Read the following information carefully and answer the question. There are five men A, B, C, D and E and six women P, Q, R, S, T and U. A, B and R are advocates; C, D, P, Q and S are doctors; and the remaining persons E, T and U are teachers. Some teams are to be selected from these eleven persons subject to the following conditions: (1) A, P and U have to be together in any team in which any one of them appears. (2) B cannot be in a team with D or R. (3) E and Q have to be together in any team in which either of them appears. (4) C and T have to be together in any team in which either of them appears. (5) D and P cannot be together. (6) C cannot be with Q. If a team is to consist of exactly two male advocates, two lady doctors and one teacher, who must be the members of the team?

Difficulty: Hard

Correct Answer: A, B, P, U, S

Explanation:


Introduction / Context:
This is a logical team-selection puzzle involving multiple roles and several constraints. You have eleven people divided into men and women, advocates, doctors and teachers. From these, you must form a team of five with a specific composition: two male advocates, two lady doctors and one teacher. Additionally, there are grouping and incompatibility conditions about who must or must not appear together. The aim is to identify the only combination that satisfies all conditions simultaneously.


Given Data / Assumptions:

    - Men: A, B, C, D, E.- Women: P, Q, R, S, T, U.- Advocates: A, B (male advocates) and R (lady advocate).- Doctors: C, D (male doctors) and P, Q, S (lady doctors).- Teachers: E (male teacher), T and U (lady teachers).- Team requirement: exactly two male advocates, two lady doctors and one teacher.- Conditions: A, P and U together; B cannot be with D or R; E and Q together; C and T together; D and P cannot go together; C cannot go with Q.


Concept / Approach:
First, satisfy the composition requirement. Two male advocates must come from A and B, because R is a female advocate and cannot count as a male advocate. Two lady doctors must be selected from P, Q and S. One teacher must be chosen from E, T and U. After that, apply the conditions that bind certain people together or forbid their co-presence, gradually eliminating impossible teams. The objective is to find the unique set that fits both the composition and all constraints.


Step-by-Step Solution:
Step 1: Since the team should consist of two male advocates, we must include both A and B.Step 2: Because A is included, and the condition says A, P and U must be together, we must also include P (lady doctor) and U (teacher). This already gives us one lady doctor (P) and the teacher (U).Step 3: Now the team has A (male advocate), B (male advocate), P (lady doctor) and U (teacher). We still need one more lady doctor, which must be chosen from Q or S.Step 4: Consider choosing Q. If Q is included, the condition that E and Q have to be together requires E also to be in the team, but there is only one teacher slot, already occupied by U. Including E would exceed the required team size of five and violate the composition (teachers would then be two). So Q cannot be in the team.Step 5: Therefore, the second lady doctor must be S. This gives the team: A, B, P, S and U.Step 6: Check all constraints: A, P and U are indeed together. B is not with D or R, because neither D nor R is in the team. E and Q are both absent, so their togetherness condition is not violated. C and T are absent, so their togetherness condition is irrelevant. D and P are not together, since D is absent. C is not with Q, as both are absent. Every condition is satisfied.


Verification / Alternative check:
Compare the derived team A, B, P, S and U with the given options. Option D exactly lists A, B, P, U and S. Option B proposes including Q, which we showed is impossible because it would force inclusion of E and would break the team composition. Options A and C contain either R or E or other combinations that do not match the required role structure of two male advocates, two lady doctors and one teacher while simultaneously satisfying all constraints. Thus, option D is the only valid team.


Why Other Options Are Wrong:
Option A includes R, a female advocate, not a male advocate, and fails to include B, so it does not have two male advocates. Option B includes Q, which forces E as well and breaks both composition and size requirements. Option C includes E, Q and R and does not contain both A and B as required male advocates. Only option D meets both the role counts and the conditional constraints.


Common Pitfalls:
Many candidates forget that A, P and U always come together, so including A without P or U is invalid. Others ignore the extra conditions such as E and Q always together or C and T always together. A structured approach that first fixes the role counts, then applies inclusion and exclusion constraints step by step, makes such puzzles far easier to manage.


Final Answer:
The required team consists of A, B, P, U and S, which corresponds to option A, B, P, U, S.

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