MATH TIPS AND TRICKS
The civil service exam math is a source of anxiety for most test takers because a lot of people have a love-hate relationship with numbers. Here are some tips & tricks to apply when dealing with word problems.
Tip & Trick # 1. Read and understand the question.
Tip & Trick # 2. Identify what the question is asking for.
Tip & Trick # 3. Apply shortcuts whenever possible.
Tip & Trick # 4. Work from the answer choices whenever possible.
Civil Service Exam Math: Common Word Problems
Let’s face it. The civil service exam math is probably one of the hardest (if not the hardest) parts of the test. Since no calculators are allowed, examinees need to perform a combination of mental and manual computations.
Knowing the common word problems that usually appear in the civil service exam math is the best way to prepare for this section. Mastering how to solve them is a must.
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 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 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 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 actually divide the given 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 both 2 and 3 as discussed above.
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:
For the past two weeks, Dan has been working on his thesis for his graduate class. On the first week, he finished 1/5 of his paper. On the second week, he finished 2/7 of the remainder. How much more does Dan 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 1st week, Dan finished 1/5 of his paper. Thus, 4/5 of his paper remained unfinished.
For the 2nd week, Dan finished 2/7 of the remainder. Thus:
2 x 4 = 8
7 5 35
For the 1st and 2nd week, Dan finished:
1 + 8
5 35
To add fractions with different denominators, first get the least common denominator (LCD). Afterwards, 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).
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).
Average / Mean = sum of all terms
number of terms
= 18 + 19 + 20 + 33 + 18 + 29 + 31 + 25 + 28
9
= 221
9
= 24.56
Solution for Question 2:
Median = 1/2 (n + 1)
= 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 is 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 travelled from Pangasinan to Tagaytay at an average rate of 65 kph for 4.5 hours. On the way home, they travelled 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).
The formula is:
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 travelled 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).
Let x = Elena’s age
Set up and solve the equation:
x – 17 = (x + 11)
__)__ __ _ _2
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 both of 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 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
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