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# If x and y are positive integers, is x a multiple of y?

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Intern
Joined: 06 Jul 2015
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Schools: Erasmus '18
If x and y are positive integers, is x a multiple of y?  [#permalink]

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24 Mar 2017, 19:14
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42% (02:11) correct 58% (02:15) wrong based on 109 sessions

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If x and y are positive integers, is x a multiple of y?

(1) 2x is a multiple of y.
(2) 2(y^2) + y = 2x
Math Expert
Joined: 02 Sep 2009
Posts: 56357
Re: If x and y are positive integers, is x a multiple of y?  [#permalink]

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25 Mar 2017, 03:04
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If x and y are positive integers, is x a multiple of y?

Is $$\frac{x}{y}=integer$$?

(1) 2x is a multiple of y --> $$\frac{2x}{y}=integer$$ --> $$\frac{x}{y}=\frac{integer}{2}$$. If that integer is even then the answer will be YES but if that integer is odd then the answer will be NO (for example, consider x=2 and y=2 AND x=1 and y=2). Not sufficient.

(2) 2(y^2) + y = 2x --> divide by 2y: $$y + \frac{1}{2} = \frac{x}{y}$$. Thus $$\frac{x}{y}=y+ \frac{1}{2}=integer+noninteger=noninteger$$. Sufficient.

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Joined: 05 Mar 2015
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If x and y are positive integers, is x a multiple of y?  [#permalink]

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24 Mar 2017, 19:58
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Omar7235 wrote:
If x and y are positive integers, is x a multiple of y?

(1) 2x is a multiple of y.
(2) 2(y^2) + y = 2x

(1) if x= 4 && y=2 then YES
if x=3 && y=2 then NO

(2) y(2y+1)=2x
two options
(a) if y =odd
then 2y+1 is odd
then odd*odd never equals 2*odd

(2)y=even
then 2y+1 =odd
even*odd=even....satisfying
lets opt some values
if y=2 ,the least value ,then
2(y)*5(2y+1)= 2*5(x)...So we have x=5,y=2
for every y to be even , x must be odd
it is not a multiple..

suff

Ans B
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Joined: 02 Sep 2009
Posts: 56357
Re: If x and y are positive integers, is x a multiple of y?  [#permalink]

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25 Mar 2017, 06:58
Omar7235 wrote:
If x and y are positive integers, is x a multiple of y?

(1) 2x is a multiple of y.
(2) 2(y^2) + y = 2x

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https://gmatclub.com/forum/if-x-and-y-a ... 10085.html
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If x and y are positive integers, is x a multiple of y?  [#permalink]

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26 Mar 2017, 02:31
Bunuel wrote:
(2) 2(y^2) + y = 2x --> divide by 2y: $$y + \frac{1}{2} = \frac{x}{y}$$. Thus $$\frac{x}{y}=y+ \frac{1}{2}=integer+noninteger=noninteger$$. Sufficient.

Dear Bunuel,

You have divided by 2y because it is mentioned that y is positive integer so we are certain that there is possibility to equal Zero.

Am I right?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 56357
Re: If x and y are positive integers, is x a multiple of y?  [#permalink]

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26 Mar 2017, 05:07
Mo2men wrote:
Bunuel wrote:
(2) 2(y^2) + y = 2x --> divide by 2y: $$y + \frac{1}{2} = \frac{x}{y}$$. Thus $$\frac{x}{y}=y+ \frac{1}{2}=integer+noninteger=noninteger$$. Sufficient.

Dear Bunuel,

You have divided by 2y because it is mentioned that y is positive integer so we are certain that there is possibility to equal Zero.

Am I right?

Thanks

_______________
Yes.
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Posts: 1329
Location: Malaysia
If x and y are positive integers, is x a multiple of y?  [#permalink]

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26 Mar 2017, 05:41
Omar7235 wrote:
If x and y are positive integers, is x a multiple of y?

(1) 2x is a multiple of y.
(2) $$2y^2 + y = 2x$$

Dear Omar7235, Could you please quote the source of the question? Thank you.
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Re: If x and y are positive integers, is x a multiple of y?  [#permalink]

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16 Aug 2018, 21:24
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Re: If x and y are positive integers, is x a multiple of y?   [#permalink] 16 Aug 2018, 21:24
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