Home Strategy If You Get This Simple Math Problem Right, You May Be More Successful

If You Get This Simple Math Problem Right, You May Be More Successful

Than Most People. Even very smart people mostly get it wrong.

By Inc.Arabia Staff
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  • 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? 

Most people say that the ball costs 10 cents. In fact, that was my answer when I read the question. But that can't be true because if it were, the bat would cost $1, and the difference in price between them would be 90 cents. The correct answer is that the ball costs 5 cents and the bat costs $1.05.

This may sound like a fun way to stump people at parties. But it has much more significance than that. In fact, this question is part of the three-question Cognitive Reflection Test, created in 2005 by Shane Frederick, marketing professor at the Yale School of Management.

Don't feel bad if you, like me, immediately came up with the wrong answer. Frederick and his team gave the test to 3,428 people at various locations, including some of our nation's most prestigious universities. Even so, 83 percent got at least one question wrong; only 17 percent got all three questions right. When they gave the test at Harvard, only 20 percent got all three questions right. At Carnegie Mellon, 25 percent got them all right; at Princeton, 26 percent did. The best scores came from the Massachusetts Institute of Technology, where 48 percent of respondents got all three questions right. But that still means more than half of them got it wrong.

Further studies confirm that even very smart people get these questions wrong--in fact, they may be likelier to get them wrong, perhaps because they're too used to quickly coming up with the right answers to problems and don't pause to mentally check their work. And that's the entire point of the test--to measure how likely you are to stop and think about a problem before coming up with an answer, versus blurting out the seemingly obvious answer that first pops into your head.

Look at it that way, and you can see that this is much more than a party trick. As the name of the test suggests, it measures whether or not you stop and think before making decisions. And while the ability to make quick decisions is important for the success of every entrepreneur, it's even more important to make the right decisions rather than jump to conclusions that seem intuitively obvious but turn out to be mistaken.

Learning to use System 2 thinking.

The difference is what earlier researchers called System 1 versus System 2 thinking. In System 1 thinking, we give answers that we intuitively know and don't need to think much about. When someone asks for your address, for example, you answer automatically and without much thought (unless you've recently moved). In System 2 thinking, you take some time and mental processing to find an answer. (The example Frederick uses for System 2 thinking is to find the square root of 19,163 to two decimal places without a calculator.)

Trouble arises, both in the Cognitive Reflection Test and in our work, when we mistakenly believe we can solve a problem using System 1 thinking when System 2 is required. And here's where things get really interesting, because a newer study conducted this year gave people 50 variations on the bat-and-ball question, and invited them to first blurt out their intuitive answer, and then reflect on the problem and give a second answer. In most cases, both the blurted answer and the second answer remained biased toward the seemingly obvious response. But a few respondents were able to correct themselves between the first quick answer and the second, more thoughtful one. And, strikingly, those who did that also learned to use System 2 thinking from then on, and both their quick and slower answers were more accurate throughout the remainder of the test.

With that in mind, here are the remaining two questions from the Cognitive Reflection Test. Now that you know that your intuitive answers may be wrong, see if you can come up with the right ones:

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

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?

Take a minute to think about each of these and find your own answers before you read on.

Got your answers? For the first question, the answer is five minutes. You can deduce from the information in the question that each machine produces one widget every five minutes. Therefore, if you have 100 machines working all at once, they can make 100 widgets in five minutes.

For the second question, the answer is 47 days. It may be tempting to say that it would take half as long--24 days--but the question tells us that the lily patch doubles every day. Therefore, one day earlier than 48 days, it would have been half as big.

Coming up with quick answers is good. Coming up with right answers is better. Understanding when a quick answer is good enough and when you might need to think things through is best of all. That ability to learn quickly from an initial wrong answer and change not only your answer but also your approach is a huge advantage for every business leader. It's something we all should try to learn.

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