Cognitive Reflection Test Rates, Ratios, and Proportional Traps 1 — Questions and Answers
Question 1: If 4 machines take 4 hours to produce 4 units, how many hours will 8 machines take to produce 8 units?
- 2 hours
- 4 hours (Correct answer)
- 8 hours
- 16 hours
Correct answer: 4 hours
Each machine produces 1 unit in 4 hours, so 8 machines still produce 8 units in the same 4 hours.
Question 2: A car travels at 60 mph for the first half of a journey (by distance) and 40 mph for the second half. What is the average speed for the entire trip?
- 50 mph
- 48 mph (Correct answer)
- 45 mph
- 52 mph
Correct answer: 48 mph
For equal distances at two speeds, average speed = harmonic mean: 2×60×40/(60+40) = 48 mph, not the arithmetic mean of 50.
Question 3: A jacket is discounted by 20%, then discounted again by 25%. What is the total percentage reduction from the original price?
- 45%
- 40% (Correct answer)
- 50%
- 35%
Correct answer: 40%
0.80 × 0.75 = 0.60, so the final price is 60% of original — a 40% total reduction, not 45%.
Question 4: Pipe A fills a tank in 6 hours and pipe B fills it in 3 hours. How long does it take with both pipes open simultaneously?
- 4.5 hours
- 3 hours
- 2 hours (Correct answer)
- 1.5 hours
Correct answer: 2 hours
Combined rate = 1/6 + 1/3 = 1/2 tank per hour, so the tank fills in 2 hours.
Question 5: A store increases a price by 25% and then decreases it by 25%. What is the net change in price?
- No change
- 6.25% decrease (Correct answer)
- 6.25% increase
- 12.5% decrease
Correct answer: 6.25% decrease
1.25 × 0.75 = 0.9375, so the price ends up 6.25% below the original — not back to the starting point.
Question 6: If it takes 3 workers 3 days to dig 3 holes, how many days does it take 1 worker to dig 1 hole?
- 1 day
- 3 days (Correct answer)
- 9 days
- 6 days
Correct answer: 3 days
Each worker digs 1 hole in 3 days; reducing both the workers and holes by the same factor leaves the time unchanged.
Question 7: A number is increased by 50% and then decreased by 50%. What is the net result compared to the original?
- Equal to the original
- 25% decrease (Correct answer)
- 25% increase
- No change
Correct answer: 25% decrease
1.50 × 0.50 = 0.75, so the result is 75% of the original — a 25% net decrease.
Cognitive Reflection Test Rates, Ratios, and Proportional Traps 1
If 4 machines take 4 hours to produce 4 units, how many hours will 8 machines take to produce 8 units?