If neither Q nor S is a representative, which of the following is the pair of fa

Question

Directions: Read the data given below to answer the questions:

The director of a B-school wishes to select four members of a faculty-student committee as representatives to meet with the school's board of directors. The faculty-student committee consist exactly four faculty members - K, L, M and N - and four students - P, Q, R and S. The director can select any of the committee members as representatives as long as he observes the following restrictions: (i) The group of four representatives must consist of exactly two faculty members and two students. (ii) Either K or L must be one of the representatives, but K and L cannot both be representatives. (iii) If P is a representatives, M must also be a representative. (iv) If R is a representatives, L cannot be a representative.

[A.T.M.A. 2006]

If neither Q nor S is a representative, which of the following is the pair of faculty members who must be representatives?

Options:

A . K and M

B . K and N

C . L and M

D . L and N

Answer: Option A
Answer: (a)
If neither Q nor S is a representative, P and R are representatives from students. If R is a representative L cannot be a representative.
Thus, K is one of the representatives from faculty members as either K or L must be one of the representatives. If P is a representative, M must also be a representative.
Hence, K and M is the pair of faculty members who must be representatives.

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