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# M06-29

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Math Expert
Joined: 02 Sep 2009
Posts: 43361

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15 Sep 2014, 23:28
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35% (medium)

Question Stats:

72% (00:56) correct 28% (01:29) wrong based on 122 sessions

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If $$x$$ and $$y$$ are integers and $$x=\frac{y}{5}+2$$, is $$xy$$ even?

(1) $$5x - 10$$ is even

(2) $$\frac{y}{x}$$ is even
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43361

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15 Sep 2014, 23:28
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Official Solution:

Since $$x$$ and $$y$$ are integers then $$xy$$ will be even if at least one of the multiple is even. From $$x=\frac{y}{5}+2$$ we have that $$y=5x-10$$

(1) $$5x - 10$$ is even. Since $$y=5x-10$$ then $$y=5x-10=\text{even}$$. Sufficient.

(2) $$\frac{y}{x}$$ is even. Given: $$\frac{y}{x}=\text{even}$$, so $$y=x*\text{even}=\text{even}$$. Sufficient.

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Joined: 10 Oct 2016
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16 Dec 2016, 03:12
Bunuel wrote:
Official Solution:

Since $$x$$ and $$y$$ are integers then $$xy$$ will be even if at least one of the multiple is even. From $$x=\frac{y}{5}+2$$ we have that $$y=5x-10$$

(1) $$5x - 10$$ is even. Since $$y=5x-10$$ then $$y=5x-10=\text{even}$$. Sufficient.

(2) $$\frac{y}{x}$$ is even. Given: $$\frac{y}{x}=\text{even}$$, so $$y=x*\text{even}=\text{even}$$. Sufficient.

Hi Bunuel,

What happens if x is 0?
Math Expert
Joined: 02 Sep 2009
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16 Dec 2016, 03:20
uvemdesalinas wrote:
Bunuel wrote:
Official Solution:

Since $$x$$ and $$y$$ are integers then $$xy$$ will be even if at least one of the multiple is even. From $$x=\frac{y}{5}+2$$ we have that $$y=5x-10$$

(1) $$5x - 10$$ is even. Since $$y=5x-10$$ then $$y=5x-10=\text{even}$$. Sufficient.

(2) $$\frac{y}{x}$$ is even. Given: $$\frac{y}{x}=\text{even}$$, so $$y=x*\text{even}=\text{even}$$. Sufficient.

Hi Bunuel,

What happens if x is 0?

For which statement? For the second statement x cannot be 0 because in this case y/x would be undefined not even.
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16 Dec 2016, 05:51
Bunuel wrote:
uvemdesalinas wrote:
Bunuel wrote:
Official Solution:

Since $$x$$ and $$y$$ are integers then $$xy$$ will be even if at least one of the multiple is even. From $$x=\frac{y}{5}+2$$ we have that $$y=5x-10$$

(1) $$5x - 10$$ is even. Since $$y=5x-10$$ then $$y=5x-10=\text{even}$$. Sufficient.

(2) $$\frac{y}{x}$$ is even. Given: $$\frac{y}{x}=\text{even}$$, so $$y=x*\text{even}=\text{even}$$. Sufficient.

Hi Bunuel,

What happens if x is 0?

For which statement? For the second statement x cannot be 0 because in this case y/x would be undefined not even.

For the first one. Y would be even (Y=-10) but X*Y=0
Math Expert
Joined: 02 Sep 2009
Posts: 43361

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16 Dec 2016, 11:29
uvemdesalinas wrote:

For the first one. Y would be even (Y=-10) but X*Y=0

0 is an even integer.
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Joined: 17 Sep 2016
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GMAT 1: 760 Q50 V41
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02 Oct 2017, 09:29
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Hi Team,
In the first statement the answer shows sufficient.
But in case x is Zero then xy will be zero, which is not even.
Hence, how can statement 1 be sufficient?
Math Expert
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02 Oct 2017, 09:51
Psahota wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Hi Team,
In the first statement the answer shows sufficient.
But in case x is Zero then xy will be zero, which is not even.
Hence, how can statement 1 be sufficient?

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

You should brush-up fundamentals before practising questions:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: M06-29   [#permalink] 02 Oct 2017, 09:51
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# M06-29

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