Civil Service Exam Numerical Reasoning Word Problems 2 — 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.
