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UPSC CSE 2025 · PYQ · Logical Reasoning / Truth-Tellers · medium

A mobile phone has been stolen. There are 3 suspects P, Q and R. They were questioned knowing that only one of them is guilty. Their responses are as follows: P: I did not steal. Q stole it. Q: R did not steal. I did not steal. R: I did not steal. I do not know who did it. Who stole the mobile phone?

  1. A.P
  2. B.Q
  3. C.R
  4. D.Cannot be concluded✓ Correct

Explanation

Test each suspect being guilty. If P is guilty: P says 'I did not steal' (false) and 'Q stole it' (false) — both false, consistent if P always lies. Q says 'R did not steal' (true) and 'I did not steal' (true) — both true. R says 'I did not steal' (true) and 'I don't know who did it' — could be true. Consistent. If Q is guilty: P says 'I did not steal' (true), 'Q stole it' (true) — both true. Q says 'R did not steal' (true), 'I did not steal' (false) — mixed. R says both true. Without rule on truth-telling pattern, multiple scenarios possible. If R is guilty: P says both 'I did not steal' (true) and 'Q stole it' (false). Q says 'R did not steal' (false), 'I did not steal' (true). Inconsistencies in all cases without a rule. Since no clear constraint on who always lies/tells truth, the guilty cannot be uniquely determined. Answer is (d) Cannot be concluded.
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