Keith Stanovich, professor of human development and applied psychology at the University of Toronto, Canada, has grappled with this apparent incongruity for 15 years. He says it applies to more people than you might think. To Stanovich, however, there is nothing incongruous about it. IQ tests are very good at measuring certain mental faculties, he says, including logic, abstract reasoning, learning ability and working-memory capacity - how much information you can hold in mind.
But the tests fall down when it comes to measuring those abilities crucial to making good judgements in real-life situations. That's because they are unable to assess things such as a person's ability to critically weigh up information, or whether an individual can override the intuitive cognitive biases that can lead us astray.
When Shane Frederick at the Yale School of Management in New Haven, Connecticut, put this and two similarly counter-intuitive questions to about 3400 students at various colleges and universities in the US - Harvard and Princeton among them - only 17 per cent got all three right (see "Test your thinking"). A third of the students failed to give any correct answers (Journal of Economic Perspectives, vol 19, p 25).
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 5 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 it?
Answers to be posted tomorrow.
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