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?
(A) P
(B) R
(C) S
(D) Q
Answer: (B)
Explanation: Given that only one person committed the crime and only one given statement is correct.
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When P is correct and Q, R, S are false: it implies,
Q committed crime, S did not commit crime, R committed crime, S committed crime.
This situation is impossible.
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When Q is correct and P, R, S are false: it implies,
Q did not commit crime, S committed crime, R committed crime, S committed crime.
This situation is impossible.
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When R is correct and P, Q, S are false: it implies,
Q did not commit crime, S did not commit crime, R did not commit crime, S committed crime.
This situation is impossible.
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When S is correct and P, Q, R are false: it implies,
Q did not commit crime, S did not commit crime, R committed crime, S did not commit crime.
This situation is possible means R has committed crime.
So, option (B) is correct.
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