Draw three circles(three charities) overlapping each other. Each circle has 8 members in total of which some of them overlap with other circles(some may be in all three some in just 2 etc...)

Case 1: The area common to all three circles(1 area)will have 4 (since 4 of them serve all three charities)

Case 2: The area thats common to each of the 2 circles (3 areas in total) will have 1 member(since its given each pair of charities have 5 memebers in common. The reason its 1 because 4 already overlap between each pair since they occur in Case 1)

Case 3: Group1 exlcusive, Group2 exlcusive and Group3 exlcusive will be 2 each.

2+2+2+4+1+1+1 = 13

This a three sets problem. Hope this helps!

Draw three circles(three charities) overlapping each other. Each circle has 8 members in total of which some of them overlap with other circles(some may be in all three some in just 2 etc...)

Case 1: The area common to all three circles(1 area)will have 4 (since 4 of them serve all three charities)

Case 2: The area thats common to each of the 2 circles (3 areas in total) will have 1 member(since its given each pair of charities have 5 memebers in common) each. The reason its 1 because 4 already overlap between each pair since they occur in Case 1

Case 3: Group1 exlcusive, Group2 exlcusive and Group3 exlcusive will be 2 each.

2+2+2+4+1+1+1 = 13

This a three sets problem. Hope this helps!

Perfect Solution!!

Thanks.

awesome..I had come across this problem in Kaplan I think. They have given a very crude solution to this. But I like your solution better. Helped me too. Thanks

Its a 3 entity set problem.

where Total (distinct) = A + B + C - (A and B) - (B and C) - (A and C) + (A and B and C)

so, A = B = C = 8 (each has 8 members)

(A and B) + (B and C) + (A and C) = 5 * 3 = 15
( each has 5 common with one of the other)

Common among all 3 = 4

so, Total (distinct) = 8 + 8 + 8 - 15 + 4 => 13