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Question

Suppose A1, A2,.....................A30 are thirty sets each having 5 elements and B1, B2,................Bn are n sets each with 3 elements, let 30i=1Ai=nj=1Bj=S and each element of S belongs to exactly 10 of Ai'S and exactly 9 of the Bj'S. Then n is equal to


A

15

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B

3

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C

45

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D

50

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Solution

The correct option is C

45


Since S =30i=1Ai

Now, element in the union S belongs to exactly 10 of the Ai'S. So n(S) = 110(5×30)=15 Again, S =nj=1Bj

So, n(S) = 19(3×n) = n3 Thus,n3 = 15 n = 45


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