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GATE CS 2019 · General Aptitude

Question 6

MCQPrinted as GA Q.62 marksWrong answer: −2/3Medium (estimate)

Question

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?

Choose one option
Official answer and solution
Official answer
B
From
Official GATE 2019 answer key

Solution

Identify contradictory statement pairs to deduce which statement must be the single true statement.

Let us examine the statements made by the four individuals:

  • P: "Q committed the crime."
  • Q: "S committed the crime."
  • R: "I did not do it."
  • S: "What Q said about me is false."

Notice that Q asserts that S committed the crime, while S asserts that Q's statement is false. These two statements are exact logical contradictions. Therefore, exactly one of Q and S must be telling the truth, and the other must be lying.

We are given that exactly one of the four statements is true. Because the single true statement must be either Q or S, all other statements must be false. In particular:

  1. P's statement is FALSE: Q did not commit the crime.
  2. R's statement is FALSE: "I did not do it" is false, which means R committed the crime!

Let us verify consistency when R committed the crime:

  • P: False (since Q did not do it).
  • Q: False (since S did not do it; R did).
  • R: False (since R did it).
  • S: True (Q said S did it, which is indeed false).

Exactly one person (S) spoke the truth, and exactly one person (R) committed the crime. Hence, R committed the crime.

Final answer

B

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2019 Computer Science and Information Technology (CS)
Question
6 of 65, printed as GA Q.6
Section
General Aptitude

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