y in terms of x

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 amFollowed by: 16 members; Thanked: 48 times

by alex.gellatly » Tue Jul 17, 2012 10:01 pm

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

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

I only
II only
I and II only
I and III only
II and III only

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Source: Beat The GMAT — Problem Solving | Tue Jul 17, 2012 10:01 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Jul 17, 2012 10:32 pm

alex.gellatly wrote:If xy does not equal 0 and x^2y^2-xy=6, which of the following could be y in terms of x?

--> (xÂ²yÂ² - xy) = 6
--> (xÂ²yÂ² - xy - 6) = 0
--> (xy + 2)(xy - 3) = 0

Hence, either xy = -2 or xy = 3
Hence, either y = -2/x or y = 3/x

The correct answer is E.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jul 18, 2012 2:07 am

alex.gellatly wrote:If xy does not equal 0 and x^2y^2-xy=6, which of the following could be y in terms of x?

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

I only
II only
I and II only
I and III only
II and III only

Let x=1.
Plugging x=1 into x^2y^2-xy=6, we get:
(1Â²)yÂ² - 1*y = 6.
yÂ² - y - 6 = 0.
(y-3)(y+2) = 0.
y=3 or y=-2. These our are targets.

Now we plug x=1 into the answers to which yield our targets 3 and -2.

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

II and III work.
The correct answer is E.

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