Question

John lost his pen. The teacher started questioning students about the theft.
Catherine said, "Tom did it". Tom said, "Alex did it" while Martha said, "I did not do it" and Alex said, "Tom is lying
about me".
If only one of the following statements is true, which of the given options is correct?​

Answer 1

Given : Statements :

Catherine said, "Tom did it",

Tom said, "Alex did it"  

Martha said, "I did not do it"

Alex said, "Tom is lying about me".

only one of the statements is true

To Find : who stole pen  ? who is lying

which of the given options is correct ?

Tom stole the pen and Catherine is right

Catherine stole the pen​

Catherine is a liar and Alex is telling the truth

Martha did not do it, and is saying the truth

Solution:

Statements :

Catherine said, "Tom did it",

Tom said, "Alex did it"  

Martha said, "I did not do it"

Alex said, "Tom is lying about me".

only one of the statement is True :

Note that :  Tom said, "Alex did it"    and  Alex said, "Tom is lying about me".

These are contradicting statement and hence one of them is TRUE and another is FALSE

so we get one of the TRUE statement  in these two

Hence Remaining two are FALSE

Catherine said, "Tom did it",   - FALSE => Tom did not steal pen

Martha said, "I did not do it"   - FALSE => Martha Stole pen

As Martha Stole pen hence  Tom said, "Alex did it"   is FALSE

Hence Alex said, "Tom is lying about me".  is TRUE

Final Conclusions :

Alex said, "Tom is lying about me".  is TRUE

Martha Stole pen

Catherine , Martha  , Tom are liars

Out of given options :

Catherine is a liar and Alex is telling the truth

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