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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?

  1. $P$
  2. $R$
  3. $S$
  4. $Q$
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6 Answers

3 votes
3 votes
Option B-R

⇒ I true: 'Q' is Criminal
II, III, IV are false.
II is false: 'S' is not criminal.
IV is also false: 'S' committed crime.
There is conflict among I, IV now as P, S both should be criminals.
⇒ II true: 'S' is criminal.
I, III, IV are false.
IV is false. So, 'S' is not criminal.
III is false. So. 'R' is criminal.
There is conflict among II, III as S, R both should be criminal.
III is true: Criminal ≠ R.
I, II, IV are false.
I is false. So, 'Q' is also not criminal.
II is false. So, 'S' is not criminal.
IV is false. So, 'S' is not criminal.
Q, R, S are not criminals. So, 'P' is criminal.
IV is true: I, II, III are false.
II is false. So, 'S' is not criminal.
IV is true. So, 'S' is criminal.
I is false. So, 'Q' is not criminal.
III is false. So, 'R' is criminal.
There is conflict, as R, S both should be criminals.
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1 votes
1 votes

Option A :  Suppose P committed crime. In that case

P says “Q committed the crime.” {incorrect as P committed crime}

Q says “S committed the crime.” {incorrect as P committed crime}   -------line1

R says “ I did not do it.”               { correct as P committed crime}

S says “What Q said about me is false”. {we already seen at line1 that  whatever Q  said is incorrect, hence this statement is correct}

Hence as can be seen there are two correct statement. Hence A is not correct option.

Option B :  Suppose R committed crime. In that case

P says “Q committed the crime.” {incorrect as R committed crime.}

Q says “S committed the crime.”{incorrect as R committed crime.} ---------line2

R says “ I did not do it.”              {incorrect as R committed crime.}

S says “What Q said about me is false”. {we already seen at line2 that  whatever Q  said is incorrect, hence this statement is correct }

Hence as can be seen there is only correct statement. Hence B is not correct option.

Option C :  Suppose S committed crime. In that case

P says “Q committed the crime.”{ incorrect as S committed crime}

Q says “S committed the crime.”  {correct as S committed crime}  ------line3

R says “ I did not do it.”                 {correct as S committed crime}

S says “What Q said about me is false”. {as can be seen on line3 whatever Q said is actually true, hence this statement is false/incorrect}

Hence as can be seen there are two correct statement. Hence C is not correct option.

Option C :  Suppose Q committed crime. In that case

P says “Q committed the crime.” {correct as Q committed crime}

Q says “S committed the crime.” {incorrect as Q committed crime} ------line4

R says “ I did not do it.”                {correct as Q committed crime}

S says “What Q said about me is false”.{correct as seen at line 4 whatever Q said is incorrect , hence this statement is correct}

Hence as can be seen there are two correct statement. Hence D is not correct option.

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