Author: Frank Chung
Do not underestimate the bat and ball question. Photo / Getty Images
The world’s shortest IQ test has just three questions, yet fewer than one in five people can answer all three correctly.
Dubbed the Cognitive Reflection Test, it comes from a 2005 paper by MIT professor Shane Frederick, who sought to demonstrate the difference between fast thought processes that occur with little conscious deliberation, and those that are slower and more reflective.
The test consists of three brain teaser-type questions that are harder than they first appear, where the immediately obvious “right” answer is actually incorrect — if you stop and think about it.
“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,” Prof Frederick wrote.
Out of 3428 people who took the test, just 17 per cent answered all three questions correctly, more than half got at least one wrong, and one third scored zero out of three.
Even among MIT students, the best-performing group, fewer than half got all three right.
Here are 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?
What most people guess:
1. 10 cents
2. 100 minutes
3. 24 days
As Prof Frederick noted, 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.”
Here are the correct answers:
1. 5 cents
2. 5 minutes
3. 47 days
Presh Talwalkar, author of The Joy of Game Theory: An Introduction to Strategic Thinking and an expert on mathematical puzzles, explains further 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.”
Interestingly, men scored “significantly higher” than women on the CRT, despite there being “no significant sex differences” on other measures including the Automated Cognitive Test (ACT), the Wonderlic Personnel Test (WPT), the Need for Cognition (NFC) scale and the SAT college admission test.
“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 example, the women who miss the ‘widgets’ problem nearly always give the erroneous intuitive answer ‘100’, whereas a modest fraction of the men give unexpected wrong answers, such as ‘20’ or ‘500’ or ‘1’.”
He added, “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.”
He also noted an unusual finding — CRT scores were more tightly correlated with “time preferences” for women than men, but more tightly linked with “risk preferences” for men than women.
“This result was unanticipated and suggests no obvious explanation,” he wrote, noting “the only related finding of which I am aware” was a 1990 study which found that “the patience of preschool girls was strongly related to their subsequent SAT scores, but the patience of preschool boys was not”.
“Expressed loosely, being smart makes women patient and makes men take more risks,” Prof. Frederick wrote.