• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If 2^{(x+y)^2} / 2^{(x-y)^2} = 2, what is the value of xy?

This topic has 3 expert replies and 0 member replies

If 2^{(x+y)^2} / 2^{(x-y)^2} = 2, what is the value of xy?

Post
$$If\ \frac{2^{\left(x+y\right)^2}}{2^{\left(x-y\right)^2}}=2,$$ What is the value of xy?

(A) -1/4
(B) 1/2
(C) 0
(D) 1/4
(E) 1/2

The OA is D.

Would any expert please break down the steps to solve this PS question, step by step? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
Quote:
$$If\ \frac{2^{\left(x+y\right)^2}}{2^{\left(x-y\right)^2}}=2,$$ What is the value of xy?

(A) -1/4
(B) 1/2
(C) 0
(D) 1/4
(E) 1/2

The OA is D.

Would any expert please break down the steps to solve this PS question, step by step? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
Hi swerve,
Let's take a look at your question.

$$\frac{2^{\left(x+y\right)^2}}{2^{\left(x-y\right)^2}}=2 ... (i)$$
Let's evaluate the square of binomials in the exponent of 2, using polynomial identities:
$$\left(x+y\right)^2=x^2+2xy+y^2$$
$$\left(x-y\right)^2=x^2-2xy+y^2$$
Eq(i) will become:
$$\frac{2^{\left(x^2+2xy+y^2\right)}}{2^{\left(x^2-2xy+y^2\right)}}=2$$
$$2^{\left(x^2+2xy+y^2\right)-\left(x^2-2xy+y^2\right)}=2$$
$$2^{x^2+2xy+y^2-x^2+2xy-y^2}=2$$
$$2^{2xy+2xy}=2$$
$$2^{4xy}=2$$
$$2^{4xy}=2^1$$
Since bases on both sides of the equation are the same, we can equate the exponents, hence,
$$4xy=1$$
$$xy=\frac{1}{4}$$
Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

GMAT/MBA Expert

Post
swerve wrote:
$$If\ \frac{2^{\left(x+y\right)^2}}{2^{\left(x-y\right)^2}}=2,$$ What is the value of xy?

(A) -1/4
(B) 1/2
(C) 0
(D) 1/4
(E) 1/2
(x + y)² = x² + 2xy + y²
(x - y)² = x² - 2xy + y²

Given: 2^(x + y)²/2^(x - y)² = 2
Expand both exponents to get: 2^(x² + 2xy + y²)/2^(x² - 2xy + y²) = 2
Apply Quotient Law to get: 2^(4xy) = 2
In other words, 2^(4xy) = 2^1
This means that: 4xy = 1
Divide both sides by 4 to get: xy = 1/4

Answer: D

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
497 members
Upvotes:
2867
GMAT Score:
800
Post
Hi swerve,

Since both the numerator and denominator of the fraction are 'base 2', we ultimately need a fraction that simplifies to (2^1)/(2^0) = 2.

Algebraically, this means that (X+Y) has to be '1 greater' than (X-Y), so we can set up the following equation:

X + Y = X - Y + 1

Then combine like terms and simplify (the X's cancel out):

2Y = 1
Y = 1/2

Plugging that value into the numerator, we have:

X + 1/2 = 1
X = 1/2

Thus, (X)(Y) = (1/2)(1/2) = 1/4

Final Answer: D

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

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 Ian Stewart 43 first replies
2 Brent@GMATPrepNow 35 first replies
3 Scott@TargetTestPrep 33 first replies
4 Jay@ManhattanReview 28 first replies
5 GMATGuruNY 19 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

149 posts
2 image description Max@Math Revolution

Math Revolution

93 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

53 posts
4 image description Ian Stewart

GMATiX Teacher

52 posts
5 image description GMATGuruNY

The Princeton Review Teacher

32 posts
See More Top Beat The GMAT Experts