type 2 selection grouping & team formation on condition puzzles Practice Questions Answers Test with Solutions & More Shortcuts

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]

Question : 36

If R is a representative and M is not a representative, the group of representatives would be completely determined if it were also true that

a) L is not a representative.

b) S is not a representative.

c) P is not a representative

d) N is a representative

Answer: (b)

If R is a representative, L cannot be a representative. Also, M is not a representative. So, K and N are the representatives from faculty members.

From (iii), since M is not a representative, so P cannot be a representative from students.

Thus, either Q or S is the second representative from students.

Question : 37

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

a) K and M

b) K and N

c) L and M

d) L and N

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.

Question : 38

If L is a representative, which of the following can be the order three representatives?

a) N, S, P

b) M, Q, P

c) M, Q, R

d) K, Q, S

Answer: (b)

From (ii), if L is a representative, K cannot be a representative.

Hence, (d) is incorrect.

From (iv), if L is a representative, R cannot be a representative. So, (c) is ruled out.

From (iii), if P is a representative, M must also be a representative. So, (a) is also wrong.

Hence, only (b) holds.

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