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# If 6xy = x2y + 9y, what is the value of xy? (1) x = 2 (2) x

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VP
Joined: 28 Dec 2005
Posts: 1499
If 6xy = x2y + 9y, what is the value of xy? (1) x = 2 (2) x [#permalink]

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05 Jan 2009, 19:26
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If 6xy = x2y + 9y, what is the value of xy?

(1) x = –2

(2) x = 3

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SVP
Joined: 07 Nov 2007
Posts: 1759
Location: New York

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05 Jan 2009, 22:47
pmenon wrote:
If 6xy = x2y + 9y, what is the value of xy?

(1) x = –2

(2) x = 3

In the above quesion I am assuming x2y = x^2*y

(1)
x=-2
-12y = 9y+9y --->30y=0
->y=0
xy=0
suffcient
(2)
x=3

18y=9y+9y --> 18y=18y
---> we don't get single solution from this equation
Y can be any thing
not sufficient

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Manager
Joined: 15 Apr 2008
Posts: 159

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06 Jan 2009, 13:17
x2suresh wrote:
pmenon wrote:
If 6xy = x2y + 9y, what is the value of xy?

(1) x = –2

(2) x = 3

In the above quesion I am assuming x2y = x^2*y

(1)
x=-2
-12y = 9y+9y --->30y=0
->y=0
xy=0
suffcient
(2)
x=3

18y=9y+9y --> 18y=18y
---> we don't get single solution from this equation
Y can be any thing
not sufficient

how did you get 9y for X^2y. shouldn't it be 4y
Manager
Joined: 04 Jan 2009
Posts: 234

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06 Jan 2009, 14:39
is there a typo in the original equation?
6xy = x2y+9y
If we treat x2y = 2xy;
4xy=9y=>y=0 or x=9/4.
So problem is solved from question stem itself.
Now if x2y = X^2*y; here is the soltuion:
6xy = x^2*y+9y=(x^2+9)*y
y=0 or
x^2-6x+9=0;
(x-3)^2 = 0 and hence x=3.
If x=3, we still need another equation to solve for y. So, (2) is not enough.
If x=-2,
-12y = 4y+9y=>-12=13 if y=!0. Thus, y=0 and xy can be determined. Hence, (1) is enough.

SVP
Joined: 07 Nov 2007
Posts: 1759
Location: New York

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06 Jan 2009, 15:08
ALD wrote:
x2suresh wrote:
pmenon wrote:
If 6xy = x2y + 9y, what is the value of xy?

(1) x = –2

(2) x = 3

In the above quesion I am assuming x2y = x^2*y

(1)
x=-2
-12y = 9y+9y --->30y=0
->y=0
xy=0
suffcient
(2)
x=3

18y=9y+9y --> 18y=18y
---> we don't get single solution from this equation
Y can be any thing
not sufficient

how did you get 9y for X^2y. shouldn't it be 4y

you are right.. it should be 4y .. type mistake..

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Smiling wins more friends than frowning

VP
Joined: 28 Dec 2005
Posts: 1499

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06 Jan 2009, 16:11
my bad guys, x2y = x^2y.

And yes, A is the correct answer
Intern
Joined: 25 Nov 2008
Posts: 7

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07 Jan 2009, 07:17
The equation: 6xy=x2y+9y
equivalent to y(x-3)^2=0
means: x=3 or y=0
A, x=-2 => y=0
B/ x=3=> insulf to determine y

hence A is the best answer

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: DS: Equations 2   [#permalink] 07 Jan 2009, 07:17
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