GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Jul 2020, 13:01

### 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

# If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te

Author Message
TAGS:

### Hide Tags

Manager
Joined: 13 Jun 2005
Posts: 212
Location: Haverhill, MA
If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

Updated on: 30 Jul 2019, 00:28
8
49
00:00

Difficulty:

15% (low)

Question Stats:

81% (02:03) correct 19% (02:24) wrong based on 2158 sessions

### HideShow timer Statistics

If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Originally posted by sperumba on 18 Jan 2006, 19:15.
Last edited by Bunuel on 30 Jul 2019, 00:28, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 64949
If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

18 Oct 2015, 12:18
11
41
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

$$x^2*y^2-xy=6$$;

$$(xy)^2-xy-6=0$$;

$$(xy-3)(xy+2)=0$$;

Either $$xy-3=0$$ and in this case $$y=\frac{3}{x}$$ or $$xy+2=0$$ and in this case $$y=-\frac{2}{x}$$.

_________________
Manager
Joined: 01 Mar 2015
Posts: 94
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

18 Oct 2015, 22:04
77
10
Bunuel wrote:
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Kudos for a correct solution.

$$x^2y^2 − xy = 6$$

taking xy = a, we have
$$a^2 − a= 6$$
=> $$a^2 − a − 6 = 0$$

solving we get a = 3 or -2

if a = xy = 3, we have y = 3/x
if a = xy = -2, we have y = -2/x

kudos, if you like the post
##### General Discussion
SVP
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2448
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be  [#permalink]

### Show Tags

28 Aug 2010, 01:54
5
1
take $$xy= a$$

$$a^2 - a- 6=0$$

$$(a-3)*(a+2) = 0$$

=> either $$a = 3$$ or $$a = -2$$ => either $$xy =3$$ or $$xy = -2$$

Hence E
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html
Intern
Joined: 15 Dec 2009
Posts: 11
Schools: Any offering one year MBA
WE 1: Information Tech
WE 2: Event Consultant for FIFA addi events and WC
Re: If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be  [#permalink]

### Show Tags

26 Sep 2010, 08:26
9
udaymathapati wrote:
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

Backsolving..
$$I) y= 1/(2x) ==> xy = 1/2$$
substituting
$$1/4 - 1/2 <> 6..$$
$$LHS <> RHS$$

$$II) y = - 2 / x$$
$$xy = -2 ..$$
subtituting in the equation.
LHS = RHS

$$III) y = 3/x ... xy = 3$$
substituting in the equation.
LHS= RHS

Hence E
Manager
Joined: 11 Sep 2013
Posts: 102
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

18 Oct 2015, 12:24
5
Bunuel wrote:
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Kudos for a correct solution.

x^2y^2 − xy = 6 => (xy-3)(xy+2)=0

=> xy=3 or xy =-2

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

Because the question is COULD BE TRUE, meaning that there exists the value of x: y=1/(2x) and x^2y^2 − xy = 6

=> 1/2x = -2/x or =3/x

=> 1=-4 or 1=6: WRONG

=> only II and III are TRUE

=> Ans: E
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11028
Location: United States (CA)
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

03 May 2016, 04:36
5
3
Bunuel wrote:
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Kudos for a correct solution.

We are given the equation, (x^2)(y^2) – xy = 6, and, although it may not be obvious, the equation is a quadratic-format equation. Thus, our first step is to set the equation equal to zero. We then factor the left side and, finally, solve for xy.

(x^2)(y^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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Math Expert
Joined: 02 Aug 2009
Posts: 8752
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

03 May 2016, 04:56
12
3
Bunuel wrote:
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Kudos for a correct solution.

Hi,
its a 700 level Q, BUT is literally begging you to make it a simpler Q by using substitution..
we have an equation - $$x^2y^2 − xy = 6$$
we have tto find OUT of 3, which all will be values of y in terms of x..

two ways-

1) factorize and then find answers
2) substitution, as we have our answers right in front of us and any value that fits in IS the answer..

[b]we can actually eliminate I at the first glance as it is giving us a 2 in denominator and hence LHS will become some fraction, but lets still try..[/b]

EQ - $$x^2y^2 − xy = 6$$
I. 1/(2x)......$$x^2\frac{1}{2x}^2 − x\frac{1}{2x} = 6$$ ..... $$\frac{1}{4}-\frac{1}{2} = 6$$... NO
II. -2/x .......$$x^2\frac{-2}{x}^2 − x\frac{-2}{x} = 6$$ ..... $$4-(-2) = 6$$..YES
III. 3/x .......$$x^2\frac{3}{x}^2 − x\frac{3}{x} = 6$$ ..... $$9-3 = 6$$..YES

so II and III are correct
E
_________________
GMAT Club Legend
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4313
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

17 Oct 2016, 03:41
1
2
Bunuel wrote:
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Kudos for a correct solution.

$$x^2y^2 − xy = 6$$

i.e. $$xy(xy − 1) = 6$$ [Please observe that xy and (xy-1) are two consecutive number]
But 3*2 = 6
also, (-2)*(-3) = 6

therefore, xy = 3 or xy = -2

i.e. , y = 3/x or y=-2/x

_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Intern
Joined: 25 Jan 2018
Posts: 4
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

01 Feb 2018, 05:55
Bunuel wrote:
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Kudos for a correct solution.

Why is it not (xy-2)(xy+3)?
GMAT Club Legend
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4313
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

01 Feb 2018, 06:07
michaelarbeid wrote:
Bunuel wrote:
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Kudos for a correct solution.

Why is it not (xy-2)(xy+3)?

I don't know if the highlighted part is a typo error but here your expression doesn't match with with the given expressions in question

I am assuming that you meant to type $$(xy+2)(xy-3)$$ which becomes $$x^2*y^2 - xy = 6$$

And if you meant $$(xy+2)(xy-3)$$ then you are absolutely correct because this also leads us to the correct result

$$xy = -2 or +3$$

Hope this helps!!!
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17010
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

01 Feb 2018, 12:25
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...

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
CEO
Joined: 03 Jun 2019
Posts: 3182
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

15 Sep 2019, 18:16
sperumba wrote:
If xy ≠ 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

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Solving the equation
xy = 3 or -2
y = 3/x or -2/x

IMO E

Posted from my mobile device
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Manager
Joined: 16 Aug 2014
Posts: 52
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

26 Jan 2020, 22:44
If anyone is uncomfortable solving this question using equation x2y2−xy=6.
It can be solved by plug in values mentioned:
Attachments

IMG_20200127_121104435.jpg [ 3.37 MiB | Viewed 6039 times ]

Intern
Joined: 18 Oct 2018
Posts: 12
Location: Thailand
GPA: 3.45
WE: Other (Other)
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

### Show Tags

13 Mar 2020, 23:17
why can't
x2y2−xy=6
xy(xy - 1) = 6
so xy = 6 or xy = 7???
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te   [#permalink] 13 Mar 2020, 23:17