Each of three charities in Novel Grove Estates has 8 persons serving : GMAT Problem Solving (PS)
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# Each of three charities in Novel Grove Estates has 8 persons serving

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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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Question Stats:

63% (02:49) correct 37% (02:36) wrong based on 66 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?

A. 8
B. 13
C. 16
D. 24
E. 27
[Reveal] Spoiler: OA
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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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solutions.doc [29 KiB]

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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
1
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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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solutions.doc [29 KiB]

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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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venn diagram.JPG [ 22.61 KiB | Viewed 3674 times ]

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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
Total - 13
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Charities.png [ 8.19 KiB | Viewed 3641 times ]

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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+8-5-5-5+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
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, 02:07
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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)+(8-1*2-4)*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] 03 Jun 2016, 08:00
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