Cognitive Reflection Test Rates, Ratios, and Proportional Traps

Question 1

If 4 machines take 4 hours to produce 4 units, how many hours will 8 machines take to produce 8 units?

Accepted Answer

4 hours

Answer

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?

Accepted Answer

48 mph

Answer

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?

Accepted Answer

40%

Answer

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?

Accepted Answer

2 hours

Answer

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?

Accepted Answer

6.25% decrease

Answer

1.25 × 0.75 = 0.9375, so the price ends up 6.25% below the original — not back to the starting point.

Cognitive Reflection Test Practice Test