y in terms of x

Expert replies

Previous Topic Next Topic

pdonaldson1990: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Thu Feb 11, 2016 5:33 amFollowed by: 1 member

by pdonaldson1990 » Tue May 17, 2016 4:32 pm

Timer

00:00

Answers

Stats

Difficulty—

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

Like this post

Source: Beat The GMAT — Problem Solving | Tue May 17, 2016 4:32 pm

OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » 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

Last edited by OptimusPrep on Thu May 19, 2016 9:55 am, edited 1 time in total.

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » 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...

Final Answer: E

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

Contact Rich at [email protected]

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed May 18, 2016 2:32 am

pdonaldson1990 wrote: If xy cannot equal zero and xÂ²yÂ² - 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

To eliminate x from the equation and make the algebra easier, let x=1.
Plugging x=1 into xÂ²yÂ² - xy = 6, we get:
(1Â²)yÂ² - (1)y = 6
yÂ² - 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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review