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GATE Overflow Test Series | Mock GATE | Test 5 | Question: 6

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There is a cat and three girls. The cat is in exactly one of the girl's house and exactly one of the following statements told by the three girls is $\text{TRUE}$.

  • $\text{Girl 1} :$ The cat is in my house.
  • $\text{Girl 2} :$ The cat is not in my house.
  • $\text{Girl 3} :$ The cat is not in Girl $1's$ house.

Which Girl's house contains the cat?

  1. Girl $1$
  2. Girl $2$
  3. Girl $3$
  4. None of them
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Girl $1$ and Girl $3$ are saying contradictory statements and so if one is false other must be true. Let Girl $1$ say the truth. But this will make Girl $2's$ statement also true which will violate the "only one true statement" requirement. So, Girl $1$ can't say the truth and so let Girl $3's$ statement be true. This means Girl $2$ must say lie and that means cat must be in Girl $2's$ house.
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