UPSC Prelims 2013·CSAT·Logical Reasoning·Arrangement and Puzzles

A, B, C, D and E belong to five different cities P, Q, R, Sand T (not necessarily in that order). Each one of them comes from a different city. Further it is given that: 1. Band C do not belong to Q. 2. Band E do not belong to P and R. 3. A and C do not belong to R, Sand T. 4. D and E do not belong to Q and T. Which one of the following statements is not correct?

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  1. AC belongs to P
  2. BD belongs to R
  3. CA belongs to Q
  4. DB belongs to SCorrect

Explanation

Let's deduce the city for each person step-by-step: 1. From clue 3 (A and C do not belong to R, S and T) and clue 1 (C does not belong to Q): C cannot be R, S, T, or Q. The only remaining city for C is P. So, C belongs to P. 2. From clue 2 (B and E do not belong to P and R) and clue 4 (D and E do not belong to Q and T): E cannot be P, R, Q, or T. The only remaining city for E is S. So, E belongs to S. Now we know: C belongs to P E belongs to S Since each person comes from a different city, P and S are now taken. 3. From clue 3 (A does not belong to R, S and T): A cannot be R, S, T. Remaining possibilities for A are P, Q. Since C belongs to P, A cannot belong to P. So, A belongs to Q. 4. From clue 4 (D does not belong to Q and T): D cannot be Q, T. Remaining possibilities for D are P, R, S. Since C belongs to P and E belongs to S, D cannot be P or S. So, D belongs to R. 5. Now, the only person left is B and the only city left is T. Let's verify this with B's clues: From clue 1 (B does not belong to Q) and clue 2 (B does not belong to P and R): B cannot be Q, P, R. Remaining possibilities for B are S, T. Since E belongs to S, B cannot belong to S. So, B belongs to T. Summary of deductions: A belongs to Q B belongs to T C belongs to P D belongs to R E belongs to S Now let's check the given options: A) C belongs to P - This is correct. B) D belongs to R - This is correct. C) A belongs to Q - This is correct. D) B belongs to S - This is incorrect, as B belongs to T. The question asks for the statement that is NOT correct. Therefore, option D is the answer.
Logical Reasoning: A, B, C, D and E belong to five different cities P, Q, R, Sand T (not necessarily in that order). Each one of them comes

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