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Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
12 Oct 2004, 12:36

2

This post was BOOKMARKED

00:00

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Difficulty:

55% (hard)

Question Stats:

60% (02:00) correct
40% (02:53) wrong based on 52 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?

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
12 Oct 2004, 19:37

1

This post received KUDOS

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]
13 Oct 2004, 03:45

1

This post received KUDOS

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]
13 Oct 2004, 03:54

1

This post received KUDOS

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]
14 May 2011, 19:38

1

This post was BOOKMARKED

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]
14 May 2011, 22:43

5

This post received 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 in Novel Grove Estates has 8 persons serving [#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". _________________

Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
15 May 2011, 22:03

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]
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 in Novel Grove Estates has 8 persons serving [#permalink]
31 May 2015, 02:07

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]
31 May 2015, 17:39

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?

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

4+(1*3)+(8-1*2-4)*3 = 4+3+6=13

Kudos.. If you like.. _________________

Impossibility is a relative concept!!

gmatclubot

Re: Each of three charities in Novel Grove Estates has 8 persons serving
[#permalink]
31 May 2015, 17:39

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