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

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Thu Sep 17, 2020 1:09 am

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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

Answer: E

Source: GMAT Club Tests

Source: Beat The GMAT — Problem Solving | Thu Sep 17, 2020 1:09 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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