Properties of Odd and Even Integers

CAT 2001 Slot 1 · Quantitative Ability · Easy · Number Systems

This is an easy Quantitative Ability question from the CAT 2001 Slot 1 paper. It tests Number Systems. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

Answer

Explanation

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

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Properties of Odd and Even Integers

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