Each set Xr contains 5 elements and each set Yr contains 2 elements and
Each set Xr contains 5 elements and each set Yr contains 2 elements and ⋃Xr(for r=1 to 20) =S=⋃Yr(for r=1 to n). If each element of S belong to exactly 10 of the Xr’s and to exactly 4 of the Yr’s, then n is
(A) 10
(B) 20
(C) 100
(D) 50
4 views
1 Answers
The correct answer is (B)
Since, n(Xr) = 5, ⋃Xr(for r=1 to 20)=S, we get n(S) = 100
But each element of S belong to exactly 10 of the Xr’s
So, 100/10 = 10 are the number of distinct elements in S.
Also each element of S belong to exactly 4 of the Yr’ s and each Yr contain 2 elements. If S has n number of Yr in it. Then
2n/4 = 10
which gives n = 20
4 views
Answered