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GATE 2022 EC GA Q.9: solution and answer

GATE 2022 · ECGA Q.9 · 2 marks · MCQ

In a class of five students P, Q, R, S and T, 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: R is telling the truth.

The investigating team had authentic information that S never lies.

Based on the information given above, the person who has copied in the exam is

  1. (A)

    R

  2. (B)

    P

  3. (C)

    Q

  4. (D)

    T

See the question in the paper
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Answer and solution

ANSWER

P copied in the exam. The answer is (B).

Official answer: BSource: Official answer key, GATE 2022 EC (IIT Kharagpur)

  1. S never lies, so S's statement "Only one of us is telling the truth" is true.

  2. S is telling the truth, so S is that one truth-teller. P, Q, R and T are all lying.

  3. R is lying, so the opposite of "P did not copy in the exam" holds: P copied.

  4. Check P: "R has copied in the exam" is false. That fits, because only one student copied and that student is P.

  5. Check Q: "S has copied in the exam" is false. That fits too.

  6. Check T: "R is telling the truth" is false because R lied, which fits. Every statement is consistent with exactly one truth-teller (S) and exactly one copier (P).

  7. Confirm that no other option works. If R, Q or T had copied, P would not have copied, so R's statement "P did not copy in the exam" would be true. R and S would then both be telling the truth, which contradicts S's true statement that only one person is. So the only possible copier is P, option (B).

KEY IDEA

Start with the one statement you know is true: S never lies, so S's claim \"Only one of us is telling the truth\" holds. S is that one person, which means P, Q, R and T are all lying. Negate R's statement and you get P as the copier. Then check that each of the other lies stays false.

WATCH OUT FOR

Students often trust P's direct accusation (\"R has copied\") and pick (A). They forget that S's true statement forces everyone except S to be lying. Another slip is to read \"Only one of us\" as leaving S out. S says \"us\", so S counts, and S is the one truth-teller.

From the GATE 2022 EC paper. Every question of this paper · Download the full paper · All 41 Reasoning questions, with notes

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