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Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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12 Oct 2004, 13:36

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65% (03:03) correct
35% (02:11) wrong based on 119 sessions

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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?

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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12 Oct 2004, 20:37

1

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Each group has 8 = 8+8+8 = 24 max
4 people are in 2 groups, subtract 4 people twice as they are counted twice
Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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13 Oct 2004, 04:45

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plz check attachment for solution..it might clear doubts..[/img]
Red means members in all three committees, blue is exactly two committees and grey is exactly one committee

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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13 Oct 2004, 04:54

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plz check attachment for solution..it might clear doubts..[/img]
Red means members in all three committees, blue is exactly two committees and grey is exactly one committee

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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14 May 2011, 20:38

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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?

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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14 May 2011, 23:43

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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 in Novel Grove Estates has 8 persons serving [#permalink]

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15 May 2011, 02:45

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 in Novel Grove Estates has 8 persons serving [#permalink]

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15 May 2011, 23:03

jamifahad wrote:

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.

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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16 May 2011, 18:11

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 in Novel Grove Estates has 8 persons serving [#permalink]

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31 May 2015, 03:07

Hello from the GMAT Club BumpBot!

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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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31 May 2015, 18:39

scoobee 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?

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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03 Jun 2016, 07:28

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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03 Jun 2016, 09:00

scoobee 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?

A. 8 B. 13 C. 16 D. 24 E. 27

Solved through venn diagram as solved by fellows above.

13 or B is the answer
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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]

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12 Aug 2017, 05:25

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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