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Question

Study the following information carefully and answer the questions given below it:
From amongst six boys A, B, C, D, E, and F and five girls P, Q, R, S, and T, a team of six is to be selected under the following conditions:
1. A and D have to be together.
2. C cannot go with S.
3. S and T have to be together.
4. B cannot be teamed with E.
5. D cannot go with P.
6. B and R have to be together.
7. C and Q have to be together
If the team including C consists of four boys, the members of the team other than C are:
  1. ADEPQ
  2. ABDQR
  3. DEFAQ
  4. BEFRQ


Solution

The correct option is B ABDQR
There are four boys including C. So there must be two girls. Now if C is present, S can’t go and if S can’t go, T won’t go. Hence three girls remain: P, Q and R. Out of these, two can be selected in the following ways: PQ, PR, QR. Now if P is selected, D can’t go and if D can’t go. A won’t go. In that case the team would have to include B and E because four boys have to be selected. But B and E can’t be together. This means that P should not be selected. Hence the only possibility of selecting two girls is QR. But R means the necessary inclusion of B, which in turns means necessary exclusion of E. Hence the possible team is CBQR. To this we should add two boys out of A, D and F. The only possibility is adding A and D because neither of these would go without the other. Hence the team is ADCBQR

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