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Each of three charities in Novel Grove Estates has 8 persons serving

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nzgmat
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Each of three charities in Novel Grove Estates has 8 persons serving [#permalink] New post   12 Oct 2004, 20:37
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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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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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B
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KarishmaB
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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink] New post   31 Jan 2011, 21:26
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m990540 wrote:
Sorry, the answer is 13. I know that this question can be found in the forum, but I'd like to know if there's a way (such as using the standard overlapping set equation) to attack the problem other than by drawing out each of the three groups!

Thanks so much!


You can use the formula for 3 sets:
n(AUBUC) = n(A) + n(B) + n (C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)

n(AUBUC) = 8 + 8 + 8 - 5 - 5 -5 + 4 = 13

Though, why would you not try using the Venn diagram for 3 overlapping sets. This question is relatively straight forward so the formula is no problem, but with the Venn diagram, it doesn't matter how much you twist the question, the answer is still apparent....
I am attaching it in case you would like to give it a look...
Attachment:
Ques2.jpg
Ques2.jpg [ 10.5 KiB | Viewed 12711 times ]
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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink] New post   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] New post   14 Oct 2004, 13:52
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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] New post   01 Feb 2011, 03:08
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m990540 wrote:
Hello,

Here's an overlapping set question that I came across and obviously got wrong.

Thanks in advance to anyone who can help me sort this one out!


Check this link for different formulas on 3 overlapping sets (theory and examples): formulae-for-3-overlapping-sets-69014.html#p729340
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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink] New post   15 May 2011, 02:39
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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] New post   15 May 2011, 13:27
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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] New post   05 Aug 2014, 21:51
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Distinct persons means addition of all colours (As per diagram below)

= 2+1+4+1+2+1+2

= 13

Answer = 13
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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink] New post   08 Aug 2023, 11:40
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Re: Each of three charities in Novel Grove Estates has 8 persons serving [#permalink]
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