Civil Service Exam Math
Read our free study guide to learn about common word problems and discover how to solve them effectively.
Math (also referred to as Numerical Ability or Numerical Reasoning) is part of the coverage of the Professional and Subprofessional levels of the Civil Service Exam.
Tips
Math is a source of anxiety for many because a lot of people have a love-hate relationship with numbers. This is probably one of the hardest (if not the hardest) parts of the test. Since no calculators are allowed, test-takers need to perform a combination of mental and manual computations.
Here are some tips to apply when dealing with word problems.
1 Read and understand the question.
2 Identify what the question is asking for.
3 Apply shortcuts whenever possible.
4 Work from the answer choices whenever possible.
Common Word Problems
Mastering the common word problems that usually appear in the test is the best way to prepare for this section.
Here are some of the common word problems with sample questions, answers, and solutions.
1 Sequences
Problem:
9, 7, 16, 23, 39, 62, 101, ?
(1) 140
(2) 139
(3) 163
(4) 175
(5) 181
Solution:
The correct answer is Choice (3).
When dealing with sequences, you have to learn how to spot the pattern.
In this example, the two preceding numbers are added to get the next number.
9 + 17 = 16
7 + 16 = 23
16 + 23 = 39
23 + 39 = 62
39 + 62 = 101
62 + 101 = 163
2 Number Analogies
Problem:
11 is to 8.25 as 17 is to ___
(1) 11.50
(2) 12.75
(3) 13.25
(4) 14.85
(5) 15.35
Solution:
The correct answer is Choice (2).
When dealing with number analogies, you have to find the relationship of the given numbers.
In this example, the first number is multiplied by 0.75 to get the second number:
For the first analogy: 11 x 0.75 = 8.25
For the second analogy: 17 x 0.75 = 12.75
3 Odd and Even Numbers
Problem:
Given that r is an even number greater than 4, and c is an odd number greater than 5, which of the following is even?
(1) 5r + c
(2) 3c – 3r
(3) 9c – r2
(4) 10 + rc
(5) 3c2 + r3
Solution:
The correct answer is Choice (4).
When dealing with odd and even numbers, use the substitution method, and plug in the smallest possible numbers.
In this example:
r can be 6 (even number greater than 4)
c can be 7 (odd number greater than 5)
Choice (1):
5r + c
= 5 (6) + 7
= 30 + 7
= 37 (odd)
Choice (2):
3c – 3r
= (3 * 7) – (3 * 6)
= 21 – 18
= 3 (odd)
Choice (3):
9c – r2
= (9 * 7) – 62
= 63 – 36
= 27 (odd)
Choice (4):
10 + rc
= 10 + (6 * 7)
= 10 + 42
= 52 (even)
Choice 5:
3c2 + r3
= 3 (7)2 + (6)3
= 3 (49) + 216
= 147 + 216
= 363 (odd)
4 Divisibility
Problem:
9,651,492 is divisible by: I. 2 II. 3 III. 4 IV. 5 V. 6 VI. 9
(1) I and II only
(2) II and III only
(3) I, II, V, and VI only
(4) I, II, III, V, and VI only
(5) I, II, III, IV, and V only
Solution:
The correct answer is Choice (4).
There is no need to divide the large number by the divisors. Just apply the divisibility rules.
Is 9,651,492 divisible by 2? Yes, because it ends with 2, which is an even number.
Is 9,651,492 divisible by 3? Yes, because the sum of the digits is divisible by 3. (9 + 6 + 5 + 1 + 4 + 9 + 2 = 36).
Is 9,651,492 divisible by 4? Yes, because the last two digits are divisible by 4. (92 ÷ 4 = 23).
Is 9,651,492 divisible by 6? Yes, because the given number is divisible by 2 and 3.
Is 9,651,492 divisible by 9? Yes, because the sum of the digits is divisible by 9. (9 + 6 + 5 + 1 + 4 + 9 + 2 = 36).
5 Exponents
Problem:
What is (98 x 93)7?
(1) 918
(2) 924
(3) 921
(4) 956
(5) 977
Solution:
The correct answer is Choice (5).
Distribute the exponents outside the parentheses to the numbers within the parentheses.
(98 x 93)7
= (9(8*7=56) x 9(3*7=21))
= 9(56+21)
= 977
6 Fractions
Problem:
Dan has been working on his thesis for his graduate class. In the first week, he finished 1/5 of his paper. In the second week, he finished 2/7 of the remainder. How much more does he need to accomplish?
(1) 4/7
(2) 15/35
(3) 4/5
(4) 5/7
(5) 8/20
Solution:
The correct answer is Choice (1).
For the first week, Dan finished 1/5 of his paper. Thus, 4/5 of his paper remained unfinished.
For the second week, Dan finished 2/7 of the remainder. Thus:
2 x 4 = 8
7 5 35
For the first and second week, Dan finished:
1 + 8
5 35
To add fractions with different denominators, first get the least common denominator (LCD). Afterward, rewrite the fractions so they will have the same denominators.
Find the LCD of 5 and 35:
5: 5, 10, 15, 20, 25, 30, 35
35: 35
Rewrite the fractions:
1 = 35 ÷ 5 x 1 = 7
5 35 35
8 = 35 ÷ 35 x 8 = 8
35 35 35
Add the fractions:
7 + 8 = 15
35 35 35
Since the problem asks how much more Dan needs to accomplish:
35 – 15 = 20 or 4
35 35 35 7
7 Percentage
Problem:
Karlita wanted a new cellphone. The cost of the particular brand and model that she liked increased from PHP31,950 to PHP37,860. How much was the increase in percentage?
(1) 14.94%
(2) 15.75%
(3) 16.61%
(4) 17.29%
(5) 18.49%
Solution:
The correct answer is Choice (5).
Remember the formula:
actual increase x 100%
original amount
To find the actual increase:
37,860 – 31,950 = 5,910
To find the increase in percentage:
5,910 x 100% = 18.49%
31,950
8 Ratio & Proportion
Problem:
Cathy has a box filled with wooden blocks. She has 17 red blocks for every 21 blue blocks. If Cathy has a total of 51 red blocks, how many blue blocks does she have?
(1) 62
(2) 63
(3) 64
(4) 65
(5) 66
Solution:
The correct answer is Choice (2).
Let x stand for the blue blocks.
Set up the ratios as fractions. Take note of the proper arrangement of the terms.
17 red = 51 red
21 blue x
To find x, cross multiply then divide:
51 * 21 = 1,071
1,071 = 63
17
9 Average
Problem:
A quiz in Constitutional Law had a highest possible score of 30. Nine students took the quiz and got the following scores: 18, 19, 20, 33, 18, 29, 31, 25, 28.
Question 1: Find the mean.
(1) 23.15
(2) 24.56
(3) 25.94
(4) 26.13
(5) 26.89
Question 2: Find the median.
(1) 18
(2) 19
(3) 25
(4) 28
(5) 31
Question 3: Find the mode.
(1) 18
(2) 20
(3) 29
(4) 31
(5) 33
Solution for Question 1:
The correct answer is Choice (2).
Remember the formula:
Average / Mean = sum of all terms
number of terms
Mean = 18 + 19 + 20 + 33 + 18 + 29 + 31 + 25 + 28
9
= 221
9
= 24.56
Solution for Question 2:
Remember the formula:
Median = 1/2 (n + 1)
Median = 1/2 (9 + 1)
= 1/2 (10)
= 5
Arrange the values from lowest to highest: 18, 18, 19, 20, 25, 28, 29, 31, 33.
The median is 25 because it occupies the 5th position.
Solution for Question 3:
The correct answer is Choice (1).
The mode is the value that occurs most often.
In this example, 18 appeared twice.
10 Consecutive Integer
Problem:
The sum of three consecutive integers is 1,266. What is the value of the greatest integer?
(1) 391
(2) 393
(3) 401
(4) 421
(5) 423
Solution:
The correct answer is Choice (5).
Let x stand for the least integer, x + 1 for the middle integer, and x + 2 for the greatest integer.
Set up the equation:
x + (x + 1) + (x + 2) = 1,266
3x + 3 = 1,266
3x = 1,266 – 3
3x = 1,263
x = 1,263
3
x = 421
To check:
x = 421
x + 1 = 422
x + 2 = 423
421 + 422 + 423 = 1,266
Since the problem asks for the value of the greatest integer, the correct answer is 423.
11 Distance Problem
Problem:
Kate and Rom traveled from Pangasinan to Tagaytay at an average rate of 65 kph for 4.5 hours. On the way home, they traveled at an average rate of 45 kph. How many hours did they travel for the entire trip?
(1) 6.5
(2) 9
(3) 11
(4) 13.5
(5) 15
Solution:
The correct answer is Choice (3).
Remember the formula:
Time = Distance
Rate
Set up a table:
Rate – Time – Distance
First Trip – 65 kph – 4.5 hours – 292.5 km
Second Trip – 45 kph – 292.5 km
Set up and solve the equation:
45t = 292.5
t = 292.5
45
t = 6.5 hours
Since the problem asks for the number of hours they traveled for the entire trip: 4.5 hours + 6.5 hours = 11 hours.
12 Age Problem
Problem:
Seventeen years ago, Elena was half of the age she would be in 11 years. What is her current age?
(1) 14
(2) 28
(3) 31
(4) 45
(5) 57
Solution:
The correct answer is Choice (4).
Set up and solve the equation:
x – 17 = (x + 11)
2
Let x = Elena’s age
2 (x – 17) = x + 11
2x – 34 = x + 11
x = 45
13 Work Problem
Problem:
Klarette can create a dress in 20 minutes. Camille can finish the same task in 80 minutes. How long will it take them to create a dress together?
(1) 16 minutes
(2) 26 minutes
(3) 36 minutes
(4) 46 minutes
(5) 56 minutes
Solution:
The correct answer is Choice (1).
Use the formula for work problems:
1 + 1 = 1
t1 t2 t3
Plug in the values:
1 + 1 = 1
20 80 t3
To add unlike denominators, get the LCD, and then rewrite the fractions:
1 + 1 = 4 + 1
20 80 80
Add the fractions:
4 + 1 = 1
80 80 t3
5 = 1
80 t3
To isolate t3, cross-multiply:
1 * 80 = 5 * t3
t3 = 80/5
t3 = 16
Source
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