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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]

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

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16 Jan 2012, 12:46
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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 $$y=\frac{3}{x}$$ or $$xy+2=0$$ and in this case $$y=-\frac{2}{x}$$.

Hope it helps.
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Re: If xy≠0 and x^2*y^2-xy=6, which of the following could be y [#permalink]

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

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02 Sep 2013, 09:57
Bumping for review and further discussion.
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Re: If xy≠0 and x^2*y^2-xy=6, which of the following could be y [#permalink]

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10 Apr 2015, 06:38
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≠0 and x^2*y^2-xy=6, which of the following could be y [#permalink]

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05 Feb 2016, 23:11
Baten80 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

Looking at the equation and below 3 options, we can figure out that xy and (xy-1) are two consecutive integers. There are only two possible combinations:
1) xy=3 and (xy-1)=2; y=3/x (Option III is correct);
2) xy=-2 and (xy-1)=-3; y=-2/x (Option II is correct).

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

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13 Feb 2016, 10:03
Simply,put the options into the equations and you will know the answer.The process takes a bit time though
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Re: If xy≠0 and x^2*y^2-xy=6, which of the following could be y [#permalink]

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16 Feb 2017, 04:20
$$x^2*y^2-xy=6; x^2*y^2-xy-6=0; a+b=-1; ab=-6; a=-3; b=2; xy=3; xy=-2; y=\frac{3}{x}; y=\frac{-2}{x}$$
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Re: If xy≠0 and x^2*y^2-xy=6, which of the following could be y [#permalink]

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21 Feb 2017, 10:27
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Baten80 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

We are given the equation x^2y^2 – xy = 6, and although it may not be obvious, the equation is a quadratic-format equation. Thus, our first step is to set one side of the equation to zero. We then factor the other side as a quadratic. .

x^2y^2 – xy – 6 = 0

(xy – 3)(xy + 2) = 0

xy – 3 = 0 or xy + 2 = 0

xy = 3 or xy = -2

Since we need y in terms of x, we can isolate y in both of our equations.

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

Thus, the expressions in II and III are correct.

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Re: If xy≠0 and x^2*y^2-xy=6, which of the following could be y   [#permalink] 21 Feb 2017, 10:27
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