NYC Civil Service Mathematical Reasoning Questions and Answers

Question 1

A city ordinance requires a ratio of at least 3 sanitation workers for every 2 collection trucks. If a depot has 18 collection trucks in operation, what is the minimum number of sanitation workers required to meet the ordinance?

Accepted Answer

27

Answer

The problem requires setting up a proportion to find the unknown number of workers. The ratio is 3 workers to 2 trucks. Let 'x' be the required number of workers for 18 trucks. The proportion is 3/2 = x/18. To solve for x, cross-multiply: 2 * x = 3 * 18, which simplifies to 2x = 54. Dividing both sides by 2 gives x = 27.

Question 2

A Parks Department crew can mow a large field in 8 hours. A second crew can mow the same field in 12 hours. If both crews work together, how long will it take them to mow the field?

Accepted Answer

4.8 hours

Answer

This is a work-rate problem. Crew 1's rate is 1/8 of the field per hour. Crew 2's rate is 1/12 of the field per hour. Their combined rate is (1/8) + (1/12). To add these fractions, find a common denominator, which is 24. So, (3/24) + (2/24) = 5/24 of the field per hour. To find the total time, take the reciprocal of the combined rate: 24/5 = 4.8 hours.

Question 3

The city's IT department has an annual budget of $4,200,000. If 40% is allocated for salaries, 25% for hardware upgrades, and 15% for software licenses, how much money remains for other expenses?

Accepted Answer

$840,000

Answer

First, calculate the total percentage of the budget that has been allocated: 40% + 25% + 15% = 80%. The remaining percentage is 100% - 80% = 20%. To find the remaining dollar amount, calculate 20% of the total budget: 0.20 * $4,200,000 = $840,000.

Question 4

A city clerk's office processed the following number of permit applications per day over a four-day period: 164, 178, 155, and 167. To achieve a five-day average of 170 applications per day, how many applications must be processed on the fifth day?

Accepted Answer

186

Answer

To have an average of 170 over 5 days, the total number of applications must be 170 * 5 = 850. The sum of the applications from the first four days is 164 + 178 + 155 + 167 = 664. To find the number needed on the fifth day, subtract the four-day total from the required five-day total: 850 - 664 = 186.

Question 5

The city plans to resurface a rectangular parking lot that is 150 feet long and 100 feet wide. The cost of resurfacing is $18 per square yard. What is the total cost to resurface the parking lot?

Accepted Answer

$30,000

Answer

The problem requires calculating area and includes a unit conversion. First, convert the dimensions from feet to yards (1 yard = 3 feet). Length = 150 ft / 3 = 50 yards. Width = 100 ft / 3 = 33.33... yards. However, it's easier to calculate the area in square feet first: 150 ft * 100 ft = 15,000 square feet. Then, convert square feet to square yards (1 square yard = 9 square feet): 15,000 sq ft / 9 = 1,666.67 sq yards. Finally, calculate the cost: 1,666.67 sq yds * $18/sq yd ≈ $30,000. A more precise way without early rounding: (150/3) * (100/3) * 18 = 50 * (100/3) * 18 = 5000/3 * 18 = 5000 * 6 = $30,000.

NYC - Civil Service Exam Practice Test

NYC - Civil Service Exam Practice Test

NYC Civil Service Mathematical Reasoning Questions and Answers