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SET THEORY MAXIMA

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Manager
Joined: 04 Sep 2006
Posts: 113

Kudos [?]: 62 [0], given: 0

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27 Jun 2009, 21:41
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A company has 30 employees and 3 clubs M, S, and Z. 10 employees joined M, 12 joined S, 5 joined Z. If members of M joined no other clubs, at most how employees joined neither of the clubs?

Kudos [?]: 62 [0], given: 0

Senior Manager
Joined: 23 Jun 2009
Posts: 360

Kudos [?]: 134 [0], given: 80

Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

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28 Jun 2009, 12:51
8 is true. Solution is right.

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Manager
Joined: 28 Jan 2004
Posts: 202

Kudos [?]: 28 [0], given: 4

Location: India

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29 Jun 2009, 21:13
Refer to the attached Venn diagram
A + B + C + D + E + F + G + X = 30
where X = members no belonging to any club
A = 10
B = C = D = 0 (because of the clause that club M members are not members of any other club)

So equation becomes
E + F + G + X = 20.....................1

Club S has 12 members so
F + G = 12............................2

Club Z has 5 members so
E + F = 5...........................3

We need to find out max. of X. Now X will be max. when E + F + G will be minimum.
Substitute eq. 2 in eq. 1
E + 12 + X = 20
For it to be minimum E can be 0 which leads to Max. X = 8.

This took me less then 1 min. and this is the std. way to solve this.
Why i did not substituted eq. 3 in eq. 1 is a question for you guys
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venn diagram.dot [25 KiB]

Kudos [?]: 28 [0], given: 4

Re: SET THEORY MAXIMA   [#permalink] 29 Jun 2009, 21:13
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