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Q.

Suppose A1,A2.......,A30 are thirty sets each with five elements and B1,B2.......,Bn are n sets each with three elements such that ∪i=130Ai=∪j=1nBj=S. If each element of S belongs to exactly ten of the Ai's and exactly 9 of the Bj's, then the value of n is

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a

15

b

135

c

45

d

90

answer is C.

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Detailed Solution

S=∪i=130Ai⇒n(S)=1105×30=15Again, S=∪j=1nBj⇒n(S)=193×n=n3.Thus n3=15⇒n=45
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