45 = 0
...
225/0
...
3 or 3/10
31
...
0
...
25 is to 0
...
25 is to 0
...
125 = 1
...
25×5 = 1
...
125×5 = 0
...
25 : 0
...
25 : n
(0
...
25)/0
...
625
32
...
80
Soln#1
Soln#2
2 : 50 = 3
...
2)/2 = 80
3
...
D
...
B
...
D
...
7184
Write down all the given numbers vertically and align all
decimals, then you can add them
...
Then the 3rd digit from the decimal point or the
thousandths place, you have 4+4 and it is 8
...
You only have choice d that has
84 on the last two digits after decimal
...
E
...
D
...
8 × n
of→”×”
44/0
...
A
...
D
...
E
...
15hrs – 12hrs) = 3:15pm
41
...
60
12/3 = 4 × 15 = 60
Every 3 siomai cost 15
There are four 3’s in 12, so 4×15, answer is 60
...
E
...
74n = 80
n = 80/1
...
977 round-off 46
43
...
62
LCM of 3, 4, 5, is 60, add 2 and the answer is 62
44
...
42
Just multiply them 2×3×7 = 42
45
...
546

Divisible by 6 are both divisible by 2 and 3
...
C
...
The ratio of girls to boys
is ___
Girls : Boys
12 : 9 = 4 : 3✔
GCF of 12 and 9 is 3
...
D
...
The ratio 8:23
compares 8 cats : [(8+12+3) = 23]
cats to all animals ✔
48
...
1 : 4
Ratio of 750m and 3km is convert km to m so that they be same
750m : 3km
750m : 3000m
75 : 300 --> divide both by GCF 75
1:4✔
49
...
16cm, 12cm
Soln#1:
Let the lengths of two sides of the parallelogram be 4n cm and
3n cm respectively
...

one side
= (4×4) cm = 16 cm✔
other side = (3×4) cm
= 12 cm✔
Soln#2

4+3=7
56 ÷ 7 = 8
4 × 8 = 32 ÷ 2 = 16cm✔
3 × 8 = 24 ÷ 2 = 12cm
50
...
11
Four consecutive integers could be represented as n, n+1, n+2,
n+3
Therefore, by saying that they have a mean of 9
...
5
(4n + 6)/4 = 9
...
5(4)
4n = 38-6
4n = 32
n = 32/4
n=8
Therefore, the largest value is
n+3=
8 + 3 = 11
51
...
28
A baseball pitcher won 80% of the games he pitched
...
8 × 35 = 28✔
52
...
75%
Jerry, an electrician, worked 9 months out of the year
...
75 = n
0
...
A
...
Sixteen of those students are
boys
...
6 = n
0
...
D
...
What was the percentage of correct answers?
48 + 12 = 60
48 is what percent of 60
48 = n × 60
48/60 = n
0
...
8 × 100% = 80% ✔
55
...
250%
120 is what percent of 48?
120 = n × 48
120/48 = n
2
...
5 × 100% = 250% ✔
56
...
60
120% of what number is 72?
120% × n = 72
1
...
2
n = 60 ✔
57
...
30
10% of 300 is what number?
10% × 300 = n
0
...
A
...
5% × n = 88
0
...
025
n = 3520✔
59
...
8
95% of people in my street have a car
...
How many do not have a car?
100% - 95% = 5%
5% of 160 don't have a car
5% × 160 =
0
...
A
...
3 × 280 = 84✔
61
...
2
note:
40% of 5 is equal to of ---> "×"
40% × 5 =
is ---> "="
0
...
4
62
...
2/23
2/25 (two twentyfifth) of the computer are defective
→Means in 25 computer, there is two defective
...
C
...

So, we will focus choice B,C,E because this are last digit na
divisible by 2
...
6+2+5+8+7+4=32 ✖÷3
C
...
1+4+2+5+4+6=22 ✖÷3
64
...
5
given:
80% water
100%-80%=20%pure orange
Solution:
20% of 25L is pure orange
20% × 25 = pure orange
0
...
E
...
A
...
A
...
25= 500,000
500,000 ÷ 4 = 125,000
68
...
21/5
2/(1/7+1/3) =

2 ÷ (3/21 + 7/21)=
2 ÷ 10/21 =
2 × 21/10 =
42/10 or 21/5
69
...
35
(a+b)^2 = a^2+2ab+b^2
(a-b)^2 = a^2-2ab+b^2
a^2+2ab+b^2 = 25
a^2-2ab+b^2 = 45 (ADD)
------------------------------(2a^2 + 2b^2 = 70)/2
a^2 + b^2 = 35
70
...
12
APPLY the RULE not the acronym
...
D
...

→population is 5000
If it increases 5% each year,
→EACH YEAR +5%
Q: what will be the approximate population at the end of 10
years?
Solution#1
5000 × 1
...
62889 =
8,144
...
)5000×1
...
)5250×1
...
5
3
...
05 = 5,787
...
)5,788×1
...
)6077×1
...
85
6
...
05 = 6700
...
)6700×1
...
)7035×1
...
75
9
...
05 = 7,756
...
)7,756×1
...
8
8,143
...
B
...
5hr
Distance = 3 km
73
...
54 kph
SOLUTION:
A boat takes 4/5 as much time to travel downstream as to its
return
...
B
...
5hr
Distance = 30 km ✔
75
...
48 mph
SOLUTION:
Rate = distance/time
time = distance/rate
Total distance:
120 × 2 = 240miles
Total time:
1st trip = 120/40 = 3hrs
Return = 120/60 = 2hrs
3hrz + 2hrs = 5hrs
Average =
Total distance ÷ total time
240m ÷ 5hrs = 48mph ✔



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