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# If xy ≠ 0 and x2y2 – xy = 6, which of the following could be

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Intern
Joined: 19 Sep 2010
Posts: 13

Kudos [?]: 49 [0], given: 4

If xy ≠ 0 and x2y2 – xy = 6, which of the following could be [#permalink]

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25 Feb 2011, 08:23
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Question Stats:

79% (01:26) correct 21% (02:34) wrong based on 157 sessions

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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

A. I only
B. II only
C. I and II
D. I and III
E. II and III
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Feb 2014, 05:08, edited 3 times in total.
Renamed the topic, edited the question and the OA.

Kudos [?]: 49 [0], given: 4

Math Expert
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128791 [2], given: 12183

If xy ≠ 0 and x2y2 – xy = 6, which of the following could be [#permalink]

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25 Feb 2011, 09:11
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naaga wrote:
If xy ≠ 0 and x2y2 – 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

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

$$x^2*y^2-xy=6$$ --> $$(xy)^2-xy-6=0$$ --> $$(xy-3)(xy+2)=0$$ --> either $$xy-3=0$$ and in this case $$y=\frac{3}{x}$$ or $$xy+2=0$$ and in this case $$y=-\frac{2}{x}$$.

naaga, please format the questions properly.

P.S. This is your third question for today with incorrect OA.
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Kudos [?]: 128791 [2], given: 12183

Manager
Joined: 17 Feb 2011
Posts: 191

Kudos [?]: 774 [0], given: 70

Concentration: Real Estate, Finance
Schools: MIT (Sloan) - Class of 2014
GMAT 1: 760 Q50 V44

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25 Feb 2011, 09:35
Fantastic approach. Thanks!

Bunuel wrote:
naaga wrote:
If xy ≠ 0 and x2y2 – 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

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 --> (xy-3)(xy+2)=0 --> either xy-3=0 and in this case y=3/x or xy+2=0 and in this case y=-2/x.

naaga, please format the questions properly.

P.S. This is your third question for today with incorrect OA.

Kudos [?]: 774 [0], given: 70

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Posts: 16681

Kudos [?]: 273 [0], given: 0

Re: If xy ≠ 0 and x2y2 – xy = 6, which of the following could be [#permalink]

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17 Jun 2015, 13:15
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Re: If xy ≠ 0 and x2y2 – xy = 6, which of the following could be [#permalink]

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07 Jul 2015, 22:37
3
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Expert's post
Hi All,

This question is quirky in that it tests you on math rules and patterns that you probably know, but in ways that you're not used to thinking about...

We're told that neither X nor Y are equal to 0. We're also told that (X^2)(Y^2) - XY = 6. We're asked which of the following COULD be the value of Y in terms of X...

The first interesting thing about this question is the use of the word COULD....that word implies that there's MORE THAN ONE possible solution.
The second interesting thing is that the 'term' (XY) can be factored out of the 'left side' of the equation. Normally, you look to factor our a single variable or number, but here, it's the product of two variables that you can factor out. Doing so gives us...

XY(XY - 1) = 6

While this looks complicated, there's an easy pattern here:

(number)(number - 1) = 6

Can you think of 2 numbers, that differ by 1, that you can multiply to get 6?

You should be thinking 2 and 3... because (3)(3-1) = 6

So XY = 3 is a possible solution. In this case, Y = 3/X. The wording of the prompt makes me think that there should be another solution though, so is there ANOTHER pair of numbers, that differ by 1, that you can multiply together to get 6? Hint: the numbers do NOT have to be positive....

(-2)(-2-1) = 6

So XY = -2 is another possible solution. In this case, Y = -2/X

There's only one answer that includes both of those solutions...

[Reveal] Spoiler:
E

GMAT assassins aren't born, they're made,
Rich
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# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Kudos [?]: 3407 [3], given: 172 Intern Joined: 12 Apr 2013 Posts: 37 Kudos [?]: 30 [1], given: 20 Concentration: Entrepreneurship, Strategy Re: If xy ≠ 0 and x2y2 – xy = 6, which of the following could be [#permalink] ### Show Tags 08 Jul 2015, 21:57 1 This post received KUDOS I tried this in the following way: Since the values given are of "y", i plugged in these values in the equation for "y". Starting with 3rd option first which is easier to plug in, x^2(3/x)^2 - x(3/x) = 6 satisfy the equation. Plugging in y = -2/x in the equation, x^2(-2/x)^2 - x(-2/x) = 6 also satisfy the equation. plugging in y = 1/(2x) doesn't satisfy the equation, Hence E. Is my approach correct? _________________ Commitment is about stretching your capabilities. It can take you across all obstacles!! Kudos [?]: 30 [1], given: 20 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9975 Kudos [?]: 3407 [1], given: 172 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If xy ≠ 0 and x2y2 – xy = 6, which of the following could be [#permalink] ### Show Tags 09 Jul 2015, 18:43 1 This post received KUDOS Expert's post Hi ash99, YES, your method for dealing with this question is just as effective as any of the others (it's essentially a variation on TEST THE ANSWERS). Based on how the the 5 answer choices are designed, once you proved that the third and second Roman Numerals were potential solutions, then you could have stopped working (since none of the answers included all 3 Roman Numerals). GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Kudos [?]: 3407 [1], given: 172

Re: If xy ≠ 0 and x2y2 – xy = 6, which of the following could be   [#permalink] 09 Jul 2015, 18:43
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