If x is not equal to 0 and x^y=1, then which… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Divisibility/Multiples/Factors

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

Answer Choices

Correct answer marked below

I only

II only

III only

I and III only

None

Correct

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Explanation

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Official Explanation

Official

We are told that

x \neq 0

and

x^y = 1

.

We need to check which of the given statements must always be true.

I.

x = 1

This is not necessarily true. For example, if

x = -1

and

y = 2

, then

(-1)^2 = 1

, but

x \neq 1

.

II.

x = 1

and

y = 0

This is also not necessarily true. Using the same counterexample:

x = -1

y = 2

satisfies

x^y = 1

but neither

x = 1

nor

y = 0

.…

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What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.

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