Parity of Odd Integer Operations

CAT 2000 Slot 1 · Quantitative Ability · Easy · Number Systems

This is an easy Quantitative Ability question from the CAT 2000 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, that are odd and positive. Which one of the following statements cannot be true?

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

Answer

Explanation

Since $x$ and $y$ are odd, $(x - y)$ is even. Product of an even number with any integer is always even. Therefore, $(x - y)(y + z)(x + y - z)$ must be even, so it can NEVER be odd.

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Parity of Odd Integer Operations

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