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# 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.

1. Committee A should consist of exactly one member more than committee B.
2. It is possible that there are no members of committee C.
3. Among Z, Y and X none can serve on committee A.
4. Among W, V and U none can serve on committee B.
5. 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?

1. 3
2. 4
3. 5
4. 6

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

1. 9
2. 8
3. 7
4. 6

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

1. W and S
2. V and T
3. U and S
4. 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

1. Z and Y
2. Z and W
3. Y and V
4. Y and U

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

1. Y and T
2. X and U
3. Y, X and W
4. 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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