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# If xy≠0 and x^2*y^2-xy=6, which of the following could be y

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If xy≠0 and x^2*y^2-xy=6, which of the following could be y [#permalink]  16 Jan 2012, 11:26
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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
[Reveal] Spoiler: OA

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Re: if xy not equal 0 and x^2*y^2 -xy = 6 [#permalink]  16 Jan 2012, 12:46
If xy≠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

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.

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Re: If xy≠0 and x^2*y^2-xy=6, which of the following could be y [#permalink]  17 Jan 2012, 03:51
Ans is E. Simply put xy = a and solve the equation to get 2 values of xy
Re: If xy≠0 and x^2*y^2-xy=6, which of the following could be y   [#permalink] 17 Jan 2012, 03:51
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