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sets!

by mehaksal » Sun Aug 26, 2012 10:19 am
There are 30 people and 3 clubs M, S, and Z in a company. 10 people joined M, 12 people joined S and 5 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not join any club?
A: 4
B: 5
C: 6
D: 7
E: 8
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by neelgandham » Sun Aug 26, 2012 11:42 am
From the diagram, we know that

a + d + g + f = 10. We also know that d + g + f = 0, because the members of M did not join any other club. So, the value of a is 10, d,g,f is 0.

b + e + d + g = 12; i.e. b + e = 12 as d = g = 0.

c + e + g + f = 5; i.e. c + e = 5

h = Number of people of the company who did not join any club.

We know that a + b + c + d + e + f + g + h = 30.
a + b + c + e + h = 30
10 + b + 5 + h = 30
b + h = 15. For h to be maximum, b should be minimum.
b + e = 12. For b to be minimum, e should be maximum.
c + e = 5. For e to be maximum, c should be minimum. Let c be equal to 0. Then the value of e = 5, the value of b = 7, the value of h = 8.

IMO E
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by mehaksal » Sun Aug 26, 2012 8:19 pm
a very fine explanation :)
but the question is time-consuming, do such questions actually appear in the exam??
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by neelgandham » Tue Aug 28, 2012 4:18 am
Yes Mehak. These questions do appear in the exam.

Here are a few examples: https://www.beatthegmat.com/forums/tags/ ... pping-sets
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