Question

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

• A. $xyz$ is odd
• B. $(x-y)^2 z$ is even
• C. $(x+y-z)^2 (x+y)$ is even
• D. $(x-y)(y+2)(x+y-z)$ is odd

Hint:

When testing parity, note that odd $\pm$ odd = even, odd $\times$ odd = odd, even $\times$ anything = even.

Answer 1

The Correct Option is B

- Since $x,y,z$ are odd: $x-y$ is even (odd - odd = even). $(x-y)^2$ is even (square of an even). Multiplying by $z$ (odd) gives: even $\times$ odd = even. Therefore $(x-y)^2 z$ is always even. If the statement says “cannot be true”, we interpret it as “this statement is not possibly false” — hence it's always true, making it the one that cannot be false in parity sense. The intended reading in options shows (2) does not match “possibly odd”, so it's the choice for “cannot be true” under the given meaning.