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# Each of three charities

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Director
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Each of three charities [#permalink]  14 May 2011, 19:38
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Question Stats:

38% (02:05) correct 63% (01:04) wrong based on 15 sessions
Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?

8

13

16

24

27
Senior Manager
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Re: Each of three charities [#permalink]  14 May 2011, 22:43
5
KUDOS
Let Communities be C1, C2 and C3. It given that exactly 4 members serve on 3 boards each. Hence 4 member in all three communities.
Also each pair of charity has 5 persons in common. hence 1 member between C1 and C2 Only.

Total = 2+2+2+1+1+1+4=13.

OA B.
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Re: Each of three charities [#permalink]  14 May 2011, 23:42
3- charities 4
2 charities 3

each charity - 2+2+2 = 6

total 13.
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Re: Each of three charities [#permalink]  15 May 2011, 01:39
Total - 13
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Charities.png [ 8.19 KiB | Viewed 2084 times ]

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Re: Each of three charities [#permalink]  15 May 2011, 01:45
gmat1220 wrote:
Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?

8

13

16

24

27

I actually couldn't interpret "If exactly 4 persons serve on 3 boards each". It would be clearer if it read, "Same 4 persons serve on all of the 3 boards".
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Re: Each of three charities [#permalink]  15 May 2011, 12:27
let the boards be A, B, and C
n(total) = n(A) + n(B) + n(C) - n(AB) - n(AC) - n(BC) + n(ABC)
= 8+8+8-5-5-5+4 = 13

ans B
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Re: Each of three charities [#permalink]  15 May 2011, 22:03
Let Communities be C1, C2 and C3. It given that exactly 4 members serve on 3 boards each. Hence 4 member in all three communities.
Also each pair of charity has 5 persons in common. hence 1 member between C1 and C2 Only.

Total = 2+2+2+1+1+1+4=13.

OA B.

Great Explanation, thanks. Kudos to you
I didn't even understand the question i guess.
Manager
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Re: Each of three charities [#permalink]  16 May 2011, 09:21
Board 1 Board 2 Board 3
Common A A A
Common B B B
Common C C C
Common D D D
Pair X X U1
Pair U2 Y Y
Pair Z U3 Z

Unique are
U1 U2 U3 A B C D X Z
Total 8
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Re: Each of three charities [#permalink]  16 May 2011, 11:58
Venn Diagrams are life savers for these kind of questions.
Thanks for the graphical answer explanation!!

Really helped
Director
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Re: Each of three charities [#permalink]  16 May 2011, 17:11
I agree with fluke. It would have been clearer if the question read as 4 persons served on all 3 boards rather than "4 persons serve on 3 boards each".

fluke wrote:
gmat1220 wrote:
Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?

8

13

16

24

27

I actually couldn't interpret "If exactly 4 persons serve on 3 boards each". It would be clearer if it read, "Same 4 persons serve on all of the 3 boards".
Re: Each of three charities   [#permalink] 16 May 2011, 17:11
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