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Let $x, y$ and $z$ be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

  1. $xyz^2$ is odd.
  2. $(x − y)^2 z$ is even.
  3. $(x + y − z)^2 (x + y)$ is even.
  4. $(x − y) (y + z) (x + y − z)$ is odd
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​​​​​​The difference of two odd integers is always an even number.

The multiplication of even integer with any(even/odd) integer is always an even integer.

Hence 4th option is not possible.

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