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August 11, 2023GATE 2019
| Question 7 |
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 above is true. Who committed the crime?
| P | |
| Q | |
| R | |
| S |
Question 7 Explanation:
⇒ I true: ‘Q’ is Criminal
II, III, IV are false.
II is false: ‘S’ is not criminal.
IV is also false: ‘S’ committed crime.
There is conflict among I, IV now as P, S both should be criminals.
⇒ II true: ‘S’ is criminal.
I, III, IV are false.
IV is false. So, ‘S’ is not criminal.
III is false. So. ‘R’ is criminal.
There is conflict among II, III as S, R both should be criminal.
III is true: Criminal ≠ R.
I, II, IV are false.
I is false. So, ‘Q’ is also not criminal.
II is false. So, ‘S’ is not criminal.
IV is false. So, ‘S’ is not criminal.
Q, R, S are not criminals. So, ‘P’ is criminal.
IV is true: I, II, III are false.
II is false. So, ‘S’ is not criminal.
IV is true. So, ‘S’ is criminal.
I is false. So, ‘Q’ is not criminal.
III is false. So, ‘R’ is criminal.
There is conflict, as R, S both should be criminals.
II, III, IV are false.
II is false: ‘S’ is not criminal.
IV is also false: ‘S’ committed crime.
There is conflict among I, IV now as P, S both should be criminals.
⇒ II true: ‘S’ is criminal.
I, III, IV are false.
IV is false. So, ‘S’ is not criminal.
III is false. So. ‘R’ is criminal.
There is conflict among II, III as S, R both should be criminal.
III is true: Criminal ≠ R.
I, II, IV are false.
I is false. So, ‘Q’ is also not criminal.
II is false. So, ‘S’ is not criminal.
IV is false. So, ‘S’ is not criminal.
Q, R, S are not criminals. So, ‘P’ is criminal.
IV is true: I, II, III are false.
II is false. So, ‘S’ is not criminal.
IV is true. So, ‘S’ is criminal.
I is false. So, ‘Q’ is not criminal.
III is false. So, ‘R’ is criminal.
There is conflict, as R, S both should be criminals.
Correct Answer: C
Question 7 Explanation:
⇒ I true: ‘Q’ is Criminal
II, III, IV are false.
II is false: ‘S’ is not criminal.
IV is also false: ‘S’ committed crime.
There is conflict among I, IV now as P, S both should be criminals.
⇒ II true: ‘S’ is criminal.
I, III, IV are false.
IV is false. So, ‘S’ is not criminal.
III is false. So. ‘R’ is criminal.
There is conflict among II, III as S, R both should be criminal.
III is true: Criminal ≠ R.
I, II, IV are false.
I is false. So, ‘Q’ is also not criminal.
II is false. So, ‘S’ is not criminal.
IV is false. So, ‘S’ is not criminal.
Q, R, S are not criminals. So, ‘P’ is criminal.
IV is true: I, II, III are false.
II is false. So, ‘S’ is not criminal.
IV is true. So, ‘S’ is criminal.
I is false. So, ‘Q’ is not criminal.
III is false. So, ‘R’ is criminal.
There is conflict, as R, S both should be criminals.
II, III, IV are false.
II is false: ‘S’ is not criminal.
IV is also false: ‘S’ committed crime.
There is conflict among I, IV now as P, S both should be criminals.
⇒ II true: ‘S’ is criminal.
I, III, IV are false.
IV is false. So, ‘S’ is not criminal.
III is false. So. ‘R’ is criminal.
There is conflict among II, III as S, R both should be criminal.
III is true: Criminal ≠ R.
I, II, IV are false.
I is false. So, ‘Q’ is also not criminal.
II is false. So, ‘S’ is not criminal.
IV is false. So, ‘S’ is not criminal.
Q, R, S are not criminals. So, ‘P’ is criminal.
IV is true: I, II, III are false.
II is false. So, ‘S’ is not criminal.
IV is true. So, ‘S’ is criminal.
I is false. So, ‘Q’ is not criminal.
III is false. So, ‘R’ is criminal.
There is conflict, as R, S both should be criminals.
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