The Cognitive Reflection Test has a pass rate of just 17 per cent, leaving the majority who attempt it boggled.
It was originally part of a research paper published in 2005 by MIT Professor Shane Frederick, and has recently resurfaced online with many people giving it a go.
As part of his research, Professor Frederick had more than 3,000 participants from a range of educational backgrounds complete the test, but even those attending top American universities such as Yale and Harvard struggled to work out all the answers.
Professor Frederick said: “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.”
So how will you get on?
What 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 are the answers?
These are the three most common answers that people guess, but they are actually incorrect:
1. 10 cents
2. 100 minutes
3. 24 days
Professor Frederick said: “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.
“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 are:
1. Five cents
2. Five minutes
3. 47 days
Here are the answers explained
Presh Talwalkar, the author of The Hoy of Game Theory: An Introduction to Strategic Thinking, explained how to work out the correct answers for each of the three questions 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.
