STAT Quantitative Reasoning in Context 2 — Questions and Answers
Question 1: 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?
- 12% increase (Correct answer)
- 20% increase
- 8% increase
- No change
Correct answer: 12% increase
1.4 × 0.8 = 1.12, so the final price is 12% above the original.
Question 2: 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?
- 62% to 68% (Correct answer)
- 60% to 70%
- 65% to 68%
- 55% to 75%
Correct answer: 62% to 68%
The margin of error is added and subtracted from the sample proportion: 65% ± 3% = 62% to 68%.
Question 3: 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?
- 60 mph (Correct answer)
- 62.5 mph
- 55 mph
- 65 mph
Correct answer: 60 mph
Total distance = 210 miles; total time = 3.5 hours; average speed = 210 ÷ 3.5 = 60 mph.
Question 4: A scientist records bacteria counts of 200, 400, 800, and 1600 over four consecutive hours. Which model best describes this growth?
- Exponential growth (Correct answer)
- Linear growth
- Quadratic growth
- Logarithmic growth
Correct answer: Exponential growth
The count doubles each hour (multiplied by a constant factor of 2), which is the defining pattern of exponential growth.
Question 5: A recipe requires 3/4 cup of sugar for 12 cookies. How many cups of sugar are needed to make 44 cookies?
- 2¾ cups (Correct answer)
- 2½ cups
- 3 cups
- 2 cups
Correct answer: 2¾ cups
(3/4) ÷ 12 × 44 = 0.0625 × 44 = 2.75 = 2¾ cups.
Question 6: An investment of $5,000 earns 4% simple annual interest. After how many years will the total value first exceed $6,000?
- 6 years
- 5 years (Correct answer)
- 4 years
- 7 years
Correct 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.
Question 7: 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?
- 90 miles (Correct answer)
- 85 miles
- 72 miles
- 100 miles
Correct answer: 90 miles
3.6 inches × 25 miles/inch = 90 miles.
STAT Quantitative Reasoning in Context 2
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?