UPSC Prelims 2025 CSAT Paper II · Q79 of 78 Logical Reasoning 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 ✓ UPSC's answer

Why the answer is (d)

• P's statement consists of two parts: 'I did not steal' and 'Q stole it'. If P is guilty, both parts are false, which is consistent with the rule that the guilty person lies.

• Q's statement consists of 'R did not steal' and 'I did not steal'. If Q is guilty, the first part is true (R is innocent) and the second is false. This creates a mix of truth and lie, which is not explicitly ruled out for the guilty party in standard logic puzzles unless specified as 'always lies'.

• R's statement consists of 'I did not steal' and 'I do not know who did it'. If R is guilty, the first part is false. The second part is subjective; a guilty person might claim ignorance. This is also consistent with lying.

• Since the statements do not contain direct logical contradictions that eliminate two suspects definitively (e.g., if P said 'Q stole it' and Q said 'P stole it', we could deduce), and the truth-value pattern (True/False vs False/False) is not strictly defined for the innocent vs guilty in the problem text, multiple scenarios remain logically possible.

• Therefore, without additional constraints on the truthfulness of the innocent suspects (e.g., 'innocent always tells the truth'), the identity of the thief cannot be uniquely determined from the given statements alone.

Why the other options are wrong

(a) P
Option (a) is incorrect because assuming P is guilty does not logically exclude Q or R as the thief based on the provided statements.
(b) Q
Option (b) is incorrect because assuming Q is guilty does not logically exclude P or R as the thief based on the provided statements.
(c) R
Option (c) is incorrect because assuming R is guilty does not logically exclude P or Q as the thief based on the provided statements.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

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