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

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

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New post 19 Oct 2017, 05:57
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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.
[Reveal] Spoiler: OA

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Re: If x and y are positive integers, is x even? [#permalink]

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New post 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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Re: If x and y are positive integers, is x even? [#permalink]

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New post 19 Oct 2017, 08:49
Answer is C.

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

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