GATE | GATE CS 2019 | Question 4

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.

• 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.

• 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.
• 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.

• 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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