Texas Civil Service Exam Mathematical Reasoning Problems 5 — Questions and Answers
Question 1: A dispatcher handles an average of 12 calls per hour. During a 3-hour surge period, call volume increases by 75%. How many calls are handled during the surge?
- 42
- 57
- 63 (Correct answer)
- 72
Correct answer: 63
Surge rate = 12 × 1.75 = 21 calls/hr; total = 21 × 3 = 63 calls.
Question 2: A rectangular city lot measures 150 feet by 200 feet. A 10-foot buffer must be maintained on all sides for construction. What is the maximum building footprint?
- 19,200 sq ft
- 23,400 sq ft (Correct answer)
- 26,000 sq ft
- 30,000 sq ft
Correct answer: 23,400 sq ft
Buildable dimensions = (150-20) × (200-20) = 130 × 180 = 23,400 sq ft.
Question 3: An employee earns $22.50 per hour and receives 1.5× pay for overtime hours beyond 40. If they work 48 hours in a week, what is their total gross pay?
- $1,008
- $1,080
- $1,170 (Correct answer)
- $1,260
Correct answer: $1,170
Regular pay = 40 × $22.50 = $900; OT = 8 × $22.50 × 1.5 = $270; total = $900 + $270 = $1,170.
Question 4: A city plans to repave 480 miles of road. Crews complete 16 miles per week. How many months will the project take? (Assume 4 weeks per month.)
- 6.0 months
- 7.5 months (Correct answer)
- 8.0 months
- 10.0 months
Correct answer: 7.5 months
Weeks needed = 480 ÷ 16 = 30 weeks; months = 30 ÷ 4 = 7.5 months.
Question 5: An applicant scores 82 on a written exam and 88 on the physical fitness test. The written exam counts for 3/4 of the final score and the physical test 1/4. What is the applicant's final score?
- 81.0
- 83.5 (Correct answer)
- 83.75
- 84.0
Correct answer: 83.5
Final score = (82 × 0.75) + (88 × 0.25) = 61.5 + 22.0 = 83.5.
Question 6: A city's water usage is 3.2 million gallons per day. A conservation campaign reduces usage by 8%. How many gallons per day are saved?
- 240,000
- 256,000 (Correct answer)
- 280,000
- 320,000
Correct answer: 256,000
Savings = 3,200,000 × 0.08 = 256,000 gallons per day.
Question 7: A fire ladder is 85 feet long and leans against a building at a 70° angle from the ground. Using sin(70°) ≈ 0.94, approximately how high does the ladder reach?
- 72 feet
- 75 feet
- 80 feet (Correct answer)
- 84 feet
Correct answer: 80 feet
Height = 85 × sin(70°) = 85 × 0.94 ≈ 79.9 ≈ 80 feet.
Texas Civil Service Exam Mathematical Reasoning Problems 5
A dispatcher handles an average of 12 calls per hour.
During a 3-hour surge period, call volume increases by 75%.
How many calls are handled during the surge?