- A. P
- B. R
- C. Q
- D. Cannot be concluded
Answer: A
Explanation
The problem states that only one person is guilty, which implies that only one person is lying (the guilty one). The innocent ones tell the truth.
Let’s analyze each suspect’s statements and assume they are the liar:
1. **Case 1: Assume P is the thief (P is lying).**
* If P is lying, then both statements by P are false: “I did not steal” is false (meaning P stole it), and “Q stole it” is false (meaning Q did not steal it). This is consistent with P being the thief.
* If P stole it, then Q and R are innocent and must be telling the truth.
* Check Q’s statements: “R did not steal” (True, as R is innocent). “I did not steal” (True, as Q is innocent). Q is telling the truth.
* Check R’s statements: “I did not steal” (True, as R is innocent). “I do not know who did it” (True, as R is innocent). R is telling the truth.
* This scenario is consistent: P is the thief and is the only liar.
2. **Case 2: Assume Q is the thief (Q is lying).**
* If Q is lying, then both statements by Q are false: “R did not steal” is false (meaning R stole it), and “I did not steal” is false (meaning Q stole it). This implies both Q and R stole the phone, which contradicts the condition that *only one* person is guilty. So, Q cannot be the thief.
3. **Case 3: Assume R is the thief (R is lying).**
* If R is lying, then “I did not steal” is false (meaning R stole it). “I do not know who did it” could be true or false, but the first statement is enough.
* If R stole it, then P and Q are innocent and must be telling the truth.
* Check P’s statements: “I did not steal” (True, as P is innocent). “Q stole it” (False, as Q is innocent). This means P is lying, but we assumed R is the *only* liar. This is a contradiction. So, R cannot be the thief.
Since only Case 1 leads to a consistent scenario, P stole the mobile phone. This problem requires careful logical deduction and case analysis, typical of CSAT reasoning questions.