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# A club with a total membership of 30 has formed 3

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Current Student
Joined: 11 May 2008
Posts: 551
A club with a total membership of 30 has formed 3  [#permalink]

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25 Jul 2008, 03:34
A club with a total membership of 30 has formed 3 committees, M, S, and R, which have 8, 12, and 5 members, respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
A. 5
B. 7
C. 8
D. 10
E. 12

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Director
Joined: 10 Sep 2007
Posts: 909

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25 Jul 2008, 03:49
m=8
s=12
r=5

Total = 30

To maximize the number of person outside of set, we need to minimize the number of people in the set. so consider that all the 5 candidates of set r also member or both m and s.

Total people in teams = m+s+r - (common to all three) = 8+12+5 - 5 = 20

Total people out of team = 30-20 = 10

IMO D.
Current Student
Joined: 11 May 2008
Posts: 551

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25 Jul 2008, 03:52
correct, thanks..

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This is not a quality discussion. It has been retired.

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Re: sets &nbs [#permalink] 25 Jul 2008, 03:52
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# A club with a total membership of 30 has formed 3

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