GATE Solved Paper 2017-19 - GATE 2019

6. 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?

  • Option : B
  • Explanation : Case I:
     CriminalsPQRS
     AssumptionFTFF
     ResultQNCSCRCSC

    S and R are criminal in the result is impossible because only one person committed the crime.
    Case II:
     CriminalsPQRS
     AssumptionTFFF
     ResultQCSNCRCSC

    Q and R are criminal in the result is impossible because only one person committed the crime.
    Case III:
     CriminalsPQRS
     AssumptionFFTF
     ResultQNCSNCRNCSC

    SNC and SC in the result which is contradiction. [S committed crime and same time not committed crime which is contradiction]
    Case IV:
     CriminalsPQRS
     AssumptionFFFT
     ResultQNCSNCRCSNC

    R is criminal in the result.
    Hence this case satisfies only one person committed the crime.
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