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?

- 3
- 4
- 5
- 6

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

- 9
- 8
- 7
- 6

**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)**