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Register now and save up to $200 Available with Beat the GMAT members only code y in terms of x This topic has 2 expert replies and 1 member reply pdonaldson1990 Newbie | Next Rank: 10 Posts Joined 11 Feb 2016 Posted: 5 messages y in terms of x Tue May 17, 2016 4:32 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) Good evening ladies and gentleman, I am a bit disgruntled about this problem, does anyone have any helpful strategies for solving these questions, especially those that involve factoring equations like these? If xy cannot equal zero 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 Answer: E Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! OptimusPrep Master | Next Rank: 500 Posts Joined 13 Mar 2015 Posted: 410 messages Followed by: 7 members Thanked: 120 times GMAT Score: 770 Tue May 17, 2016 6:08 pm pdonaldson1990 wrote: Good evening ladies and gentleman, I am a bit disgruntled about this problem, does anyone have any helpful strategies for solving these questions, especially those that involve factoring equations like these? If xy cannot equal zero 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 Answer: E x^2y^2-xy=6 (xy)^2 - xy - 6 = 0 (xy)^2 - 3xy + 2xy - 6 = 0 (xy - 3)(xy + 2) = 0 Hence xy = 3 , - 2 y = 3/x or -2/x Correct Option: E _________________ Ankur 99th Percentile GMAT Tutor | Optimus Prep™ Optimus Prep™ GMAT Courses: www.Optimus-Prep.com/GMAT Free Online Trial Hour: http://www.optimus-prep.com/request-free-online-trial-hour/ Free GMAT Study Plan: http://www.optimus-prep.com/ebook/ Optimus Prep™ Rates: GMAT Private Tutoring Online:$80-100/hr.*
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Last edited by OptimusPrep on Thu May 19, 2016 9:55 am; edited 1 time in total

Thanked by: pdonaldson1990

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Tue May 17, 2016 10:57 pm
Hi pdonaldson1990,

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...

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

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Thanked by: pdonaldson1990

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Wed May 18, 2016 2:32 am
pdonaldson1990 wrote:
If xy cannot equal zero 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

To eliminate x from the equation and make the algebra easier, let x=1.
Plugging x=1 into x²y² - xy = 6, we get:
(1²)y² - (1)y = 6
y² - y - 6 = 0
(y-3)(y+2) = 0
y=3 or y=-2.

The question stem asks for possible values of y.
Thus, our targets are 3 and -2.

Now plug x=1 into I, II and III to see which yields 3 or -2.

I: (1/2)x = (1/2)1 = 1/2
II: -2/x = -2/1 = -2
III: 3/x = 3/1 = 3

Since II and III work, the correct answer choice must include II and III.

The correct answer is E.

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Thanked by: pdonaldson1990
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