Cognitive Reflection Classic Numerical Reasoning Problems Questions and Answers 1 — Questions and Answers
Question 1: A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
- $0.10
- $1.00
- $0.05 (Correct answer)
- $0.50
Correct answer: $0.05
If the ball costs $0.05, the bat costs $1.00 more, which is $1.05. Together, they cost $1.05 + $0.05 = $1.10. The common but incorrect intuitive answer is $0.10, which would make the bat $1.10 and the total $1.20.
Question 2: If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
- 100 minutes
- 5 minutes (Correct answer)
- 20 minutes
- 1 minute
Correct answer: 5 minutes
The initial information establishes the rate of production: one machine makes one widget in 5 minutes. Since the machines work in parallel, 100 machines can each produce one widget simultaneously, completing the task of making 100 widgets in 5 minutes.
Question 3: In a lake, there is a patch of lily pads that doubles in size every day. If it takes 48 days for the patch to cover the entire lake, on which day does the patch cover half of the lake?
- Day 24
- Day 36
- Day 12
- Day 47 (Correct answer)
Correct answer: Day 47
Since the patch of lily pads doubles in size every day, the lake must have been half-covered on the day before it was fully covered. If the lake is fully covered on day 48, it was therefore half-covered on day 47.
Question 4: A sock drawer contains 10 black socks and 10 white socks, all mixed together. You are pulling socks out in the dark. Which of the following is the minimum number of socks you must pull to guarantee you have a matching pair?
- 11
- 3 (Correct answer)
- 2
- 20
Correct answer: 3
This is a worst-case scenario problem. You could pull out one black sock first, and then one white sock. The third sock you pull, however, must be either black or white, thus guaranteeing a match with one of the first two socks.
Question 5: A two-volume set of books is on a shelf in correct order (Vol. 1, Vol. 2). Each cover is 1/8 inch thick, and the pages of each book are 1 inch thick. A bookworm starts on the first page of Volume 1 and eats in a straight line to the last page of Volume 2. What is the total distance the bookworm travels?
- 2 1/4 inches
- 2 inches
- 1/4 inch (Correct answer)
- 0 inches
Correct answer: 1/4 inch
When books are shelved conventionally, the 'first page' of Volume 1 is on the book's right side, adjacent to Volume 2. The 'last page' of Volume 2 is on its left side, adjacent to Volume 1. The bookworm only needs to travel through the back cover of Volume 1 (1/8 inch) and the front cover of Volume 2 (1/8 inch), for a total distance of 1/4 inch.
Question 6: A father is twice as old as his son. Twenty years ago, the father was four times as old as his son. What is the son's current age?
- 60
- 40
- 25
- 30 (Correct answer)
Correct answer: 30
Let F be the father's current age and S be the son's current age. The equations are F = 2S and (F-20) = 4(S-20). Substituting the first equation into the second gives 2S - 20 = 4S - 80. Solving this equation yields 2S = 60, so S = 30.
Cognitive Reflection Classic Numerical Reasoning Problems Questions and Answers 1
A bat and a ball cost $1.10 in total.
The bat costs $1.00 more than the ball.
How much does the ball cost?