The Math Tutor: Of Watermelons, Problem Solving, and Gut Feelings

Posted by Entela Nako on 9/23/13 9:35 AM

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Dean Gallagher of the School of Watermelon Impact Studies

A few weeks ago, I was enjoying one of the last days of the summer by having a barbeque with my friends. One of them, a neuroscience professor at Harvard, was talking about the questions he likes to ask future graduate students during interviews. While some people ask research-specific questions, he likes to use a different approach. To show us, he posed one of those questions to us:

A 100kg watermelon is 99% water (yes, that’s a very large watermelon, but bear with me). After standing in the sun for a few hours, it is 98% water. How much does the watermelon weigh now?

A few of my friends answered almost instantaneously: “But that's easy! You ask PhD candidates that? It is 99kg now.” When asked to explain their answer, they said: “Well, it was 99% water from 100kg. Now it is 98% water. It lost 1% water (99%-98%=1%), or 1kg (since it weighs 100kg and 1% of 100kg is 1kg), so it must be 99kg now.

But they were wrong—very wrong.

The correct answer is 50kg!

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Dean Gallagher demonstrates the Cambridge Coaching Approach to Annoying Math Problems

How can several people, most of whom have a PhD in science or at the very least a master's in it, get this wrong? They weren’t even close to the correct answer. They were really off. I mean, these are smart, accomplished people and I am not saying that just because they are my friends.

What’s more interesting is that, when told their answer was wrong, and after spending a few minutes thinking about it, everyone got the right answer.

This illustrates a very important phenomenon; that even very smart and well-trained people can make mistakes when going with what seems like the easiest and most straightforward answer, and not taking the time to make sure that the answer is correct. Whether the question is about watermelons or one's weight in space, taking the time to check your process of reasoning can really pay off. You might not look as cool as the person who was able to answer instantaneously, but you will be the person that answered correctly. And trust me, that is way more important than looking cool.

Am I suggesting that you should ignore your gut feeling when taking exams or standardized tests, and never choose the answer that seems the most straightforward? Of course not!

What I am suggesting is that you take a few more moments to confirm that your gut feeling is, in fact, correct.

This is especially important for problems that involve calculations. Like my friends, when you go through the problem and think for a bit, you may realize that the correct answer is a different one.

For those of you that are curious about the right answer, it goes like this:

At the initial stage, the watermelon weight 99kg water and 1kg dry mass. The dry mass never changes since it cannot evaporate. So even after having been in the sun for a few hours, it still has 1kg of dry mass. However, now that 1kg is 2% of the total weight (since now it is 98% water). So, 1=0.2*X, where x is the mass of the watermelon after standing in the sun. If one 1kg is 2%, then 0.5 kg must be 1%, and as a result the whole watermelon weighs 50kg.

For more problem solving techniques and ways to quickly and efficiently check your work, talk to your teachers, or consider studying with a tutor!

 

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Tags: math