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# If x and y are integers great than 1, is x a multiple of y?

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Intern
Joined: 01 Jul 2010
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Schools: LBS, Harvard, Booth, Stanford, ISB, NTU
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If x and y are integers great than 1, is x a multiple of y?  [#permalink]

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13 Aug 2010, 03:07
2
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Difficulty:

65% (hard)

Question Stats:

56% (01:53) correct 44% (02:03) wrong based on 82 sessions

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If x and y are integers great than 1, is x a multiple of y?

(1) $$3y^2+7y=x$$

(2) $$x^2-x$$ is a multiple of y

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Prep1.jpg [ 103.95 KiB | Viewed 2319 times ]
Math Expert
Joined: 02 Sep 2009
Posts: 50059
Re: If x and y are integers great than 1, is x a multiple of y?  [#permalink]

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13 Aug 2010, 03:21
3
1
If x and y are integers great than 1, is x a multiple of y?

Question: is $$x=ny$$?

(1) $$3y^2+7y=x$$ --> $$y(3y+7)=x$$ --> as $$3y+7$$ is an integer, so $$x$$ is a multiple of $$y$$. Sufficient.

(2) $$x^2-x$$ is a multiple of y --> $$x^2-x=my$$ --> $$x(x-1)=my$$ --> $$x$$ can be multiple of $$y$$ ($$x=2$$ and $$y=2$$) OR $$x-1$$ can be multiple of $$y$$ ($$x=3$$ and $$y=2$$) or their product can be multiple of $$y$$ ($$x=3$$ and $$y=6$$). Not sufficient.

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Re: If x and y are integers great than 1, is x a multiple of y?  [#permalink]

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14 Aug 2010, 09:03
I also fell for D. But thanks to Bunel's explanation, i spotted the detail.
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Re: If x and y are integers great than 1, is x a multiple of y?  [#permalink]

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23 Aug 2016, 21:16
jananijayakumar wrote:
If x and y are integers great than 1, is x a multiple of y?

(1) $$3y^2+7y=x$$

(2) $$x^2-x$$ is a multiple of y

Attachment:
The attachment Prep1.jpg is no longer available

Please find the solution as mentioned in attachment
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File comment: www.GMATinsight.com

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Re: If x and y are integers great than 1, is x a multiple of y?  [#permalink]

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20 Apr 2018, 07:39
Top Contributor
jananijayakumar wrote:
If x and y are integers great than 1, is x a multiple of y?

(1) $$3y^2+7y=x$$

(2) $$x^2-x$$ is a multiple of y

Attachment:
Prep1.jpg

Target question: Is x a multiple of y?
Asking whether x is a multiple of y is the same as asking whether x = (y)(some integer)
For example, 12 is a multiple of 3 because 12 = (3)(4)
So, let's rephrase the question as...
REPHRASED target question: Does x = (y)(some integer)?

Statement 1: 3y² + 7y = x
Factor to get x = y(3y + 7)
If y is an integer, then (3y + 7) must be an integer
In other words: x = y(some integer)
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x² - x is a multiple of y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 4 and y = 2 (this satisfies statement 2 because x² - x = 12, and 12 is a multiple of 2). In this case, x IS a multiple of y
Case b: x = 5 and y = 2 (this satisfies statement 2 because x² - x = 20, and 20 is a multiple of 2). In this case, x is NOT a multiple of y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Re: If x and y are integers great than 1, is x a multiple of y? &nbs [#permalink] 20 Apr 2018, 07:39
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