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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e  [#permalink]

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Difficulty:   15% (low)

Question Stats: 81% (00:50) correct 19% (01:00) wrong based on 70 sessions

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

1) $$x+y$$ is odd
2) $$x^y$$ is even

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Director  V
Joined: 04 Dec 2015
Posts: 751
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e  [#permalink]

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1
MathRevolution wrote:
If x and y are positive integers, is xy even?

1) $$x+y$$ is odd
2) $$x^y$$ is even

1) $$x+y$$ is odd

$$Even + Odd = Odd$$

Therefore either $$x$$ or $$y$$ has to be even.

Hence $$xy$$ will be Even.

I is Sufficient.

2) $$x^y$$ is even

Even raised to any integer is even.

Odd raised to any integer will be odd.

$$x$$ is even. Therefore $$xy$$ will be even.

II is Sufficient.

Answer (D)...
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Please Press "+1 Kudos" to appreciate. Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e  [#permalink]

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==> If you modify the original condition and the question, in order to get xy=even, it can either be x=even? or y=even?. For con 1), from (x,y)=(odd,even),(even,odd), you always get yes, hence it is sufficient. For con 2), you always get x=even, hence it is yes and sufficient.

The answer is D.
Answer: D
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Intern  B
Joined: 02 Sep 2018
Posts: 24
Re: If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e  [#permalink]

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sashiim20 wrote:
MathRevolution wrote:
If x and y are positive integers, is xy even?

1) $$x+y$$ is odd
2) $$x^y$$ is even

1) $$x+y$$ is odd

$$Even + Odd = Odd$$

Therefore either $$x$$ or $$y$$ has to be even.

Hence $$xy$$ will be Even.

I is Sufficient.

2) $$x^y$$ is even

Even raised to any integer is even.

Odd raised to any integer will be odd.

$$x$$ is even. Therefore $$xy$$ will be even.

II is Sufficient.

Answer (D)...
_________________
Please Press "+1 Kudos" to appreciate. When u r saying that x^y , for any number the answer will be even if x is even and odd if x is odd.

So in this case y can be odd or even .

hence the product xy can be even or odd .
So how come the condition is sufficint
Manager  G
Joined: 21 Feb 2019
Posts: 118
Location: Italy
Re: If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e  [#permalink]

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aaggarwal191 wrote:
sashiim20 wrote:
MathRevolution wrote:
If x and y are positive integers, is xy even?

1) $$x+y$$ is odd
2) $$x^y$$ is even

1) $$x+y$$ is odd

$$Even + Odd = Odd$$

Therefore either $$x$$ or $$y$$ has to be even.

Hence $$xy$$ will be Even.

I is Sufficient.

2) $$x^y$$ is even

Even raised to any integer is even.

Odd raised to any integer will be odd.

$$x$$ is even. Therefore $$xy$$ will be even.

II is Sufficient.

Answer (D)...
_________________
Please Press "+1 Kudos" to appreciate. When u r saying that x^y , for any number the answer will be even if x is even and odd if x is odd.

So in this case y can be odd or even .

hence the product xy can be even or odd .
So how come the condition is sufficint

Even * Even = Even
Even * Odd = Even
Odd * Even = Even
Odd * Odd = Odd

Given: $$x^y$$ even. Hence, $$x$$ is even. If it was odd, it would be: $$odd * odd * odd$$ y times, which would give us an odd number.
Regardless of $$y$$ nature (even or odd), $$xy$$ will be always even.

Hope it's clear.
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MEMENTO AUDERE SEMPER Re: If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e   [#permalink] 02 Apr 2019, 10:16
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# If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e

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