If xy ≠ 0 and x2y2 – xy = 6, which of the following could be : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 16:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 19 Sep 2010
Posts: 15
Followers: 0

Kudos [?]: 28 [0], given: 4

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

### Show Tags

25 Feb 2011, 07:23
2
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

79% (02:25) correct 21% (02:37) wrong based on 146 sessions

### HideShow timer Statistics

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, 04:08, edited 3 times in total.
Renamed the topic, edited the question and the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93362 [2] , given: 10557

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

### Show Tags

25 Feb 2011, 08:11
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.
_________________
Manager
Joined: 17 Feb 2011
Posts: 200
Concentration: Real Estate, Finance
Schools: MIT (Sloan) - Class of 2014
GMAT 1: 760 Q50 V44
Followers: 44

Kudos [?]: 708 [0], given: 70

### Show Tags

25 Feb 2011, 08:35
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.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13489
Followers: 576

Kudos [?]: 163 [0], given: 0

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

### Show Tags

17 Jun 2015, 12:15
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8314
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 381

Kudos [?]: 2467 [3] , given: 163

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

### Show Tags

07 Jul 2015, 21:37
3
KUDOS
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
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 12 Apr 2013 Posts: 38 Concentration: Entrepreneurship, Strategy Followers: 0 Kudos [?]: 22 [1] , given: 20 Re: If xy ≠ 0 and x2y2 – xy = 6, which of the following could be [#permalink] ### Show Tags 08 Jul 2015, 20:57 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!! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8314 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 381 Kudos [?]: 2467 [1] , given: 163 Re: If xy ≠ 0 and x2y2 – xy = 6, which of the following could be [#permalink] ### Show Tags 09 Jul 2015, 17:43 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 _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If xy ≠ 0 and x2y2 – xy = 6, which of the following could be   [#permalink] 09 Jul 2015, 17:43
Similar topics Replies Last post
Similar
Topics:
If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2? 1 18 Jan 2016, 21:43
19 If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te 12 18 Oct 2015, 12:18
5 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? 11 19 Jan 2012, 12:21
13 If xy≠0 and x^2*y^2-xy=6, which of the following could be y 6 16 Jan 2012, 10:26
18 If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be 5 28 Aug 2010, 01:45
Display posts from previous: Sort by