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. Th…

Question

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 answer)

Correct Answer

Option D — Cannot be concluded

Detailed Solution & Explanation

The correct answer is Cannot be concluded.

Key Points

• If P stole: P's statement "I didn't steal" = false, "Q stole" = false.
• Q's statements both become "R didn't steal" (true) and "I didn't steal" (true — Q didn't steal).
• R: "I didn't steal" (true).
• P has 1 false statement — possible for a guilty person.
• If Q stole: P says "Q stole" = true, but a guilty person should have at least one false statement.
• Q says "I didn't steal" = false ✓.
• If R stole: R says "I don't know who did it" — but R knows they did it, so false.
• However multiple consistent interpretations exist.
• Answer: Cannot be concluded.