Civil Service Exam Numerical Reasoning Word Problems — Questions and Answers

Question 1: A government office orders 15 boxes of paper at $32.50 per box. If there is a 10% bulk discount and 8% sales tax applied after the discount, what is the total cost?

$438.75
$473.85 (Correct answer)
$487.50
$526.50

Correct answer: $473.85

Subtotal: 15 x $32.50 = $487.50. After 10% discount: $487.50 x 0.90 = $438.75. With 8% tax: $438.75 x 1.08 = $473.85.

Step 1: Base cost: 15 x $32.50 = $487.50. Step 2: 10% discount: $487.50 x 0.10 = $48.75; $487.50 - $48.75 = $438.75. Step 3: 8% tax on discounted price: $438.75 x 0.08 = $35.10; $438.75 + $35.10 = $473.85.

Question 2: An employee works 7.5 hours per day, 5 days per week. If the employee takes 3 days of leave in a month with 22 working days, how many hours did the employee work?

142.5 hours (Correct answer)
150.0 hours
157.5 hours
165.0 hours

Correct answer: 142.5 hours

Working days: 22 - 3 = 19 days. Hours worked: 19 x 7.5 = 142.5 hours.

Total working days: 22. Days of leave: 3. Actual days worked: 22 - 3 = 19. Hours per day: 7.5. Total: 19 x 7.5 = 142.5 hours.

Question 3: A department's budget is allocated as follows: Personnel 65%, Operations 20%, Training 10%, Miscellaneous 5%. If the total budget is $2,400,000, how much more is spent on Personnel than on Operations and Training combined?

$840,000 (Correct answer)
$720,000
$960,000
$1,080,000

Correct answer: $840,000

Personnel: 65% of $2,400,000 = $1,560,000. Operations + Training: 30% of $2,400,000 = $720,000. Difference: $840,000.

Personnel: 0.65 x $2,400,000 = $1,560,000. Operations: 0.20 x $2,400,000 = $480,000. Training: 0.10 x $2,400,000 = $240,000. Combined: $720,000. Difference: $1,560,000 - $720,000 = $840,000.

Question 4: A civil service exam has 120 questions. To pass, a candidate needs 70%. If a candidate answered 78 questions correctly, by how many questions did they pass or fail?

Passed by 6 questions
Failed by 6 questions (Correct answer)
Passed by 4 questions
Failed by 4 questions

Correct answer: Failed by 6 questions

Passing threshold: 70% of 120 = 84 questions. The candidate answered 78, which is 6 questions below passing.

Passing score: 70% x 120 = 84 questions needed. The candidate got 78 correct. Since 78 < 84, they failed by 84 - 78 = 6 questions. Their actual score was 65%.

Question 5: A clerk processes 45 forms per hour. A second clerk processes 38 forms per hour. Working together, how long will it take them to process 415 forms?

4 hours
5 hours (Correct answer)
5.5 hours
6 hours

Correct answer: 5 hours

Combined rate: 45 + 38 = 83 forms per hour. Time: 415 / 83 = 5 hours.

Clerk 1: 45 forms/hour. Clerk 2: 38 forms/hour. Combined: 83 forms/hour. Time: 415 / 83 = 5.0 hours exactly.

Question 6: A government vehicle travels 324 miles on 12 gallons of fuel. At this rate, how many gallons are needed for a 513-mile trip?

18 gallons
19 gallons (Correct answer)
20 gallons
21 gallons

Correct answer: 19 gallons

Fuel efficiency: 324 / 12 = 27 mpg. Fuel needed: 513 / 27 = 19 gallons.

Fuel efficiency: 324 / 12 = 27 mpg. Fuel for 513 miles: 513 / 27 = 19 gallons. Alternatively: 12/324 = x/513; x = 6,156/324 = 19.

Question 7: Three employees share a project. Employee A completes 2/5, Employee B completes 1/3, and Employee C finishes the rest. What fraction did Employee C complete?

1/15
2/15
3/15
4/15 (Correct answer)

Correct answer: 4/15

A + B = 2/5 + 1/3 = 6/15 + 5/15 = 11/15. Employee C: 1 - 11/15 = 4/15.

Common denominator for 5 and 3 is 15. A: 2/5 = 6/15. B: 1/3 = 5/15. Combined: 11/15. C completed: 15/15 - 11/15 = 4/15, approximately 26.7%.

Question 8: A department's overtime hours increased from 240 in January to 312 in February. What was the percentage increase?

23%
25%
30% (Correct answer)
72%

Correct answer: 30%

Increase: 312 - 240 = 72. Percentage: (72 / 240) x 100 = 30%.

Change: 312 - 240 = 72 hours. Percentage increase: (72 / 240) x 100 = 30%. A common error is dividing by the new value (72/312 = 23.1%). Always use the starting value as the base.

Question 9: A rectangular office measures 18 feet by 24 feet. Carpet tiles cost $4.50 per square foot and installation costs $1.50 per square foot. What is the total cost?

$1,944
$2,592 (Correct answer)
$2,160
$648

Correct answer: $2,592

Area: 18 x 24 = 432 sq ft. Total per sq ft: $4.50 + $1.50 = $6.00. Total: 432 x $6.00 = $2,592.

Area: 18 x 24 = 432 square feet. Combined cost: $4.50 + $1.50 = $6.00/sq ft. Total: 432 x $6.00 = $2,592. Or separately: materials $1,944 + installation $648 = $2,592.

Question 10: An agency processes 1,250 applications per week with 8 clerks. Due to budget cuts, staff is reduced to 6 clerks. How many applications can be processed weekly?

937.5 (Correct answer)
937
938
950

Correct answer: 937.5

Per clerk: 1,250 / 8 = 156.25. With 6 clerks: 156.25 x 6 = 937.5 applications/week.

Rate per clerk: 1,250 / 8 = 156.25 applications/week. With 6 clerks: 156.25 x 6 = 937.5. This is a 25% reduction matching the 25% staff cut (8 to 6).

Question 11: A government employee earns $28.40/hour for the first 40 hours and 1.5x for overtime. If they work 47 hours in one week, what is the gross pay?

$1,434.20 (Correct answer)
$1,334.80
$1,435.00
$1,136.00

Correct answer: $1,434.20

Regular: 40 x $28.40 = $1,136.00. Overtime rate: $28.40 x 1.5 = $42.60. Overtime: 7 x $42.60 = $298.20. Total: $1,434.20.

Regular pay: 40 x $28.40 = $1,136.00. Overtime rate: $28.40 x 1.5 = $42.60/hr. Overtime hours: 47 - 40 = 7. Overtime pay: 7 x $42.60 = $298.20. Total: $1,136.00 + $298.20 = $1,434.20.

Question 12: A supply room has 3 cases of black ink (24 per case), 2 cases of color ink (18 per case), and 4 cases of paper (10 reams per case). If 25% of black ink and 1/3 of color ink have been used, how many ink cartridges remain?

78 (Correct answer)
66
72
84

Correct answer: 78

Black: 72 total, 25% used = 18, remaining = 54. Color: 36 total, 1/3 used = 12, remaining = 24. Total: 78.

Black ink: 3 x 24 = 72. Used: 25% of 72 = 18. Remaining: 54. Color ink: 2 x 18 = 36. Used: 1/3 of 36 = 12. Remaining: 24. Total remaining ink: 54 + 24 = 78. The paper information is extraneous.

Civil Service Exam Numerical Reasoning Word Problems

A government office orders 15 boxes of paper at $32.50 per box.
If there is a 10% bulk discount and 8% sales tax applied after the discount, what is the total cost?

🃏 Study This Quiz as Flashcards →

📚 Want to go deeper? Read the Full Exam Study Guide →

What Practice Test Geeks adds beyond an AI chat for Civil Service Exam

An AI chatbot can quiz you, but it can't reproduce the exam conditions or keep your record. Here you get:

A timed, full-length Civil Service Exam mock exam — 100 questions in 90 minutes with a 70% pass mark, modeled on the official exam's question count and time limit, followed by a score report broken down by exam domain.
A fixed Civil Service Exam question bank: the same test every attempt, so your score is comparable from one try to the next instead of changing with every regenerated quiz.
Progress saved on your device: completed tests, scores and missed questions stay in My Progress, so you can retake only what you got wrong.
A printable Civil Service Exam cheat sheet you can print or save as a PDF.
Civil Service Exam flashcards built from the same question bank.

Start the Timed Civil Service Exam Mock Exam →

These practice questions were written with AI tools. They are not real exam questions. We have not yet matched this exam's facts to an official source, so confirm fees, dates and rules with the exam body. Not reviewed by a subject-matter expert. Editorial policy