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

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Director
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02 Nov 2006, 19:04
If x and y are integers greater 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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02 Nov 2006, 19:36
A for me.

from 1. u can see x/y is an integer. Suff.

from 2. u can't get x/y is an integer. e.g. x = 9, y = 6.
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Re: If x and y... [#permalink]

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04 Nov 2006, 11:20
uphillclimb wrote:
If x and y are integers greater than 1, is x a multiple of y?

1)3y^2 +7y = x
2)x^2-x is a multiple of y

I think it's D

1) is fine

2) is x(x-1) is a multiple of y. and x-1 is an integer, so x is a multiple of y.
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Re: If x and y... [#permalink]

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04 Nov 2006, 12:32
uphillclimb wrote:
If x and y are integers greater than 1, is x a multiple of y?

1)3y^2 +7y = x
2)x^2-x is a multiple of y

From S1, 3y^2 +7y = x
Divide bothe sides by y,
3y+7=x/y
hence suff

from s2, x^2-x=ky
x(x-1)=ky
Dividing both sides by y, we get

x/y=k/x-1
right hand side may or maynot be an integer, hence insuff.

Hence A.
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DS: x multiple of y? (gmatprep) [#permalink]

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15 Jan 2007, 15:05
If x and y are integers greater 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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15 Jan 2007, 15:18
If x and y are integers greater than 1 is x a multiple of y?

(1) 3y^2 + 7y = x
(2) x^2 - x is a multiple of y

REPHRASE QUESTION ...is y a factor of x ie : wn deviding x by y it has to give no remainder

from one

3y^2 + 7y = x

ie 3y^2 + 7y / y = intiger ........suff

from two

clearly insuff

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15 Jan 2007, 17:22
mine too A :
first one has y component , if you take y common -->

y * ( 3y +7) = x.
so x has to be multiple of y.

second one has no such relation.
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kiddrek try it ? if X and Y are integers than [#permalink]

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24 Apr 2008, 10:25
if X and Y are integers than 1, is X a multiple of Y ?

(1) 3y² +7y = x
(2) X²- X is a a multiple of Y
OA is :A

Last edited by shobuj on 24 Apr 2008, 22:03, edited 1 time in total.
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Re: if X and Y are integers than [#permalink]

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24 Apr 2008, 22:00
if X and Y are integers greater than 1, is X a multiple of Y ?

(1) 3y² +7y = x
(2) X²- X is a a multiple of Y

i came up with something like this:

statement :1

y=3; 27+21=84
y=2; 12+14=26 so they are multiple

but i cannot

figure out B
can anyone explain it clearly
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Re: if X and Y are integers than [#permalink]

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24 Apr 2008, 22:51
shobuj wrote:
if X and Y are integers greater than 1, is X a multiple of Y ?

(1) 3y² +7y = x
(2) X²- X is a a multiple of Y

i came up with something like this:

statement :1

y=3; 27+21=84
y=2; 12+14=26 so they are multiple

but i cannot

figure out B
can anyone explain it clearly

i solved it this way

1) can be represented as x=y*(3y+7) so sufficient , no need to plug in values
2) can be represted as y*z= x(x-1) since x(x-1) is muliple of y

pick y=3 , z=24 , x=9 , x-1=8 ; x is mulitple of y
pick y=24 , z=3 ,x=9 ,x-1=8 ;x is not multiple of y

so 2 is insuff
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Re: if X and Y are integers than [#permalink]

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25 Apr 2008, 00:21
shobuj wrote:
if X and Y are integers greater than 1, is X a multiple of Y ?

(1) 3y² +7y = x
(2) X²- X is a a multiple of Y

i came up with something like this:

statement :1

y=3; 27+21=84
y=2; 12+14=26 so they are multiple

but i cannot

figure out B
can anyone explain it clearly

2 means that X(X-1) is multiple of Y. In the product X(X-1), there are two case (even three case)
a. X is multiple of Y, but X-1 is not
b. X-1 is multiple of Y, but X is not
c. must be X(X-1) just enough to be multiple of Y

So?
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DS from Gmat Prep - multiple of y [#permalink]

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28 Jan 2009, 14:38
Hi,

I am not sure whether this question has been asked here before,..

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

i) 3y^2 + 7y = x

ii) x^2 - x is a multiple of y

thanks
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Re: DS from Gmat Prep - multiple of y [#permalink]

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28 Jan 2009, 18:48
ongste wrote:
Hi,

I am not sure whether this question has been asked here before,..

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

i) 3y^2 + 7y = x
ii) x^2 - x is a multiple of y

thanks

i) 3y^2 + 7y = x
y (3y + 7) = x
since y is an integer, (3y + 7) is also an integer.
x is (3y + 7) times of y. suff.

ii) x^2 - x = yk
x (x - 1) = yk

Not suff cuz we do not know whether k is an integer. however x, y and (x-1) all are integers, by k = ? do not know.
lets say x = 5, x-1 = 4 and y = 3. k = 20/3. no
x = 5, x-1 = 4 and y = 10. k = 2. yes.

so nsf.

A.
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Re: DS from Gmat Prep - multiple of y [#permalink]

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28 Jan 2009, 18:57
Agree with GT, same approach.
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Re: DS from Gmat Prep - multiple of y [#permalink]

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29 Jan 2009, 18:18
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Re: DS from Gmat Prep - multiple of y [#permalink]

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30 Jan 2009, 08:14
IMO A. Similar approach as GMATTIGER.
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22 Nov 2009, 19:25
what is the OA guys???
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27 Apr 2010, 04:47
If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

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

OA
[Reveal] Spoiler:
A
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27 Apr 2010, 05:10
If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

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

Using 1 we get
x = 3y^2 + 7y
x =y(3y+7)

So clearly from above x is a multiple of y. So 1 is sufficient.

Using 2 we get
x^2 -x = y
y = x(x-1).

So from above we get y is multiple of x and x-1. So x will be a multiple of y in case both x =y=2 we get
2 = 2*(2-1). However not true for other values of x, so 2 is insufficient.

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26 Jul 2011, 19:47
If X and Y are integers greater than 1, is X a multiple of Y?

$$(1) 3Y^2 + 7Y = X$$

$$(2) X^2 - X$$ is a multiple of $$Y.$$

______
Thank you

Last edited by Yalephd on 27 Jul 2011, 05:40, edited 1 time in total.
X and Y   [#permalink] 26 Jul 2011, 19:47

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