LRDI sets (Elementary) 15

Nine individuals - Z, Y, X, W, V, U, T, S and R - are the only candidates, who can serve on three committees A, B and C, and each candidate should serve on exactly one of the committees.

Committee A should consist of exactly one member more than committee B.
It is possible that there are no members of committee C.
Among Z, Y and X none can serve on committee A.
Among W, V and U none can serve on committee B.
Among T, S and R none can serve on committee C.

Q1. In case T and Z are the individuals serving on committee B, how many of the nine individuals should serve on committee C?

Q2. Of the nine individuals, the largest number that can serve together on committee C is

Q3. In case R is the only individual serving on committee B, which among the following should serve on committee A?

W and S
V and T
U and S
T and S

Q4. In case T, S and X are the only individuals serving on committee B, the total membership of committee C should be

Z and Y
Z and W
Y and V
Y and U

Q5. Among the following combinations which could constitute the membership of committee C?

Y and T
X and U
Y, X and W
W, V and U

Explanations

Q1. If T and Z are serving on committee B. X and Y must serve on committee C. Since they can't serve on committee A. And R and S must serve on committee A since they cannot be on C. Also A must consist 3 members because there are 2 members on committee B. So one of U, V and W will be on committee A and other two will be on C. Hence there are 4 members who should serve on committee C. Ans.(2)

Q2. Out of 9 individuals there are 3 members R, S and T who cannot serve on committee C and Two of them can serve on A and one on B. Hence maximum people who can serve on committee C is 6. Ans (4)

Q3. If R is the only individual serving on committee B, S and T must serve on committee A. Ans.(4)

Q4. Since T, S, and X are serving on committee B committee A must consist 4 members but x and y cannot serve on committee A, so they will be on committee C and remaining four members will serve on committee A. Ans.(1)

Q5. Option 1 T cannot serve on committee C.

Option 3 and 4 If 3 members serve on committee C then remaining 6 members cannot serve on committee A and B in a manner that A will consist of exactly one members more than B.

Hence option "2" must be true. Ans.(2)

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LRDI sets (Elementary) 15

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