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If x and y are positive integers, is x even?

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Manager
Joined: 07 Jun 2017
Posts: 174
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
If x and y are positive integers, is x even?  [#permalink]

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19 Oct 2017, 05:57
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Difficulty:

45% (medium)

Question Stats:

67% (02:05) correct 33% (01:46) wrong based on 60 sessions

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If $$x$$ and $$y$$ are positive integers, is $$x$$ even?

(1)$$x^y + y^x$$ is even.

(2) $$y^x + 4x$$ is odd.

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Manager
Joined: 21 Jun 2014
Posts: 62
Re: If x and y are positive integers, is x even?  [#permalink]

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19 Oct 2017, 07:32
C
Statement 1 :
Both must be even or both must be odd. X can be even or odd.
Statement 2: y^x has to be odd. This means y is odd but x can be even or odd.

Combining 2 Y^x = odd so x^y has to be odd. This means x cannot be even. Hence C

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Joined: 25 Jul 2017
Posts: 38
Re: If x and y are positive integers, is x even?  [#permalink]

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19 Oct 2017, 08:49

1/ x^y + y^x is even => x^y and y^x are both even or both odd => x may be even or odd => insuff

2/ y^x + 4x is odd. 4x is always even => y^x is odd. x maybe even or odd => insuff

Combine 1 and 2: y^x is odd (2) => x^y is odd, too => x is odd => suff

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Re: If x and y are positive integers, is x even? &nbs [#permalink] 19 Oct 2017, 08:49
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