The Potato Problem!

How well do you think you can estimate something? How good are you at guessing the answers to problems? How fast can you do it? How accurate are your guesses? In this note, we're going to put your abilities to the test. And we're going to do that with a simple math problem. Are you ready?

I want you read the following problem carefully and (this part is really important) not do the calculations in your mind or on a piece of paper. I want you to simply guess. Also note down how fast you're doing the guessing. We're going to take that into consideration as well. Got that? Here comes the problem:

Suppose you have \(100\) pounds of potatoes. And these potatoes consist of \(99\) % water. You decide to leave the potatoes outside and let them dehydrate until they consist of \(98\) % water. Now the potatoes should weigh a little less than they were before. How much do they weigh now?

Okay, I want you to guess ... now! Don't do the math. Just guess [you'll miss out on something fun if you don't]. And you don't have to worry about being correct. You just have to get something close to the correct answer. Have you done that? Write your guess down.

So, how well do you think you did? What was your answer? \(99\) pounds? \(98\) pounds? \(90\) pounds? Prior to writing this note, I did a little survey on this problem with about \(20\) people. And the average answer was \(98.7\) pounds. Was your answer in this ballpark?

Surprisingly, the correct answer is \(50\) pounds! Yes, the weight decreases by \(50\)% because of the \(1\)% decrease of water! People find this answer very non-intuitive.

Here's a short solution of the problem. Since initially you had \(99\)% water, the water weighed \(99\) pounds while the non-water part weighed \(1\) pound. After the potatoes dehydrate, you're left with \(98\)% water and \(2\)% non-water stuff. Remember that the weight of the non-water stuff never decreases. So, \(2\)% of the new weight is equal to \(1\) pound.

\(1\) pound is \(2\)% of how many pounds? \(\boxed{50}\) pounds and that is our answer.

Were you surprised to see this answer? You're not alone. Your brain probably thought, "Hey, the water decreased by \(1\)%. The weight of the potato can't decrease that much." So, you went with an answer that wasn't too far off from \(100\) pounds.

Feel free to post what your guess was in the comments section. And if you have any feedback, I'll be happy to hear it.

The picture was taken from here

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The Potato Problem!

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