NYC Mathematical Reasoning and Number Facility 3 — Questions and Answers
Question 1: A city block has 24 buildings. Exactly 1/3 have fire escapes and exactly 1/4 have sprinkler systems (no building has both). How many buildings have neither feature?
- 10 (Correct answer)
- 8
- 14
- 6
Correct answer: 10
Fire escapes = 8; sprinklers = 6; neither = 24 − 8 − 6 = 10.
Question 2: An elevator has a weight limit of 2,000 lbs. Eleven people with an average weight of 165 lbs board, along with a supply cart weighing 250 lbs. By how many pounds is the weight limit exceeded?
- 65 lbs (Correct answer)
- 165 lbs
- 250 lbs
- The limit is not exceeded
Correct answer: 65 lbs
Total = (11 × 165) + 250 = 1,815 + 250 = 2,065 lbs; 2,065 − 2,000 = 65 lbs over the limit.
Question 3: A city agency must reduce its 840-person workforce by 15% due to budget cuts. How many employees remain after the reduction?
- 714 (Correct answer)
- 126
- 756
- 700
Correct answer: 714
Reduction = 0.15 × 840 = 126; remaining = 840 − 126 = 714.
Question 4: A road crew paves 0.75 miles per day. A 12-mile road must be completed working 5 days per week. How many full weeks will the project require?
- 4 weeks (Correct answer)
- 3 weeks
- 2 weeks
- 5 weeks
Correct answer: 4 weeks
Weekly output = 0.75 × 5 = 3.75 miles; 12 ÷ 3.75 = 3.2 weeks → must round up to 4 full weeks.
Question 5: A transit card charges $2.90 per ride. A monthly unlimited pass costs $132. A commuter makes 2 rides per day for 22 working days. Which option costs less, and by how much?
- Pay-per-ride, by $4.40 (Correct answer)
- Monthly pass, by $4.40
- Pay-per-ride, by $5.60
- They cost the same
Correct answer: Pay-per-ride, by $4.40
Pay-per-ride = 44 × $2.90 = $127.60; pass = $132.00; pay-per-ride saves $132.00 − $127.60 = $4.40.
Question 6: A 480-page government report must be cut to 75% of its original length. How many pages will the revised report contain?
- 360 (Correct answer)
- 120
- 400
- 340
Correct answer: 360
480 × 0.75 = 360 pages.
Question 7: A city parking meter collects an average of $18.40 per day. Approximately how much does it collect over a full 365-day year?
- $6,716 (Correct answer)
- $67,160
- $671.60
- $6,570
Correct answer: $6,716
$18.40 × 365 = $6,716.
NYC Mathematical Reasoning and Number Facility 3
A city block has 24 buildings.
Exactly 1/3 have fire escapes and exactly 1/4 have sprinkler systems (no building has both).
How many buildings have neither feature?