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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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New post 13 Aug 2010, 02:07
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A
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D
E

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Question Stats:

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

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New post 13 Aug 2010, 02:21
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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.

Answer: A.
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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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New post 23 Aug 2016, 20:16
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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

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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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New post 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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New post 20 Apr 2018, 06:39
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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

Answer: A

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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New post 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

Answer: A

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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New post 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

Answer: A

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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New post 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?
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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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