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

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11 Dec 2010, 08:32

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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?

Re: A club with a total membership of 30 [#permalink]

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11 Dec 2010, 08:50

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ajit257 wrote:

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

How to solve these types ?

As "no member of committee M is on either of the other 2 committees" then 30-M=30-8=22 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees

General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.

So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S, which has 12 members (if R is subset of S), then total # of members of committee S and committee R would be minimized and equal to 12. Which means that 22-12=10 is the greatest possible number of members in the club who are on none of the committees.

Re: A club with a total membership of 30 [#permalink]

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25 Jun 2011, 07:49

Total club members = 30

no members of M is in any other club. Hence, exclusive members in M = 8 Now, for max. of members who are not part of any group, there might be 5 members in R who all are in group S.

Hence, total number of members in group = members in M + members in S 12+8 = 20.

hence, number of members who are not in any group= 30-20 =10. IMO D _________________

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Re: A club with a total membership of 30 [#permalink]

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31 May 2013, 13:47

Total number of people = 30 Number of people on m = 8 So pool of people left = 22

To maximize people on no committees assume all members of R are also part of S

So people on no committees = 22 - 12= 10 _________________

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Re: A club with a total membership of 30 has formed 3 committees [#permalink]

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15 Jul 2014, 06:03

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Re: A club with a total membership of 30 has formed 3 committees [#permalink]

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16 Oct 2015, 23:45

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