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If x is not equal to 0 and x^y=1, then which of...

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by BTGmoderatorLU » Tue Dec 19, 2017 11:01 am
If x is not equal to 0 and x^y=1, then whcih 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

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
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by [email protected] » Tue Dec 19, 2017 12:22 pm
Hi LUANDATO,

We're told that X is NOT equal to 0 and X^Y=1. We're asked which of the following MUST be true. When a question asks what MUST be true, what it's really asking is "which of the following is ALWAYS TRUE no matter how many different examples you can come up with."

This question is a great 'concept question', meaning that you don't have to do much math to answer it IF you recognize the concepts involved. Since X cannot be 0, there are three possible ways for X^Y to equal 1.
1) X=1 and Y could be ANY value.
2) Y=0 and X could be any value except 0.
3) X = -1 and Y is an EVEN integer.

Since any of these situations will lead to a value of 1, none of them individually must be true. The three Roman Numerals are:

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

None of these 3 options is always true.

Final Answer: E

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Rich
Contact Rich at [email protected]
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by Gaylyder » Sun Nov 10, 2019 10:36 pm
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