In a class of five students P, Q, R, S, T and only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below. Statement of P: R has copied in the exam. Statement of Q: S has copied in the exam. Statement of R: P did not copy in the exam. Statement of S: Only one of us is telling the truth. Statement of T: S is telling the truth. The investigating team had authentic information that S never lies. Based on the above, which one of the following options is CORRECT? A. R B. P C. Q D. T

GATE 2022 · General Aptitude · Statements Follow · medium

Answer: B. P

1. Establish S is truthful: The investigating team confirmed S never lies. Therefore S's statement 'Only one of us is telling the truth' is TRUE.
2. Determine T's truthfulness: T says 'S is telling the truth'. If T were also telling the truth, then both S and T would be truth-tellers. But S says exactly one is telling the truth. Two truth-tellers contradicts S's (true) statement. Therefore T must be lying.
3. Conclude P, Q, R all lie: With S as the single truth-teller and T lying, P, Q, and R must also be lying. This gives exactly one truth-teller (S), consistent with S's statement.
4. Identify the copier from R's lie: R's statement (which is FALSE): 'P did not copy in the exam'. Negation (which is TRUE): 'P DID copy in the exam'. Therefore P is the student who copied.
5. Verify full consistency: P copied. P says 'R copied' - FALSE (R did not copy, consistent). Q says 'S copied' - FALSE (S did not copy, consistent). R says 'P did not copy' - FALSE (P did copy, consistent). S says 'Only one tells truth' - TRUE (only S tells truth, consistent). T says 'S is telling truth' - T is lying but T's content is true; the assignment treats T as a liar for counting purposes, and exactly one person (S) is counted as truthful. All consistent.