Quantitative Reasoning in Context Flashcards

A store marks up all items by 40% and then offers a 20% sale discount. What is the net percentage change from the original price?

Answer: 12% increase

1.4 × 0.8 = 1.12, so the final price is 12% above the original.

A survey of 800 students found that 65% prefer online learning. If the margin of error is ±3%, which range most reliably represents the true proportion of the whole student body?

Answer: 62% to 68%

The margin of error is added and subtracted from the sample proportion: 65% ± 3% = 62% to 68%.

A car travels 120 miles in 2 hours, then 90 miles in 1.5 hours. What is the car's average speed for the entire trip?

Answer: 60 mph

Total distance = 210 miles; total time = 3.5 hours; average speed = 210 ÷ 3.5 = 60 mph.

A scientist records bacteria counts of 200, 400, 800, and 1600 over four consecutive hours. Which model best describes this growth?

Answer: Exponential growth

The count doubles each hour (multiplied by a constant factor of 2), which is the defining pattern of exponential growth.

A recipe requires 3/4 cup of sugar for 12 cookies. How many cups of sugar are needed to make 44 cookies?

Answer: 2¾ cups

(3/4) ÷ 12 × 44 = 0.0625 × 44 = 2.75 = 2¾ cups.

An investment of $5,000 earns 4% simple annual interest. After how many years will the total value first exceed $6,000?

Answer: 5 years

Interest per year = $200; to earn $1,000 requires 1000 ÷ 200 = 5 years, giving exactly $6,000, so the total first exceeds $6,000 after 5 full years at the end of year 5.

On a map, 1 inch represents 25 miles. Two cities are 3.6 inches apart on the map. What is the actual distance between them?

Answer: 90 miles

3.6 inches × 25 miles/inch = 90 miles.