Properties of Odd and Even Integers

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?

Accepted Answer

A. $x$ is odd, $z$ is even $\implies (x - z)$ is odd $\implies (x - z)^2$ is odd. $y$ is odd, so $y(x - z)^2 = 	ext{odd} 	imes 	ext{odd} = 	ext{odd}$. Therefore, $y(x - z)^2$ can never be even.

Answer

$y(x - z)^2$ is even

Answer

$y^2(x - z)$ is odd

Answer

$y(x - z)$ is odd

Answer

$z(x - y)^2$ is even

Properties of Odd and Even Integers

Explanation

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