Cognitive Reflection Test Rates, Ratios, and Proportional Traps 2 — Questions and Answers
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?
- 60 mph
- 45 mph (Correct answer)
- 54 mph
- 50 mph
Correct answer: 45 mph
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?
- 6,000
- 32,000 (Correct answer)
- 16,000
- 64,000
Correct answer: 32,000
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?
- 12.5 days
- 6 days (Correct answer)
- 7 days
- 5 days
Correct answer: 6 days
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?
- 175 g
- 100 g
- 140 g (Correct answer)
- 70 g
Correct answer: 140 g
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?
- 56
- 70 (Correct answer)
- 84
- 63
Correct answer: 70
20% = 40 means the whole number is 200; 35% of 200 = 70.
Question 6: A car uses fuel at 1 liter per 15 km in the city and 1 liter per 25 km on the highway. If you drive 75 km in the city and 75 km on the highway, how many liters do you use in total?
- 7 liters
- 8 liters (Correct answer)
- 5 liters
- 6 liters
Correct answer: 8 liters
City: 75/15 = 5 liters; highway: 75/25 = 3 liters; total = 8 liters.
Question 7: A car's gas tank is 3/4 full. After a trip, it is 1/4 full. What fraction of the tank's total capacity was used during the trip?
- 1/4
- 3/4
- 1/2 (Correct answer)
- 2/3
Correct answer: 1/2
3/4 − 1/4 = 2/4 = 1/2 of the tank's capacity was consumed.
Cognitive Reflection Test Rates, Ratios, and Proportional Traps 2
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?