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# If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin

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Manager
Joined: 13 Jun 2005
Posts: 246
Location: Haverhill, MA
If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin  [#permalink]

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Updated on: 07 Nov 2013, 08:37
4
7
00:00

Difficulty:

35% (medium)

Question Stats:

78% (01:28) correct 22% (01:53) wrong based on 303 sessions

### HideShow timer Statistics

If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be y in terms of x?

I. 1/2x
II. -2/x
III. 3/x

A. I only
B. II only
C. I and II
D. I and III
E. II and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-xy-0-and-x-2-y-2-xy-6-which-of-the-following-could-be-y-126166.html

Originally posted by sperumba on 18 Jan 2006, 19:15.
Last edited by Bunuel on 07 Nov 2013, 08:37, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
VP
Joined: 21 Sep 2003
Posts: 1023
Location: USA

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18 Jan 2006, 19:42
11
3
Is it E?

Let xy = k

So the eqn becomes k^2 -k -6 = 0
=> (k-3) (k+2) = 0

k =3 or k = -2

xy = 3 or xy = -2

y = 3/x or y = -2/x ---> II & III
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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Senior Manager
Joined: 05 Jan 2006
Posts: 373

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18 Jan 2006, 21:49
x2y2 â€“ xy = 6
x2y2-xy-6 = 0
(xy-3)(xy+2)=0

xy = 3 or xy=-2
y = 3/x or y = -2/x

II and III only ans E
CEO
Joined: 20 Nov 2005
Posts: 2774
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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19 Jan 2006, 03:01
Instead of solving the main equation, I validated all three choices and then found E as answer.

But I agree that approach of solving will certainly save you time.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Joined: 13 Jun 2005
Posts: 246
Location: Haverhill, MA

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19 Jan 2006, 19:39
good job guys the OA is E.
Math Expert
Joined: 02 Sep 2009
Posts: 52284
Re: If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin  [#permalink]

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07 Nov 2013, 08:44
4
2
sperumba wrote:
If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be y in terms of x?

I. 1/2x
II. -2/x
III. 3/x

A. I only
B. II only
C. I and II
D. I and III
E. II and III

x^2*y^2-xy=6 --> (xy)^2-xy-6=0 --> factor quadratics for xy: (xy-3)(xy+2)=0 (or just solve quadratics for xy) --> either xy-3=0 and in this case y=3/x or xy+2=0 and in this case y=-2/x.

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-xy-0-and-x-2-y-2-xy-6-which-of-the-following-could-be-y-126166.html
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Non-Human User
Joined: 09 Sep 2013
Posts: 9426
Re: If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin  [#permalink]

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03 Aug 2018, 21:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin &nbs [#permalink] 03 Aug 2018, 21:58
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