Think quickly: can you ace the world's shortest intelligence test?

academics math

Below is the world's shortest intelligence test. See how many questions you can answer!

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?

2) If it takes 5 machines 5 minutes to make 5 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?

This is Shane Frederick's Cognitive Reflection Test. Although the test is simply worded and only has four possible scores, when it was given to groups of students at various universities, it correlated fairly well to other, longer intelligence tests. (For reference, students from MIT averaged 2.18 correct answers.) The neat part is that the questions in the test are designed to trick you. They all have nice, intuitive answers which spring right to the forefront of your mind when you read the question. A brain caught unawares will think "of course the ball must cost $0.10, that is how much I should add to $1.00 to get the total of their costs, $1.10!" Questions 2 and 3 have similar "pitfall" lines of reasoning of their own, resulting in the answers of 100 minutes and 24 days, respectively.

You might have just had a small moment of panic or disappointment if you recognized one of your answers in the previous paragraph. It is possible that you stopped, went back to the question, worked through it more carefully, and saw why the answers above are incorrect. (If you have not yet done so, I highly recommend it.) This would be an example of you switching from using your lightning-fast intuition to a slower and more measured approach. You can see the comparison between these in action when I ask you whether 1003 is even and whether 1003 is prime.

If you have seen one of these questions before (the first question is commonly shared on social media), you may have been ready for a trick. You may have engaged your careful reasoning in advance and you may have gotten past my elaborate defenses: trying to get you to use your intuition by cunningly concealing "Think Quickly" in the title. When reading these questions in a decently large font in a nice solid color, the conditions were perfect for letting intuition take over and giving you an answer to the questions in a snap.

Amazingly, what researchers found was that printing the question in a small, grey, italicized font, making it much harder to read, actually increased the scores of students from Princeton from 1.9 to 2.45! The fraction of students that made at least one mistake dropped from 90% to 35%. What happened was that shrinking the font and making the question harder to read engaged the process of analytical thinking. It became harder for the students to jump to an answer because it is tricky to get an intuition for a problem which is difficult to read.

Although this test was just for fun, the implications and consequences of these modes of thinking can be dangerous to the unprepared if you are taking a test with more at stake, such as the SAT or GRE. Standardized test questions are printed in nice fonts, use simple words, and they have multiple choices. The answers are already right on the page for your intuition to grab onto, especially given that SAT questions will deliberately include answers that feel correct, but are actually produced by solutions with common mistakes. Not only that, but these tests will often place you under time pressure and not give you enough time per question to confirm and triple-check your answer every time. Being able to engage your analytical thinking skills, avoid the pitfall answers, and maintain accuracy without sacrificing speed is key to success when taking such tests, so do not let your guard down!

Feel free to share this test with your friends! Below are the solutions.

1) $0.05. The bat costs a dollar more than the ball, so the $1.10 can be split as ball + (ball + $1.00), making the ball $0.05 and the bat $1.05.

2) 5 minutes. 5 machines work in parallel, each making its own widget in 5 minutes. 100 machines making 100 widgets have 20 times the work to do but do it with 20 times as many machines. Each still makes its own widget in 5 minutes.

3) 47 days. If the patch doubles in size every day, one day before covering half of the lake, it would cover half of it. Thus, it takes 47 days for the patch to cover half of the lake.

For references and further reading, see "Thinking Fast and Slow" by Daniel Kahneman and "David and Goliath" by Malcolm Gladwell.

Andrey graduated from the University of Toronto with a Math and Physics Specialist degree. He's now pursuing a PhD in Mathematics at MIT, focusing on quantum computing and quantum information.

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