If someone were to ask you a simple math problem- “A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?” what would your answer be? Your reflexively would come up with the answer “$.10”. But, if you were to solve it mathematically, your answer would actually be wrong. For, if the ball costs 10 cents, then the bat would cost $1.10, making the total price $1.20.
The correct answer, in this particular scenario, would be $.5 and $1.05 for the price of ball and bat, respectively. For those wondering about the necessity of such a math problem, this was a part of the Cognitive Reflection Test, which was first instituted in 2005 by Shane Frederick, a psychologist. The psychologist had set this test up because he wanted to see how people fought or surrendered to their intuitive thinking.
The original CRT tests had a few more math problems. One of them asked, if it took five machines around five minutes to make five separate widgets, how long would it take 100 machines to create 100 widgets? And the second question read, “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?” The research results for this test and how far it measures intelligence and cognitive ability have been mixed. Interestingly, many individuals bring in wrong answers to the questions due to a psychological trap that we fall into. This same trap hinders our ability to make sound and well-informed decisions.
Why Do We Get This Simple Math Problem Wrong?
There is a reason why we get this math problem wrong. First, psychologists discuss the cognitive processes as System 1 and System 2. For those unaware, System 1 is one’s initial reaction- something that happens reflexively. But System 2 comes out of conscious thought. This was popularized by Daniel Kahneman in his bestselling book, “Thinking, Fast and Slow.” If we want our conscious mind to come into play and give us the correct answer, then we must acknowledge that the subconscious mind has provided us with the wrong answer.
A recent study regarding this math problem also mentioned that if people were given two chances to check the sum, they would still be making the same mistake- for they would be loyal to their knee-jerk answer. The study reads, “Results showed that both people’s first hunches and the responses they gave after deliberation predominantly remained biased from start to finish. But in the rare cases in which participants did learn to correct themselves, they immediately managed to apply the solution strategy and gave a correct hunch on the subsequent problems.”
This makes it prudent for us to understand that it is not always necessary, or even correct to just go with our hunch. Sometimes, we might have to reevaluate what we believe or chose previously. On the flip side, we might be convinced that our hunch is correct- but that just might not be the case- just like the math problem.
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