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

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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, 02:07
1
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Difficulty:

75% (hard)

Question Stats:

51% (02:02) correct 49% (02:13) wrong based on 184 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 3396 times ]
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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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13 Aug 2010, 02:21
4
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, 08:03
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, 20:16
2
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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Re: If x and y are integers great than 1, is x a multiple of y?  [#permalink]

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20 Apr 2018, 06:39
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?  [#permalink]

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15 Sep 2019, 05:55
GMATPrepNow wrote:
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

If 20 is a multiple of 2 then how X is not a multiple of Y?
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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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15 Sep 2019, 06:24
Top Contributor
ypetrunina wrote:
GMATPrepNow wrote:
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

If 20 is a multiple of 2 then how X is not a multiple of Y?

When x = 5 and y = 2, we see that x² - x = 20, and 20 is a multiple of 2
In other words, x² - x is a multiple of 2
However, the target question asks b]Is x a multiple of y?[/b](not Is x² - x a multiple of y?)

If x = 5 and y = 2, then x is NOT a multiple of y

Cheers,
Brent
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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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07 Nov 2019, 00:15
Would this be a valid way of looking at it?

Target Question: is x = y*I (where I is an integer)

Statement I: same as all of your solutions above - SUFF.

Statement II :

x^2 - x = y*I (where I is some integer)
x (x - 1) = y*I
x = (y*I)/(x-1)
x = y* (I/(x-1))

Now, we know (x-1) is definitely an integer and so is I, but we have no idea whether the ratio of I and (x-1) is ALSO an integer. Thus, statement II is INSUFF.

Thoughts?
Re: If x and y are integers great than 1, is x a multiple of y?   [#permalink] 07 Nov 2019, 00:15
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