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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 30r=1 = nf=1Bj=S and each of S belongs to exactly 10 of the Asi and exactly 9 of the Bsi, then n is equal to


A

15

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B

3

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C

45

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D

35

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Solution

The correct option is C

45


If elements are not repeated, then number of elements in A1A2A,......A30×5

But each element is used 10 times, so

S=30×510=15

If elements in B1,B2,Bn are not repeated, then total number of elements in3n but each element is repeated 9 times, so

S=3n915=3n9

n= 45


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