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Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
12 Oct 2004, 12:36
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This post was BOOKMARKED
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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!
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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
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31 May 2015, 17:39
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