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

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Intern
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A club with a total membership of 30 has formed 3 [#permalink]

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30 Oct 2007, 06:16
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A club with a total membership of 30 has formed 3 committees: M, S, and R, which have 8, 12, 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

Intern
Joined: 30 Oct 2007
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30 Oct 2007, 06:44
D

because M has no member in either of the club S and R. so it's separated from them.

And as the question ask u to find the greatest possible value for those who join neither club.

As R<S (5<12), so u can assume all the members in R are also in S.

So 30-8-12=30-20=10
Director
Joined: 11 Jun 2007
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Re: PS - Committee Seclection [#permalink]

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30 Oct 2007, 07:01
alohagirl wrote:
A club with a total membership of 30 has formed 3 committees: M, S, and R, which have 8, 12, 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

i also get D.10

using a Venn diagram would be helpful
only M = 8 (since no overlap with the other two)
for R = 5 (but all 5 members are also in S)
for S = 7
R&S = 5
30-8-5-7 = 10 in none
Manager
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30 Oct 2007, 07:12
Should have paid more attention to question, yes it's 10.
How I got it wrong:
Assumption that members of both R and S are not in any other committee.
Maximum which are not in any of the committee = 30 -(8+12+5-5) = 10
30 Oct 2007, 07:12
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