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

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

by M7MBA » Thu Sep 17, 2020 1:09 am

00:00

A

B

C

D

E

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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

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

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.