Question

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

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

Hint:

For parity questions, test with small numbers to quickly see possible even/odd outcomes.

Answer 1

The Correct Option is B

Since $x$ and $y$ are odd, $x - z$ is odd - even = odd. $(x - z)^2$ is odd$^2$ = odd. $y \cdot$ odd = odd, so (1) cannot be even — possible error. Check each:
(1) Odd × odd = odd $\rightarrow$ cannot be even — possible false. (2) $y^2$ is odd, odd × odd = odd — possible. Wait, they ask cannot be true. If $y^2$ odd × $(x-z)$ odd = odd — this is true, so (2) could be true. Testing values confirms (2) is correct as cannot be even. Detailed parity check finalises answer.