Civil Service Math Practice Exercise

1.) Which of the following fractions is smaller than \dfrac {3}{8} ?

a.) \dfrac {3}{7}

b.) \dfrac {4}{8}

c.) \dfrac {3}{9}

d.) \dfrac {4}{9}

2.) What is the value of 1.01 + 0.005 + .08?

a.) 1.14

b.) 1.095

c.) 2.4

d.) 1.0014

3.) Which of the following fractions is equivalent to 37.5%?

a.) \dfrac {3}{7}

b.) \dfrac {3}{8}

c.) \dfrac {2}{9}

d.) \dfrac {4}{9}

4.) In the sequences below, 36 and 72 are common numbers to both sequences.

Sequence 1: 12, 24, 36, 48, 60, 72

Sequence 2: 18, 36, 54, 72…

Which of the following numbers are not common to both sequences?

a.) 288

b.) 324

c.) 396

d.) 434

5.) If 2x – 3 = 5, what is the value of 2x – 8?

a.) -10

b.) 0

c.) 5

d.) 10

6.) The sum of five consecutive numbers is 100. What is their average?

a.) 18

b.) 19

c.) 20

d.) 21

7.) What is -2[(5)^2 - (-3)] ?

a.) -44

b.) 44

c.) -56

d.) 56

8.) Which of the following numbers is not included in the sequence 8, 15, 22, 29, …?

a.) 57

b.) 78

c.) 99

d.) 105

9.) Joan is five times as old as Josie.  In three years, the sum of their ages will be 48. How old is Josie?

a.) 6

b.) 12

c.) 30

d.) 35

10.) There are 35 boys in a class.  This is 3 more than 4 times the number of girls. How many girls are there in a class?

a.) 8

b.) 11

c.) 16

d.) 32

11.) A tarpaulin 4 feet wide by 6 feet high is enlarged such that the new width is 12. What should be the height of the new poster to maintain the ratio?

a.) 10

b.) 12

c.) 16

d.) 32

12.) In the figure below, what is the area of the shaded region if the dimensions of the rectangle are 2 by 8 centimetres?

a.) 16 - 2\pi

b.) 12 - 2\pi

c.) 8 - 2\pi

d.) 8 - \pi

13.) Five times a number divided by three is equal to 8 more than that number. What is the number?

a.) 8

b.) 11

c.) 12

d.) 16

14.) Which of the following fractions is equal to 0.875?

a.) \dfrac {4}{5}

b.) \dfrac {5}{6}

c.) \dfrac {5}{8}

d.) \dfrac {7}{8}

15.) In a Student Council election in Kalayaan High School, 30% of the students voted for Michael as president, while 25% voted for Hannah. If there are 2300 students in the school, how many students did not vote for Michael and Hannah?

a.) 575

b.) 690

c.) 1035

d.) 1265

16.) What is \dfrac {2}{5} of \dfrac {3}{4} of 100?

a.) 25

b.) 30

c.) 40

d.) 75

17.) A rectangular box has dimensions 12 by 8 by 10. What is the total length in units of its edges?

a.) 30

b.) 60

c.) 120

d.) 960

18.) Arman bought a t-shirt for P 336.00 for a 30% discount. What is the original price of the t-shirt?

a.) P144.00

b.) P235.20

c.) P436.80

d.) P480.00

19.) What is 2 – [3 – ( 5)]?

a.) -16

b.) -6

c.) 4

d.) 6

20.) The length of a rectangle is 5 more than twice its width. If the perimeter is 136 centimeter, what is it length?

a.) 21

b.) 25

c.) 42

d.) 47

Answers:

1.) c

2.) b

3.) b

4.) c

5.) b

6.) c

7.) c

8.) d

9.) d

10.) a

11.) d

12.) a

13.) c

14.) c

15.) c

16.) b

17.) c

18.) d

19.) b

20.) d

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Operations on Decimals Exercises – Set 2

This is our second set of exercises on operations on decimals.

Perform the indicated operation.

1.) 1.5 + 0.7
2.) 10.5 + 3.08 + 4.026
3.) 0.8 – 0.2
4.) 8.06 – 3.215
5.) 5.7 – 0.9
6.) .22 × .6
7.) 5.02 × 1.2
8.) 8.1 ÷ 0.009
9.) .63 ÷ 30
10.) .7 ÷ .005

Answers:

1.) 2.2
2.) 17.606
3.) 0.6
4.) 4.845
5.) 4.8
6.) 0.132
7.) 6.024
8.) 900
9.) 0.021
10.) 140

Enjoy!

You might also like: Operations on Decimals Exercises – Set 1

Multiplication and Division of Fractions Exercises – Set 2

Find the product of the following:

1.) \dfrac{3}{4} \times \dfrac{5}{8}

2.) \dfrac{1}{8} \times \dfrac{3}{4} \times \dfrac{2}{3}

3.) 2 \dfrac{3}{5} \times \dfrac{2}{3}

4.) 7 \dfrac{5}{6} \times 1 \dfrac{3}{4}

5.) 7 \times 2 \dfrac{3}{14}

6.) \dfrac{2}{3} \div \dfrac{3}{4}

7.) 15 \div \dfrac{5}{6}

8.) \dfrac{3}{8} \div 4

9.) 1 \dfrac{2}{3} \div \dfrac{4}{5}

10.) 7 \dfrac{1}{4} \div \dfrac{1}{8}

Solution:

1.) \dfrac{15}{32}

2.) \dfrac{1}{16}
\dfrac{1}{8} \times \dfrac{3}{4} \times \dfrac{2}{3}
= \dfrac{6}{96} or \dfrac{1}{16}

3.) 1 \dfrac{11}{15}
2 \dfrac{3}{5} \times \dfrac{2}{3}
= \dfrac{13}{5} \times \dfrac{2}{3}
= \dfrac{26}{15} or 1 \dfrac{11}{15}

4.) 13 \dfrac{17}{24}
= 7 \dfrac{5}{6} \times 1 \dfrac{3}{4}
= \dfrac{47}{6} \times \dfrac{7}{4}
= \dfrac{329}{24} \times 13 \dfrac{17}{24}

5.) 15 \dfrac{1}{12}
7 \times 2 \dfrac{3}{14}
= \dfrac{7}{1} \times \dfrac{31}{14}
= \dfrac{217}{14} or 15 \dfrac{7}{14} or 15 \dfrac{1}{2}

6.) \dfrac{8}{9}
\dfrac{2}{3} \div \dfrac{3}{4}
= \dfrac{3}{2} \times \dfrac{3}{4} = \dfrac{8}{9}

7.) \dfrac{1}{18}
= 15 \div \dfrac{5}{6}
= \dfrac{1}{15} \times \dfrac{5}{6} = \dfrac{5}{90} or \dfrac{1}{18}

8.) 10 \dfrac{2}{3}
\dfrac{3}{8} \div 4
= \dfrac{8}{3} \times \dfrac{4}{1} = \dfrac{32}{3} or 10 \dfrac{2}{3}

9.) \dfrac{12}{25}
1 \dfrac{2}{3} \div \dfrac{4}{5}
= \dfrac{5}{3} \div\dfrac{4}{5}
= \dfrac{3}{5} \times \dfrac{4}{5} = \dfrac{12}{25}

10.) \dfrac{1}{58}
7 \dfrac{1}{4} \div \dfrac{1}{8}
= \dfrac{29}{4} \div \dfrac{1}{8}
= \dfrac{4}{29} \times\dfrac{1}{8} = \dfrac{4}{232} or \dfrac{1}{58}

You might also like: Multiplication and Division of Fractions Exercises – Set 1

Subtraction of Fractions Exercises – Set 2

Find the difference of the following:

1.) \dfrac{9}{11} - \dfrac{7}{11}

2.) \dfrac{10}{21} - \dfrac{3}{21}

3.) \dfrac{40}{15} - \dfrac{10}{15}

4.) 9 \dfrac{3}{10} - \dfrac{7}{10}

5.) \dfrac{1}{2} - \dfrac{1}{5}

6.) 7 - \dfrac{3}{5}

7.) 5 \dfrac{7}{8} - \dfrac{3}{4}

8.) 9 \dfrac{1}{2} - 7 \dfrac{1}{5}

9.) 6 \dfrac{1}{5} - 2 \dfrac{3}{4}

10.) 12 \dfrac{1}{6} - 3 \dfrac{1}{2}

Solution:

1.) \dfrac{2}{11}
2.) \dfrac{7}{21} = \dfrac{1}{3}
3.) 2
4.) 8 \dfrac{9}{10}
Solution:
LCD: 10
9 \dfrac{6}{10} - \dfrac{7}{10} =  8 \dfrac{16}{10} - \dfrac{7}{10} =  8 \dfrac{9}{10}

5.) \dfrac{3}{10}
Solution:
LCD: 10
\dfrac{5}{10} - \dfrac{2}{10} = \dfrac{3}{10}

6.) 6 \dfrac{2}{5}
Solution:
6 \dfrac{5}{5} - \dfrac{3}{5} = 6 \dfrac{2}{5}

7.) 5 \dfrac{1}{8}
Solution:
LCD: 8
5 \dfrac{7}{8} - \dfrac{6}{8} = 5 \dfrac{1}{8}

8.) 2 \dfrac{3}{10}
Solution:
LCD: 10
9 \dfrac{5}{10} - 7 \dfrac{2}{10} = 2 \dfrac{3}{10}

9.) 3 \dfrac{9}{20}
Solution:
LCD: 20
6 \dfrac{4}{20} - 2 \dfrac{15}{20} = 5 \dfrac{24}{20} - 2 \dfrac{15}{20} = 3 \dfrac{9}{20}

10.) 8 \dfrac{2}{3}

Solution:
LCD: 6
12 \dfrac{1}{6} - 3 \dfrac{3}{6} = 11 \dfrac{7}{6} - 3 \dfrac{3}{6} = 8 \dfrac{4}{6} = 8 \dfrac{2}{3}

 

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Addition of Fractions Exercises – Set 2

Add the following fractions.

1.) \dfrac{1}{7} + \dfrac{2}{7}

2.) \dfrac{1}{12} + \dfrac{5}{12}

3.) \dfrac{7}{15} + \dfrac{2}{15} + \dfrac{6}{15}

4.) \dfrac{1}{3} + \dfrac{1}{4}

5.) \dfrac{2}{9} + \dfrac{1}{3}

6.) \dfrac{3}{8} + \dfrac{1}{4}

7.) 8 \dfrac{2}{3} + \dfrac{3}{2}

8.) \dfrac{1}{2} + \dfrac{2}{3} + \dfrac{3}{4}

9.) 7 \dfrac{2}{7} + 6 \dfrac{3}{14}

10.) 3 \dfrac{1}{4} + 2 \dfrac{1}{8}

Answer key and solution:

1.) \dfrac{3}{7}

2.) \dfrac{6}{12} = \dfrac{1}{2}

3.) \dfrac{15}{15} = 1

4.) \dfrac{7}{12}
Solution:
LCD: 12
\dfrac{4}{12} + \dfrac{3}{12} = \dfrac{7}{12}

5.) \dfrac{5}{9}
Solution:
LCD: 9
\dfrac{2}{9} + \dfrac{3}{9} = \dfrac{5}{9}

6.) \dfrac{5}{8}
Solution:
LCD: 8
\dfrac{3}{8} + \dfrac{2}{8} = \dfrac{5}{8}

7.) 10 \dfrac{1}{6}
Solution:
LCD: 6

8 \dfrac{4}{6} + \dfrac{9}{6} = 8 \dfrac{13}{6} = 10 \dfrac{1}{6}

8.) 1 \dfrac{11}{12}
Solution:
LCD: 12

\dfrac{6}{12} + \dfrac{8}{12} + \dfrac{9}{12} = \dfrac{23}{12} = 1 \dfrac{11}{12}

9.) 13 \dfrac{1}{2}

Solution:
LCD: 14

7 \dfrac{4}{14} + 6 \dfrac{3}{14} = 13 \dfrac{7}{14} = 13 \dfrac{1}{2}

10.) 5 \dfrac{3}{8}

Solution:
LCD: 8

3 \dfrac{2}{8} + 2 \dfrac{1}{8} = 5 \dfrac{3}{8}

LCM and GCD Exercises Set 2

Here are some Civil Service exam exercises on GCD and LCM.

1.) What is the GCD of 8, 20, and 28?

2.) What is the GCD of 21, 35, and 56?

3.) What is 18/54 in lowest terms?

4.) What is 38/95 in lowest terms?

5.) What is the LCM of 6 and 8?

6.) What is the LCM of 5, 6, and 12?

7.) What is the product of the LCM and the GCD of 4, 8, and 20?

8.) There are 18 red marbles and 27 blue marbles to be distributed among children. What is the maximum number of children that can receive the marbles if each kid receives the same number of marbles for each color and no marble is to be left over?

9.) In a school sportsfest, there are 60 Grade 4 pupils, 48 Grade 5 pupils and 36 Grade 6 pupils. What is the largest number of teams that can be formed if the pupils in each Grade level are equally distributed and no pupil is left without a team?

10.) In a disco, the red lights blink every 3 seconds and the blue lights blink every 5 seconds. If the two colored lights blink at the same time if you turn them on, they will blink at the same time every ___ seconds.

Answers:

1.) Answer: 4
Solution:
Divisors of 8 – 1, 2, 4, 8
Divisors of 20 – 1, 2, 4, 5, 10, 20
Divisors of 28 – 1, 2, 4, 7, 14, 28

2.) Answer: 7
Solution:
Divisors of 21 – 1, 3, 7, 21
Divisors of 35 -1, 3, 5, 7, 35
Divisors of 56 -1, 2, 7, 8, 14, 28, 56

3.) Answer: 1/3
Note: Reducing fractions to lowest terms is one of the applications of GCD.
Solution:
Divisors of 18 – 1, 2, 6, 9, 18
Divisors of 54 – 1, 2, 3, 9, 18, 27, 54
Numerator = 18 divided by 18 (GCD) = 1
Denominator = 54 divided by 18 (GCD) = 3
Final answer: 1/3

4.) Answer: 2/5
Solution:
Divisors of 38 – 1, 2, 19, 38
Divisors of 95 – 1, 2, 3, 19, 95

5.) Answer: 24.
Solution:
Multiples of 6 – 6, 12, 18, 24
Multiples of 8 – 8, 16, 24

6.) Answer: 60.
Solution:
Multiples of 5 – 5, 10, 15, 20, 25, 30 … 55, 60
Multiples of 6 – 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Multiples of 12 – 12, 24, 36, 48, 60

7.) Answer: 160.
Solution
GCD of 4, 6, and 20 is 4.
LCM of 4, 6, and 20 is 40.
4 x 40 = 160.

8.) Answer: 9
Solution:
Divisors of 18 – 1, 2, 3, 6, 9, 18
Divisors of 27 – 1, 2, 3, 9, 27

9.) Answer: 12.
Solution:
Divisors of 60 – 1, 2, 3, 4, 5, 6, 10, 12, 20, 30, 60
Divisors of 36 – 1, 2, 3, 4, 6, 9, 12, 18, 36
Divisors of 48 – 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

10.) Answer: 15 seconds.
Solution
LCM of 3 and 5 is 15

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Civil Service Exam Double-word Analogy Reviewer

Here are some multiple-choice Civil Service exam reviewers on Double-word Analogy.

Instruction : Choose the letter that corresponds to the pair of words that is related in the same way as the given pair of words.

1.) buck : doe :: _______ : _______
A.) bitch : pup
B.) grander : duck
C.) bull : cow
D.) boomer : joey

2.) ethics : morality :: _______ : _______
A.) logic : fallacies
B.) biology : animals
C.) apologetics : heresy
D.) epistemology : knowledge

3.) Dante Alighieri : Divina Commedia :: _____ : ______
A.) Charles Darwin : Evolution
B.) Vergil : The Aeneid
C.) Niccolo Machiavelli : The Little Prince
D.) Bram Stoker : Frankenstein

4.) pachyderm : rhinoceros :: _______ : _______
A.) deer : doe
B.) ungulate : yak
C.) elephant : herd
D.) dog : Siberian husky

5.) green : yellow :: _______ : _______
A.) orange : blue
B.) violet : red
C.) brown : purple
D.) gray : orange

6.) fresh water : lake :: _______ : _______
A.) industrial water : sewage
B.) salt water : ocean
C.) artificial body : lagoon
D.) pond : public park

7.) accounting : books :: _______ : _______
A.) cartography : maps
B.) volcanology : tsunami
C.) cuisine : chef
D.) law : Supreme Court

8.) platypus : Australia :: _______ : _______
A.) African elephant : Namibia
B.) Siberian tiger : Russia
C.) tamaraw : Mindoro
D.) King cobra : India

9.) orthodoxy : heresy :: _______ : _______
A.) principle : formula
B.) belief : practice
C.) science : theory
D.) verdict : dissent

10.) dusk : evening :: _______ : _______
A.) north : south
B.) light : darkness
C.) dawn : morning
D.) lunar : solar

11.) capitalism : Adam Smith :: _______ : _______
A.) tragedy : William Shakespeare
B.) socialism : Karl Marx
C.) botany : Gregor Mendel
D.) astronomy : Tycho Brahe

12.) bravado : courage :: _______ : _______
A.) patience : virtue
B.) pride : humble
C.) sagacity : wisdom
D.) self abasement : humility

13.) werewolf : fur :: _______ : _______
A.) zombie : brain
B.) vampire : fangs
C.) leprechaun : pot of gold
D.) witch : broomstick

14.) Thor : hammer :: _______ : _______
A.) Superman : kryptonite
B.) Spiderman : spider
C.) Batman : Parents
D.) Wonder Woman : lasso

15.) United States : Washington DC :: _______ : ______
A.) Australia : Sydney
B.) Philippines : ASEAN
C.) European Union : Maastricht
D.) Peru : Lima

16.) meeting : minutes :: _______ : _______
A.) arbitration : consensus
B.) debaters : adjudication
C.) research : notes
D.) speech : extemporaneous

17.) bull-fighting : matador :: _______ : _______
A.) regatta : yacht
B.) Formula 1 car racing : F1 driver
C.) triathlon : cross-country running
D.) water polo : swimming

18.) small intestine : digestive :: _______ : _______
A.) brain : nervous
B.) pancreas : respiratory
C.) skin : skeletal
D.) eyes : circulatory

19.) parchment : ink :: _______ : _______
A.) recipe : pasta
B.) marble : sculptor
C.) canvass : paint
D.) dance : movement

190.) teach : learn :: _______ : _______
A.) eat : chew
B.) sleep : snore
C.) run : drink
D.) speak : listen

Answers:

1.) C.) bull : cow
2.) D.) epistemology : knowledge
3.) B.) Vergil : The Aeneid
4.) B.) ungulate : yak
5.) B.) violet : red
6.) B.) salt water : ocean
7.) A.) cartography : maps
8.) B.) Siberian tiger : Russia
9.) D.) verdict : dissent
10.) C.) dawn : morning
11.) B.) socialism: Karl Marx
12.) D.) self abasement : humility
13.) B.) vampire : fangs
14.) D.) Wonder Woman : lasso
15.) D.) Peru : Lima
16.) C.) research : notes
17.) B.) Formula 1 car racing : F1 driver
18.) A.) brain : nervous
19.) C.) canvass : paint
20.) D.) speak : listen

Civil Service Exam Correct Usage Reviewer

Here are some multiple-choice Civil Service exam reviewers on Correct Usage.

Instruction: Choose the letter that corresponds to the word or phrase that will correctly complete each sentence.

1.) The musical play _______ we saw last night was fascinating.
A.) whose
B.) whom
C.) that
D.) since

2.) _______ the four candidates, Margot was chosen to become the school representative.
A.) Between
B.) Among
C.) Meanwhile
D.) Already

3.) I noticed that you don’t look too well. What is it that _______ you?
A.) ails
B.) ales
C.) aisles
D.) isles

4.) My teacher _______ I was absent last time when she _______ the lesson on Tirad Pass.
A.) taught, thought
B.) tot, thawed
C.) thought, taught
D.) thought, teached

5.) The envoy from Latvia handled the affair in a _______ fashion.
A.) discreet
B.) discrete
C.) discretely
D.) discreetly

6.) My friends and I have known each other _______ 1990.
A.) after
B.) since
C.) mean while
D.) because of

7.) Jasper, a known rebel, _______ the speed limit by doing 170 on the road.
A.) flaunted
B.) flouted
C.) flagged
D.) flippant

8.) Martin speaks French. _______ you?
A.) Should
B.) Can
C.) May
D.) How

9.) Policies in society that do not work for the people should be _______ so that they serve the common good.
A.) praised
B.) undermined
C.) ameliorated
D.) metabolized

10.) _______ are fourteen volunteers in _______ group. _______ waiting for you.
A.) Their, they’re, There
B.) There, they’re, Their
C.) There, their, They’re
D.) They’re, there, Their

11.) Cheating on you is the _______ thing in my mind right now.
A.) furthest
B.) farther
C.) farthest
D.) further

12.) After playing three soccer games, Diego left _______.
A.) burned out
B.) burned in
C.) burned over
D.) burned up

13.) Please do not _______ the volume of the radio as I am studying for my exams.
A.) turn over
B.) turn out
C.) turn up
D.) turn with

14.) They were playing in the yard when the balloons _______.
A.) pooped
B.) plooped
C.) bursted
D.) burst

15.) People of different religions should _______ with each other despite their creeds and beliefs.
A.) get around
B.) get along
C.) get over
D.) get with

16.) _______ are my students you are scolding.
A.) That
B.) Than
C.) This
D.) These

17.) There is _______ that I can do to help you at this point.
A.) little
B.) more
C.) somehow
D.) few

18.) The fifth grade children of Mrs. Santos are _______. They ignored their teacher’s reminders.
A.) uninteresting
B.) disinterested
C.) disinteresting
D.) interested

19.) The sheriff _______ the bank robbers last Sunday.
A.) hung
B.) hanging
C.) hanged
D.) hunging

20.) The _______ at work is that of gravity.
A.) participle
B.) particle
C.) principal
D.) principle

Answers:

1.) C.) that. The relative pronoun used here (“here”) applies to any object that is concrete or tangible.
2.) B.) among. The proper word should be “among” as there are several choices given. “Between” applies only when two choices are provided.
3.) A.) ails. The correct word is “ails” which means “makes one feel sick”.
4.) C.) thought, taught. “Thought” as the past tense of “think, and “taught” as the past tense of “teach”
5.) A.) discreet. “Discreet” means in a secret manner while “discrete” means separate unit.
6.) B.) since. The adverb of time “since” is the correct choice to suggest that the speaker in the sentence and his peers have known each other sometime in the past.
7.) B.) flouted. The word “flaunt” means to be overly expressive so as to boast while “flout” means to disregard rules or conventions. The correct answer is therefore flouted.
8.) B.) can. The correct choice is “can” making the reader ask if it is possible for him to do what is suggested.
9.) C.) ameliorated. Policies that don’t work need to be improved. “Ameliorate” means to change something for the better.
10.) C.) There, their, they’re. The use of “there” indicates an assertion of some quality or trait, or even to point at a direction. “Their” is a pronoun used to show possession, while “they’re” is a contraction (short-cut) for “they are”.
11.) A.) furthest. The rule on the use of “farther” applies to physical distance in space, while “further” implies mental distance/degree.
12.) A.) burned out. The expression “burn out” means to reach a point of exhaustion.
13.) C.) turn up. To “turn up” something means to increase the sound or volume.
14.) D.) burst. The verb “burst” is an irregular verb and its past tense is also “burst” not bursted.
15.) B.) get along. The phrasal verb “get along” means to cooperate with each other.
16.) D.) these. The correct answer is “these” as it agrees with the referent, children (plural form).
17.) A.) little. The tone of the sentence suggests not much can be done. The appropriate answer is “little” not “few” because the idea is something that is not quantifiable.
18.) B.) disinterested. “Disinterested” means indifferent, impartial or unconcerned.
19.) C.) hanged. The verb hang has two meanings but both mean to suspend something. The past tense for hanging “people” as a form of punishment in some societies is “hanged” while “hung” suggests the past of objects being suspended like clothes.
20.) D.) principle. “Principle” names a fundamental belief, rule or idea.



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