Mathematical Reasoning and Number Facility Flashcards

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?

Answer: 10

Fire escapes = 8; sprinklers = 6; neither = 24 − 8 − 6 = 10.

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?

Answer: 65 lbs

Total = (11 × 165) + 250 = 1,815 + 250 = 2,065 lbs; 2,065 − 2,000 = 65 lbs over the limit.

A city agency must reduce its 840-person workforce by 15% due to budget cuts. How many employees remain after the reduction?

Answer: 714

Reduction = 0.15 × 840 = 126; remaining = 840 − 126 = 714.

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?

Answer: 4 weeks

Weekly output = 0.75 × 5 = 3.75 miles; 12 ÷ 3.75 = 3.2 weeks → must round up to 4 full weeks.

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?

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.

A 480-page government report must be cut to 75% of its original length. How many pages will the revised report contain?

Answer: 360

480 × 0.75 = 360 pages.

A city parking meter collects an average of $18.40 per day. Approximately how much does it collect over a full 365-day year?

Answer: $6,716

$18.40 × 365 = $6,716.