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CAT 2006 — DILR Question 22

SelectionEasy
Passage / Data

Answer the following question based on the information given below.

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

  • A team must include exactly one among P, R, and S.
  • A team must include either M or Q, but not both. 
  • If a team includes K, then it must also include L, and vice versa.
  • If a team includes one among S, U, and W, then it must also include the other two.
  • L and N cannot be members of the same team.
  • L and U cannot be members of the same team.
  • The size of a team is defined as the number of members in the team.

In how many ways a team can be constituted so that the team includes N?

Answer & solution

  • A

    2

  • B

    3

  • C

    4

  • D

    5

  • 6

Solution

If the team includes N, it does not include L and K.

One out of M and Q can be included and one out of P, S and R can be included.

If S is a member, so are U and W.

Thus the possible teams are:

  1. N, M, P
  2. N, M, R
  3. N, Q, P
  4. N, Q, R
  5. N, M, S, U, W
  6. N, Q, S, U, W

Hence, option (e).

CAT 2006 DILR Q22: In how many ways a team can be constituted so that the team includes N? — Solution | TheCATExam