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Venn diagram?

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Venn diagram?

by ankita1709 » Sat Jun 02, 2012 7:13 am
Each of 3 charities in Ginglo Kiru has 8 persons serving on its board of directors. if exactly 4 persons serve on 3 board 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

How can we do this with Venn diagram

Answer is B

But can't trust this completely.
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by Birottam Dutta » Sat Jun 02, 2012 8:03 am
Check the attachment.

x=y=z comes out to be 2 each. This makes it 6 people.

4 people are common to all three charities.

Finally, 1 each is common to pairs of charities.

Notice that since 5 are common to each pair of charities and 4 are already common to all three charities, therefore, only 1 more ( as common to a pair of charity) is needed to make it 5!

Therefore, total = 6+4+1+1+1 = 13.

Hence, B!
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