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Three Overlapping Sets - Equation

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by topspin360 » Sun Oct 13, 2013 8:42 am
Hello,

I know how to do the following using Venn diagrams. Just wondering why doesn't the following equation (that I have seen being recommended multiple times) not work?

Equation is: Total = Group1 + Group2 + Group3 - (Sum of 2 group overlaps) - 2*(Sum of three group overlaps) + Neither

Problem: The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedies are there?

My answer using equation above: 38 = 10 + 20 + 18 - 5 - 3 - 4 - 2x

Thanks!
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by [email protected] » Sun Oct 13, 2013 2:30 pm
Hi topspin360,

The equation that you've listed is correct for a 3-circle Venn diagram calculation.

I'm curious about where this question came from. The "problem" with it is that the numbers in the question make a solution impossible (essentially, whoever wrote this question didn't double check that the math actually leads to a solution).

In the given equation, you'd have:
38 = 10 + 20 + 18 - 5 - 3 - 4 - 2x
38 = 36 - 2x
2 = -2x

There is no positive solution for x, so this question (as it's written) doesn't have an answer.

Either the "total" number of movies needs to be decreased OR the number of the individual action, drama and comedy movies needs to be increased.

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