The police arrested four criminals — P, Q, R, and S. The criminals knew each other. They made the following statements: - P says "Q committed the crime." - Q says "S committed the crime." - R says "I did not do it." - S says "What Q said about me is false". Assume only one of the arrested four committed the crime and only one of the statements made is true. Who committed the crime? A. P B. R C. S D. Q

GATE 2019 · General Aptitude · Verbal Reasoning · medium

Answer: R committed the crime. Under this assumption, only S's statement ('what Q said about me is false') is true, satisfying the condition of exactly one true statement.

1. Case: P committed the crime: P says Q did it -> FALSE (P did it). Q says S did it -> FALSE. R says I did not do it -> TRUE (R is innocent). S says Q's claim about S is false -> TRUE (Q claimed S, which is false; so S's denial is true). That gives 2 true statements. Reject.
2. Case: Q committed the crime: P says Q did it -> TRUE. Q says S did it -> FALSE. R says I did not do it -> TRUE (R is innocent). S says Q's claim is false -> FALSE (Q correctly named S... wait: Q said S did it, but Q is the criminal, so Q's claim is false; S is correctly calling it false -> TRUE). That gives 3 true statements. Reject.
3. Case: R committed the crime: P says Q did it -> FALSE (R did it). Q says S did it -> FALSE. R says I did not do it -> FALSE (R is the criminal; this is a lie). S says Q's claim about S is false -> TRUE (Q said S did it, but actually R did it, so Q's claim IS false; S correctly calls it false). Count of true statements: exactly 1 (S's statement). Accept.
4. Case: S committed the crime (verification): P says Q did it -> FALSE. Q says S did it -> TRUE. R says I did not do it -> TRUE. S says Q's claim is false -> FALSE (Q correctly said S did it, so S's denial is a lie). Count: 2 true statements. Reject.