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

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

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New post 16 Dec 2019, 01:51
1
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:26) correct 35% (02:11) wrong based on 25 sessions

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Re: If x is a positive integer and x^y = 1, what is the value of x?  [#permalink]

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New post 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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Re: If x is a positive integer and x^y = 1, what is the value of x?  [#permalink]

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New post 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

Answer: D

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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