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

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If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin [#permalink] New post 18 Jan 2006, 19:15
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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
[Reveal] Spoiler: OA

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.
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 [#permalink] New post 18 Jan 2006, 19:42
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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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 [#permalink] New post 18 Jan 2006, 21:49
x2y2 – 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
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 [#permalink] New post 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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 [#permalink] New post 19 Jan 2006, 19:39
good job guys the OA is E.
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Re: If xy ≠ 0 and x2y2 xy = 6, which of the following [#permalink] New post 07 Nov 2013, 08:04
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Re: If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin [#permalink] New post 07 Nov 2013, 08:44
Expert's post
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.

Answer: E.

Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm

Solving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm

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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Re: If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin   [#permalink] 07 Nov 2013, 08:44
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If xy not equal 0 and x^2*y^2 -xy = 6, which of the followin

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