InterviewSolution
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InterviewSolution
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K, L, M, N, P, Q, R, S, U and W are the only 10 members in a department. There is a proposal to form a term within the members of the department, subject to the following conditions. (a) A team must include exactly one among P, R and S (b) If a team include either M or Q but not both (c) If a team includes one among S, U and W, then it must also include the other two (d) If a team includes K, then it must also include L and vice versa (e) L and N cannot be member of the same team (f) L and U cannot be members of the same team 1. What would be the size of the largest possible team? (1) 8 (2) 7 (3) 6 (4) 5 2. What would be the size of a team that includes K? (1) 2 and 3 (2) 2 and 4 (3) only 2 (4) only 4 3. In how many ways a team can be constituted so that team includes N? (1) 6 (2) 5 (3) 4 (4) 3 4. Who can not be a member of a team of size 3? (1) L (2) M (3) N (4) P 5. Who can be a member of a team of size 5? (1) K (2) L (3) M (4) P |
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Answer» 1. (4) 5 From statement (a) and (b) Two members are to be selected, Of the remaining seven To maximize the size of the team we would choose S U and W are included in the team(statement (c)). We cannot include K or L because we would then have to leave out N and U(from statement (e) and (f)) 2. (4) only 4 If ‘K’ is included ‘L’ has to be included (statement(d)). If ‘L’ is choose neither N nor U can be chosen(statement(e & f)). S, W are also not included because S, U, W have to be always together(statement(c)). Hence, one of P or R would be selected (statement(a)) And one of M or Q would be selected (statement(b)). 3. (1) 6 If a team includes N, it cannot include ‘L’ and therefore not even ‘K’ (statement (e) and (d)). According to the statement (a), one of P or R or S has to be included. According to the statement(b) one of M or Q has to be selected. So following cases are possible: PQN, RQN, PMN, RMN If ‘S’ is selected SUWMN, SUWQN These are the only possible cases Thus, in all 4 + 2 = 6 ways 4. (1) L From the statement (a) and (b) One of P, R, S and one of M, Q are to be selected. But from statement(d) K, L are always together. Thus, L cannot be included in a team of 3 members 5. (3) M From statement (a) one of P, R, S has to be selected. To make a team of 5. S will be chosen(which leaves out P and R) If ’S’ is chosen, ‘U’ has to be chosen (statement(c)) If ’U’ is chosen, ‘L’ has to be chosen (statement(c)) K cannot be chosen(statement(d)) and from statement(b); one of M or Q has to be chosen |
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