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?

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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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

Scott Woodbury-Stewart
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scott@targettestprep.com

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