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Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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12 Oct 2004, 12:36
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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? A. 8 B. 13 C. 16 D. 24 E. 27
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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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12 Oct 2004, 19:37
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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
Ans: 8+8+8(2(4))  3 = 13



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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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13 Oct 2004, 03:45
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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



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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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13 Oct 2004, 03:54
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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



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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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14 Oct 2004, 12:52
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Charity 1, 8 people:
a,b,c,d,e,f,g,h
Charity 2, 8 people:
a,b,c,d,e,x,y,z
Charity 3, 8 people:
a,b,c,d,f,p,q,z
Total distinct people from 3 charities: a,b,c,d,e,f,g,h,p,q,x,y,z = 13 people



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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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14 May 2011, 19:38
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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? 8 13 16 24 27



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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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14 May 2011, 22:43
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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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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 in Novel Grove Estates has 8 persons serving [#permalink]
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15 May 2011, 01:39
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Total  13 Answer  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, 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 in Novel Grove Estates has 8 persons serving [#permalink]
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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+8555+4 = 13
ans 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, 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.



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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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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 in Novel Grove Estates has 8 persons serving [#permalink]
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16 May 2011, 11:58
Venn Diagrams are life savers for these kind of questions. Thanks for the graphical answer explanation!! Really helped



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



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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, 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)+(81*24)*3 = 4+3+6=13 Kudos.. If you like..
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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, 06:28
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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, 08:00
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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