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# The 39 parents participating in the Smithville PTA have been

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Intern
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The 39 parents participating in the Smithville PTA have been [#permalink]  27 Sep 2013, 06:33
00:00

Difficulty:

35% (medium)

Question Stats:

67% (02:22) correct 33% (02:10) wrong based on 58 sessions
The 39 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?

A. 4
B. 6
C. 8
D. 9
E. 10
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Sep 2013, 07:31, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
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Re: The 39 parents participating in the Smithville PTA [#permalink]  27 Sep 2013, 07:30
Expert's post
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violetsplash wrote:
The 39 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?

A. 4
B. 6
C. 8
D. 9
E. 10

$$Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither$$.

Since each parent is assigned to at least 1 of 3 committees, then the # of parents assigned to neither of them is 0.

$$39=21+18+19-x-2*5+0$$ --> $$x=9$$.

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Re: The 39 parents participating in the Smithville PTA have been [#permalink]  27 Sep 2013, 10:09
The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=39
solving for x you get 9
Re: The 39 parents participating in the Smithville PTA have been   [#permalink] 27 Sep 2013, 10:09
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