Reasoning : Logical Reasoning & Analytical Ability

Q 285 / 325

UPSC CSE Prelims 2013

A, B, C, D and E belong to five different cities P, Q, R, S and T (not necessarily in that order). Each one of them comes from a different city. Further it is given that:

  1. B and C do not belong to Q
  2. B and E do not belong to P and R
  3. A and C do not belong to R, S and T
  4. D and E do not belong to Q and T

Which one of the following statements is not correct?

EXPLANATION

Correct Option (4)

The statement "B belongs to S" is not correct.

A systematic deduction of individuals' city affiliations based on the given conditions yields the following:

  • From condition 1 (C does not belong to Q) and condition 3 (C does not belong to R, S, T), it is established that C must belong to P.
  • Given that C belongs to P, and from condition 3 (A does not belong to R, S, T), it is deduced that A cannot belong to P, R, S, or T. Therefore, A must belong to Q.
  • Considering C belongs to P and A belongs to Q, along with condition 2 (E does not belong to P, R) and condition 4 (E does not belong to Q, T), it is determined that E cannot belong to P, Q, R, or T. Consequently, E must belong to S.
  • With C belonging to P, A to Q, and E to S, and from condition 1 (B does not belong to Q) and condition 2 (B does not belong to P, R), it is concluded that B cannot belong to P, Q, R, or S. Hence, B must belong to T.
  • The remaining individual is D, and the only remaining city is R. Therefore, D belongs to R.

Based on these deductions, B belongs to T. Thus, the statement "B belongs to S" is incorrect.

Incorrect Options:

  • C belongs to P:

    This statement is correct. Based on conditions 1 (C does not belong to Q) and 3 (C does not belong to R, S, T), P is the only possible city for C.

  • D belongs to R:

    This statement is correct. After C, A, E, and B are assigned to P, Q, S, and T respectively, D is the only remaining individual and R is the only remaining city. Thus, D belongs to R.

  • A belongs to Q:

    This statement is correct. From condition 3 (A does not belong to R, S, T) and the assignment of C to P (A cannot belong to P), Q is the only remaining possible city for A.