The police arrested four criminals – P, Q, R and S. The criminals knew each…
2019
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?
Answer: B. R — Key idea: Exactly one person is guilty and exactly one of the four statements is true. Test each person as the culprit and count how many statements would be…
- A.
P
- B.
R
- C.
S
- D.
Q
Attempted by 64 students.
Show answer & explanation
Correct answer: B
Key idea: Exactly one person is guilty and exactly one of the four statements is true. Test each person as the culprit and count how many statements would be true.
Assume P committed the crime: P's statement that Q did it is false; Q's statement that S did it is false; R's statement that he did not do it is true; S's statement that Q's statement about S is false is true. This gives two true statements, so this case is impossible.
Assume Q committed the crime: P's statement is true; Q's statement is false; R's statement is true; S's statement is true. That gives three true statements, so this case is impossible.
Assume R committed the crime: P's statement is false; Q's statement is false; R's statement that he did not do it is false; S's statement that Q's statement about S is false is true. Exactly one statement is true, so this case satisfies the condition.
Assume S committed the crime: P's statement is false; Q's statement is true; R's statement is true; S's statement is false. That gives two true statements, so this case is impossible.
Conclusion: R committed the crime, because only in that scenario exactly one statement (S's) is true.
A video solution is available for this question — log in and enroll to watch it.