Cognitive Reflection Test Rates, Ratios, and Proportional Traps 2

Question 1

You drive from A to B at 30 mph and return at 90 mph over the same route. What is your average speed for the round trip?

Accepted Answer

45 mph

Answer

Harmonic mean for equal distances: 2×30×90/(30+90) = 5400/120 = 45 mph, not the intuitive 60 mph.

Question 2

A population doubles every 10 years. If a town had 1,000 people in 1980, how many will it have in 2030?

Accepted Answer

32,000

Answer

From 1980 to 2030 is 50 years = 5 doubling periods; 1,000 × 2^5 = 32,000.

Question 3

Worker A completes a job in 10 days; Worker B completes the same job in 15 days. How many days does it take them working together?

Accepted Answer

6 days

Answer

Combined rate = 1/10 + 1/15 = 5/30 = 1/6 job per day, so together they finish in 6 days.

Question 4

A recipe uses flour and sugar in a 5:2 ratio. If you use 350 g of flour, how much sugar do you need?

Accepted Answer

140 g

Answer

Sugar = (2/5) × 350 = 140 g, since sugar is 2 parts for every 5 parts of flour.

Question 5

If 20% of a number is 40, what is 35% of that same number?

Accepted Answer

70

Answer

20% = 40 means the whole number is 200; 35% of 200 = 70.

Cognitive Reflection Test Practice Test