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# S99-10

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Math Expert
Joined: 02 Sep 2009
Posts: 54376

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16 Sep 2014, 01:53
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Difficulty:

35% (medium)

Question Stats:

74% (01:12) correct 26% (01:07) wrong based on 54 sessions

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

(1) $$xy$$ is even

(2) $$\frac{x}{y}$$ is even

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Math Expert
Joined: 02 Sep 2009
Posts: 54376

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16 Sep 2014, 01:53
Official Solution:

For the sum of $$x$$ and $$y$$ to be even, the two variables must both be even or both be odd.

Statement (1): INSUFFICIENT. We know that at least one of the variables is even, but we do not know whether they are both even.

Statement (2): INSUFFICIENT. We know that $$x = y \times \text{(some even integer)}$$. Since an even integer multiplied by any other integer is also even, we know that $$x$$ is even. However, we do not know whether $$y$$ is even.

Statements (1) &amp; (2): INSUFFICIENT. Using both statements, we only know that $$x$$ is even. Meanwhile, y could be even, but it does not have to be. As a result, we cannot determine whether the sum of $$x$$ and $$y$$ is even or odd. All of these results can be confirmed by picking numbers.

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Joined: 29 Jul 2012
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15 Aug 2017, 01:11
Shouldn't answer be B, because if we divide x + y with y, we get x/y + 1, we know x/y is even, so even + 1 will be odd and therefore, B should be sufficient to answer the Q.
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15 Aug 2017, 01:16
ravjai81 wrote:
Shouldn't answer be B, because if we divide x + y with y, we get x/y + 1, we know x/y is even, so even + 1 will be odd and therefore, B should be sufficient to answer the Q.

We should find whether x+y is even, not (x + y)/y is even.
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16 Aug 2017, 01:23
If $$x$$ and $$y$$ are positive integers, is $$x + y$$ even?

(1) $$xy$$ is even

Let x = 12 & y =3....Answer to question is N0

Let x = 12 & y =2....Answer to question is Yes

Insufficient

(2) $$\frac{x}{y}$$ is even

Let x = 12 & y =3....Answer to question is N0

Let x = 12 & y =2....Answer to question is Yes

Insufficient

Combining 1 &

Use same examples in both statements. We still can reach a solution

S99-10   [#permalink] 16 Aug 2017, 01:23
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# S99-10

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