Free NYC Civil Service Mathematical Reasoning Problems Questions and Answers — Questions and Answers
Question 1: A city's sanitation department has two models of street sweepers. Model A can sweep a designated 5-mile route in 3 hours. Model B can sweep the same route in 2 hours. If both models are used simultaneously, how long will it take to sweep the entire 5-mile route?
- 2.5 hours
- 1.2 hours (Correct answer)
- 5 hours
- 1.5 hours
Correct answer: 1.2 hours
This is a work-rate problem. Model A's rate is 1/3 of the route per hour. Model B's rate is 1/2 of the route per hour. Their combined rate is (1/3) + (1/2) = (2/6) + (3/6) = 5/6 of the route per hour. To find the time it takes to complete the job (1 whole route), you take the reciprocal of the combined rate: Time = 1 / (5/6) = 6/5 hours, which is equal to 1.2 hours.
Question 2: A municipal budget of $2,400,000 is allocated to three departments: Police, Fire, and Public Works, in the ratio of 5:3:2, respectively. How much money is allocated to the Public Works department?
- $1,200,000
- $720,000
- $240,000
- $480,000 (Correct answer)
Correct answer: $480,000
First, find the total number of parts in the ratio: 5 + 3 + 2 = 10 parts. Next, divide the total budget by the total number of parts to find the value of one part: $2,400,000 / 10 = $240,000. Finally, multiply the value of one part by the number of parts for Public Works: $240,000 * 2 = $480,000.
Question 3: A city parks department is planning a new rectangular playground. The length of the playground is set at 90 feet. If the total area of the playground must be 5,400 square feet, what is the width of the playground?
- 60 feet (Correct answer)
- 50 feet
- 48 feet
- 75 feet
Correct answer: 60 feet
The formula for the area of a rectangle is Area = Length × Width. You are given the area (5,400 sq ft) and the length (90 ft). To find the width, you rearrange the formula: Width = Area / Length. So, Width = 5,400 / 90 = 60 feet.
Question 4: A city clerk issued 45 permits on Monday, 62 on Tuesday, 51 on Wednesday, and 38 on Thursday. To achieve an average of 55 permits issued per day over a five-day work week, how many permits must the clerk issue on Friday?
- 55
- 79
- 64
- 84 (Correct answer)
Correct answer: 84
To have an average of 55 permits over 5 days, the total number of permits must be 55 * 5 = 275. The total number of permits issued from Monday to Thursday is 45 + 62 + 51 + 38 = 196. To find the number needed on Friday, subtract the current total from the target total: 275 - 196 = 79.
Question 5: A city water tank is being filled at a rate of 40 gallons per minute. The tank has a capacity of 15,000 gallons but already contains 3,000 gallons of water. How many hours will it take to fill the rest of the tank?
- 4.5 hours
- 6.25 hours
- 5 hours (Correct answer)
- 300 hours
Correct answer: 5 hours
First, determine the amount of water needed to fill the tank: 15,000 gallons (capacity) - 3,000 gallons (current) = 12,000 gallons. Next, calculate the time in minutes it will take to fill this amount: 12,000 gallons / 40 gallons per minute = 300 minutes. Finally, convert the time from minutes to hours: 300 minutes / 60 minutes per hour = 5 hours.
Question 6: A city agency purchased new office chairs at a cost of $120 per chair. Due to a bulk discount, the price was reduced by 15%. If the agency bought 50 chairs, what was the total cost after the discount was applied?
- $5,100 (Correct answer)
- $900
- $6,000
- $5,400
Correct answer: $5,100
First, calculate the discount amount per chair: $120 * 0.15 = $18. Then, find the discounted price per chair: $120 - $18 = $102. Finally, calculate the total cost for 50 chairs: $102 * 50 = $5,100. Alternatively, you can calculate the undiscounted total cost ($120 * 50 = $6,000) and then subtract the total discount ($6,000 * 0.15 = $900), which also gives $5,100.
Free NYC Civil Service Mathematical Reasoning Problems Questions and Answers
A city's sanitation department has two models of street sweepers.
Model A can sweep a designated 5-mile route in 3 hours.
Model B can sweep the same route in 2 hours.
If both models are used simultaneously, how long will it take to sweep the entire 5-mile route?