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# If x is a positive integer and x^y = 1, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 61195
If x is a positive integer and x^y = 1, what is the value of x?  [#permalink]

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16 Dec 2019, 01:51
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If x is a positive integer and $$x^y = 1$$, what is the value of x?

(1) $$y^x = 2$$

(2) y is a positive integer

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Joined: 08 Aug 2014
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GMAT Date: 10-02-2015
Re: If x is a positive integer and x^y = 1, what is the value of x?  [#permalink]

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16 Dec 2019, 03:15
We have been told x is a positive integer...

Statement 1: y^x =2
The only condition for this expression to equal 2, is if y=2 and x= 1

From this, we can deduce that in the equation x^y= 1, x has to be 1.

Statement 1 is sufficient.

Statement 2: y is a positive integer

Because we were earlier told that x is a positive integer, then x has to be 1.
Statement 2 is sufficient..

Option D is the answer.

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Joined: 11 Sep 2015
Posts: 4318
Re: If x is a positive integer and x^y = 1, what is the value of x?  [#permalink]

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16 Dec 2019, 06:11
Top Contributor
Bunuel wrote:
If x is a positive integer and $$x^y = 1$$, what is the value of x?

(1) $$y^x = 2$$

(2) y is a positive integer

Given: x is a positive integer and $$x^y = 1$$
From the given information, there are exactly two possible cases:
case i: x = 1 and y = any value
case ii: x = any positive integer and y = 0

Target question: What is the value of x?

Statement 1: $$y^x = 2$$
This rules out case ii (since $$0^x=0$$), which means case i must be true
If case i is true, then x = 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y is a positive integer
This rules out case ii (since 0 is not a positive integer), which means case i must be true
If case i is true, then x = 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: If x is a positive integer and x^y = 1, what is the value of x?   [#permalink] 16 Dec 2019, 06:11
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# If x is a positive integer and x^y = 1, what is the value of x?

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