P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order). The rank of P is 4, the rank of Q is not 5, the rank of R is 1, the rank of S is not 2, the rank of T is not 3. Then which of the following is/are correct? I. If the rank of S is 3, then that of T is 2. II. If the rank of Q is 3, then that of T is 5. Select the answer using the code given below.

This question is a classic constraint satisfaction problem commonly found in the Analytical Reasoning section of the civil services aptitude test. To solve it, we evaluate the definite assignments and systematically apply the negative constraints to the remaining variables.

Initial Analysis: According to the premises, the available ranks are 1 to 5.

• Fixed Assignments: R = 1 and P = 4.
• The remaining ranks to be filled are 2, 3, and 5.
• The remaining persons to be ranked are Q, S, and T.
• Negative Constraints: Q ≠ 5, S ≠ 2, and T ≠ 3.

Evaluating Statement I: If the rank of S is 3, then that of T is 2.

• Assume S = 3. The available ranks for Q and T are now 2 and 5.
• Given the constraint Q ≠ 5, Q must take rank 2.
• Consequently, T must take the only remaining rank, which is 5.
• Statement I claims T is 2, which mathematically contradicts our deduction (T is 5). Thus, Statement I is incorrect.

Evaluating Statement II: If the rank of Q is 3, then that of T is 5.

• Assume Q = 3. The available ranks for S and T are now 2 and 5.
• Given the constraint S ≠ 2, S must take rank 5.
• Consequently, T must take the only remaining rank, which is 2.
• Statement II claims T is 5, which contradicts our deduction (T is 2). Thus, Statement II is incorrect.

Option Analysis:

• Option A (I only): Incorrect, because assuming S = 3 logically results in T = 5, not 2.
• Option B (II only): Incorrect, because assuming Q = 3 logically results in T = 2, not 5.
• Option C (Both I and II): Incorrect, as both conditional statements are proven invalid.
• Option D (Neither I nor II): Correct, since neither statement holds true under the given constraints.

Takeaway: When solving negative constraint puzzles, mapping variables on a 'Possibility Matrix' helps eliminate choices efficiently and prevents overlapping logic errors.