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Senior Manager  S
Joined: 08 Jun 2015
Posts: 420
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33

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Good catch ... thanks for posting this question.
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Intern  B
Joined: 11 Aug 2017
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Schools: AGSM '21 (A\$)
GMAT 1: 710 Q48 V40 GPA: 3.8

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58453

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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.
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what if Y>X?
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Joined: 12 Feb 2018
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Bunuel wrote:
Senthil7 wrote:
I think this is a poor-quality question and I don't agree with the explanation. if x+y is a multiple of 8 as stated by statement 2, then x^2 - y^2 is divisible by 8 as well since the 8 divides the (x+y) in (x+y)(x-y) form of the expression. Why is this logic wrong , this is not addressed in this thread.

Even if x+y is a multiple of 8, (x+y)(x-y) might not be an integer. Divisibility is applied to integers on the GMAT.

Hi bunuel,
By this you mean to say that "only an integer value is divisible by an other integer value" even though the non integer value when divided with an integer gives a remainder which equals zero ?
Please give an assertion to this
Math Expert V
Joined: 02 Sep 2009
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PreethiVishwanathan wrote:
Bunuel wrote:
Senthil7 wrote:
I think this is a poor-quality question and I don't agree with the explanation. if x+y is a multiple of 8 as stated by statement 2, then x^2 - y^2 is divisible by 8 as well since the 8 divides the (x+y) in (x+y)(x-y) form of the expression. Why is this logic wrong , this is not addressed in this thread.

Even if x+y is a multiple of 8, (x+y)(x-y) might not be an integer. Divisibility is applied to integers on the GMAT.

Hi bunuel,
By this you mean to say that "only an integer value is divisible by an other integer value" even though the non integer value when divided with an integer gives a remainder which equals zero ?
Please give an assertion to this

Yes. x is divisible by y means that x is integer, y is an integer and x/y is an integer.
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Joined: 09 Oct 2016
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I think this the explanation isn't clear enough, please elaborate. Even if x and y are not integers x^2-y^2 could still be written as (x+y)(x-y) and since x+y is divisible by 8 (x+y)(x-y) should be divisible by 8.
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Joined: 02 Sep 2009
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Anishajha wrote:
I think this the explanation isn't clear enough, please elaborate. Even if x and y are not integers x^2-y^2 could still be written as (x+y)(x-y) and since x+y is divisible by 8 (x+y)(x-y) should be divisible by 8.

a is divisible by b means that a is integer, b is an integer and a/b is an integer. In the case you mention we cannot be sure that (x+y)(x-y) and (x+y)(x-y)/8 are integers.
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I think this the explanation isn't clear enough, please elaborate.
Intern  B
Joined: 05 Sep 2017
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I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
Director  G
Joined: 22 Nov 2018
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GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Show Tags

I think this is a high-quality question and I agree with explanation.
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Intern  B
Joined: 24 Feb 2014
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Location: United States (GA)
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I think this is a high-quality question and I agree with explanation. Wow !! Eye opener.. Re M15-23   [#permalink] 25 Sep 2019, 18:28

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