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?

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Solution

The correct option is A R
Suffix C as criminal, NC as not criminal.

Case I:

Criminals P Q R S

Assumption T F F F

Result $Q_{C}$ $S_{N C}$ $R_{C}$ $S_{C}$

Q and R are criminal in the result is impossible because only one person committed the crime.

Case II:

Criminals P Q R S

Assumption F T F F

Result $Q_{N C}$ $S_{C}$ $R_{C}$ $S_{C}$

S and R are criminal in the result is impossible because only one person committed the crime.

Case III:

Criminals P Q R S

Assumption F F T F

Result $Q_{N C}$ $S_{N C}$ $R_{N C}$ $S_{C}$

$S_{N C} and S_{C}$ in the result which is contradiction. [S committed crime and same time not committed crime which is contradiction]

Case IV:

Criminals P Q R S

Assumption F F F T

Result $Q_{N C}$ $S_{N C}$ $R_{C}$ $S_{N C}$

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

So, option (a) is correct.

Suggest Corrections

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Criminals	P	Q	R	S
Assumption	T	F	F	F
Result	$Q_{C}$	$S_{N C}$	$R_{C}$	$S_{C}$