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# M15-23

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Senior Manager
Joined: 08 Jun 2015
Posts: 365

Kudos [?]: 27 [0], given: 106

Location: India
GMAT 1: 640 Q48 V29

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27 Jan 2017, 06:54
Good catch ... thanks for posting this question.
_________________

" The few , the fearless "

Kudos [?]: 27 [0], given: 106

Intern
Joined: 11 Aug 2017
Posts: 2

Kudos [?]: 0 [0], given: 2

Location: India

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15 Dec 2017, 08:41
Bunuel wrote:
Official Solution:

(1) $$x$$ and $$y$$ are even integers. Clearly insufficient, consider $$x=y=0$$ for an YES answer and $$x=2$$ and $$y=0$$ for a NO answer.

(2) $$x + y$$ is divisible by $$8$$. Now, $$x^2 - y^2=(x+y)(x-y)$$, if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that $$x$$ and $$y$$ are integers. If $$x=4.8$$ and $$y=3.2$$, $$x+y$$ is divisible by $$8$$, BUT $$x^2 - y^2$$ is not. Not sufficient.

(1)+(2) $$x$$ and $$y$$ integers. $$x+y$$ divisible by 8. Hence $$(x+y)(x-y)$$ is divisible by $$8$$. Sufficient.

What if X-Y is Negative? We know they're even integers but don't know if X>Y or not.

Kudos [?]: 0 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139638 [0], given: 12794

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15 Dec 2017, 08:43
sambha wrote:
Bunuel wrote:
Official Solution:

(1) $$x$$ and $$y$$ are even integers. Clearly insufficient, consider $$x=y=0$$ for an YES answer and $$x=2$$ and $$y=0$$ for a NO answer.

(2) $$x + y$$ is divisible by $$8$$. Now, $$x^2 - y^2=(x+y)(x-y)$$, if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that $$x$$ and $$y$$ are integers. If $$x=4.8$$ and $$y=3.2$$, $$x+y$$ is divisible by $$8$$, BUT $$x^2 - y^2$$ is not. Not sufficient.

(1)+(2) $$x$$ and $$y$$ integers. $$x+y$$ divisible by 8. Hence $$(x+y)(x-y)$$ is divisible by $$8$$. Sufficient.

What if X-Y is Negative? We know they're even integers but don't know if X>Y or not.

Can't a negative integer be divisible by 8? For example, -8 IS divisible by 8.
_________________

Kudos [?]: 139638 [0], given: 12794

Re: M15-23   [#permalink] 15 Dec 2017, 08:43

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# M15-23

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