Properties of Numbers - Parity of Exponents

CAT 1998 Slot 1 · QA · Easy · Number System

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$n^3$ is odd. Which of the following statement(s) is(are) true?

I. $n$ is odd. II. $n^2$ is odd. III. $n^2$ is even.

A.
I only
B.
II only
C.
I and II
D.
I and III

Answer

C

Explanation

If $n^3$ is odd, then $n$ must be an odd integer. Since $n$ is odd, $n^2$ is also odd. Thus, both statements I and II are true.

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