Fewer than one in five people can answer all three questions in the world’s shortest IQ test.

This test is dubbed the “Cognitive Reflection Test” and comes from a 2005 paper by MIT professor Shane Frederick. He sought to demonstrate the difference between fast thought processes that are done with little conscious deliberation and those that are slower and more reflective.

The test is made up of only three questions that are harder than they first appear.

“The three items on the CRT are ‘easy’ in the sense that their solution is easily understood when explained, yet reaching the correct answer often requires the suppression of an erroneous answer that springs ‘impulsively’ to mind,” Professor Frederick wrote.

The questions

1. A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

2. If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?

3. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

Do you have your answers?

Here’s what most people guess

1. 10 cents

2. 100 minutes

3. 24 days

Professor Frederick noted that the intuitive answer to the first question is 10 cents, but this “impulsive answer” is wrong.

“Anyone who reflects upon it for even a moment would recognise that the difference between $1 and 10 cents is only 90 cents, not $1 as the problem stipulates,” he wrote.

“In this case, catching that error is tantamount to solving the problem, since nearly everyone who does not respond ‘10 cents’ does, in fact, give the correct response.”

The correct answers

1. 5 cents

2. 5 minutes

3. 47 days

Presh Talwalker, who is the author of The Joy of Game Theory: An Introduction to Strategic Thinking, explained the answers on his blog, Mind Your Decisions.   

1. “Say the ball costs X. Then the bat costs $1 more, so it is X + 1. So we have bat + ball = X + (X + 1) = 1.1 because together they cost $1.10. This means 2X + 1 = 1.1, then 2X = 0.1, so X = 0.05. This means the ball costs five cents and the bat costs $1.05.”

2. “If it takes five machines five minutes to make five widgets, then it takes one machine five minutes to make one widget (each machine is making a widget in five minutes). If we have 100 machines working together, then each can make a widget in five minutes. So there will be 100 widgets in five minutes.”

3. “Every day FORWARD the patch doubles in size. So every day BACKWARDS means the patch halves in size. So on day 47 the lake is half full.”

The answers between men and women also varied.

“Even if one focuses only on respondents who gave the wrong answers, men and women differ. Women’s mistakes tend to be of the intuitive variety, whereas men make a wider variety of errors,” Prof. Frederick wrote.

“For every CRT item the ratio of ‘intuitive’ mistakes to ‘other’ mistakes is higher for women than for men. Thus, the data suggest that men are more likely to reflect on their answers and less inclined to go with their intuitive responses.”