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

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Joined: 02 Sep 2009
Posts: 52344
If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

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18 Oct 2015, 12:18
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Question Stats:

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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.

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Math Expert
Joined: 02 Aug 2009
Posts: 7212
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

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03 May 2016, 04:56
9
1
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
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Joined: 01 Mar 2015
Posts: 76
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

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18 Oct 2015, 22:04
53
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.

$$x^2y^2 − xy = 6$$

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
Manager
Joined: 11 Sep 2013
Posts: 108
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

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

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18 Oct 2015, 12:37
I believe the question should be structured differently
otherwise it is very ambiguous
is it x^2 * y^2 or

x to the power of 2y^2
Manager
Joined: 13 Oct 2013
Posts: 139
Concentration: Strategy, Entrepreneurship
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

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18 Oct 2015, 14:22
x^2y^2 − xy = 6

x^2y^2 − xy -6=0
by solving this equation, we get
xy =3 and xy=-2

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

so it satisfies II and III

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Manager
Joined: 13 Jun 2012
Posts: 202
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

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18 Oct 2015, 15:34
We have xy = 3 or xy =-2 . So y=3/x or -2/x. Answer is E
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Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te  [#permalink]

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18 Oct 2015, 20:44
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.

xy(xy-1) = 6

Possible solutions (2,3) (-2,-3) (1,6) (-1,-6) (3,2) (-3,-2) (-6,-1)

1) 1/2x = y so xy = 1/2 but we know that xy has to be integer - (see solutions above)
2) -2/x =y so xy = -2 (xy-1 = -3) Yes we can get this.
3) 3/x = y so xy =3 (yes we can get this one too)

Ans E.
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Joined: 23 Mar 2016
Posts: 29
Schools: Tulane '18 (M$) Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te [#permalink] ### Show Tags 02 May 2016, 14:46 this is a (x+1)(x+2) type question on mild steroids x^2y^2 - xy = 6 x^2y^2 - xy - 6 = 0 (xy - 3)(xy + 2) = 0 (because -3*2 = -6 and because -3xy + 2xy = -xy) xy = 3, xy = -2 y = 3/x , y = -2/x Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4596 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 4 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. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 11 Dec 2015 Posts: 8 Concentration: Finance, Strategy GPA: 3.1 WE: Business Development (Other) 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, 01:25 Question looks confusing at first sight. Kindly restructure the Question as : (x^2) * (y^2) - xy = 6. Thanks. Math Expert Joined: 02 Sep 2009 Posts: 52344 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, 01:57 cmpunk1990 wrote: Question looks confusing at first sight. Kindly restructure the Question as : (x^2) * (y^2) - xy = 6. Thanks. Mathematically x^2y^2 can only mean x^2*y^2, nothing else. Still edited to avoid confusion. _________________ CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2726 Location: India GMAT: INSIGHT Schools: Darden '21 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 1 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 Answer: option E _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Intern Joined: 25 Jan 2018 Posts: 4 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)? CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2726 Location: India GMAT: INSIGHT Schools: Darden '21 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!!! _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13368 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.... How about -2 and -3.... (-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... Final Answer: 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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Re: If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te &nbs [#permalink] 01 Feb 2018, 12:25
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