If $x$ is not equal to $0$ and $x^y=1,$ then which of the following must be true?

If $x$ is not equal to $0$ and $x^y=1,$ then which of the following must be true?

I. $x=1$
II. $x=1$ and $y=0$
III. $x=1$ or $y=0$

A. I only
B. II only
C. III only
D. I and III only
E. None

Answer: E

Source: GMAT Club Tests

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Re: If $x$ is not equal to $0$ and $x^y=1,$ then which of the following must be true?

by Scott@TargetTestPrep » Mon Sep 21, 2020 6:31 am

M7MBA wrote: ↑
Thu Sep 17, 2020 1:09 am
If $x$ is not equal to $0$ and $x^y=1,$ then which of the following must be true?

I. $x=1$
II. $x=1$ and $y=0$
III. $x=1$ or $y=0$

A. I only
B. II only
C. III only
D. I and III only
E. None

Answer: E

Source: GMAT Club Tests

Solution:

If x is 1, then y can be any number. So statement II need not to be true. If x is not 1, then y must be 0. This means statement I need not be true, but statement III must be true.

Answer: C

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