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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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