Questions about the world of GRE Math from other sources and general math related questions.
yellowpad
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venn diagram question

by yellowpad Sat Dec 21, 2013 3:10 am

In a group of 25 students attending an after-school sports club, 15 opt for volleyball, 12 take martial arts and 8 take basketball. Each student is taking at least one sports class. What is the biggest number of students that can take all classes?


Tried to solve it, thought the answer could be 7 but cant offer a decent explanation. Please help, thanks.
tommywallach
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Re: venn diagram question

by tommywallach Tue Dec 24, 2013 5:53 pm

Hey Yellowpad,

Consider this equation:

Total People = V + M + B - (# of people in exactly 2 groups) - 2 * (# of people in all 3 groups) + No group people (question says there aren't any of these, because everyone takes a sport)

Does this make sense? Anyone in 2 groups has been counted twice, and anyone in all 3 groups has been counted three times, so we have to toss out those duplicates.

25 = 15 + 12 + 8 - (2 group people) - 2 * (3 group people) + 0

25 = 35 - 2 group people - 2 * (3 group people)

So how many people can take all three? Well, if we assume NO ONE is in just 2 groups, then all of our overlap could be attributed to people in all 3 groups.

25 = 35 - 0 - 2 * (3 group people)

0 = 10 - 2 * (3 group people)

2 * (3 group people) = 10

3 group people = 5

The answer is 5. I don't know where your solution came from. : )

(feel free to ask follow-ups...I know this can be confusing)

-t
yellowpad
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Re: venn diagram question

by yellowpad Thu Dec 26, 2013 4:18 am

Hey Tommy,

I think mastering the formula really helps here, the problem is indeed a bit confusing, I need some time to digest your explanation :) will get back if I have any questions. Thanks
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: venn diagram question

by tommywallach Tue Dec 31, 2013 6:18 pm

Glad to help!

-t
michele.malpede
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Re: venn diagram question

by michele.malpede Thu Jan 09, 2014 1:00 pm

Hi,
I am a little bit puzzled about the formula mentioned.

Total People = V + M + B - (# of people in exactly 2 groups) - 2 * (# of people in all 3 groups) - No group people

Shouldn't it be Total= Group1+Group2+Group3 - (# of people in exactly 2 groups)- 2*(# of people in all 3 groups) + Neither ??

Can someone please explain me why so?
Thanks a lot
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: venn diagram question

by tommywallach Thu Jan 09, 2014 4:57 pm

Yep! My mistake. I've changed it in my original equation, so no one gets confused, but I absolutely wrote it wrong the first time around. Good catch!

-t