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

Question

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

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

KarishmaB · Accepted Answer

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... Ques2.jpg

jamifahad · Answer

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.

jinino · Answer

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

Bunuel · Answer

Check this link for different formulas on 3 overlapping sets (theory and examples): formulae-for-3-overlapping-sets-69014.html#p729340

subhashghosh · Answer

Total - 13
Answer - B

dreambeliever · Answer

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

PareshGmat · Answer

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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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

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