GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If 2^{(x+y)^2} / 2^{(x-y)^2} = 2, what is the value of xy?
[#permalink]
18 Dec 2022, 09:14
18 Dec 2022, 09:14
1
Expert Reply
00:00
Question Stats:
100% (01:59) correct
0% (00:00) wrong based on 2 sessions
Hide Show timer Statistics
If \(\frac{2^{(x+y)^2}}{2^{(x-y)^2}} = 2\), what is the value of xy?
(A) -1/4
(B) 1/2
(C) 0
(D) 1/4
(E) 1/2
(A) -1/4
(B) 1/2
(C) 0
(D) 1/4
(E) 1/2
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: If 2^{(x+y)^2} / 2^{(x-y)^2} = 2, what is the value of xy?
[#permalink]
20 Dec 2022, 01:08
20 Dec 2022, 01:08
1
Expert Reply
\(2^{(x^2 +y^2 + 2xy) - (x^2 +y^2 - 2xy)}= 2^1\)
Or, \(2^{x^2 +y^2 + 2xy - x^2 - y^2 + 2xy}= 2^1\)
Or, \(2^{4xy}= 2^1\)
Or, \(4xy = 1\)
So, \(xy = \frac{1}{4}\)
Thus, answer will be (D) \(\frac{1}{4}\) ...
Or, \(2^{x^2 +y^2 + 2xy - x^2 - y^2 + 2xy}= 2^1\)
Or, \(2^{4xy}= 2^1\)
Or, \(4xy = 1\)
So, \(xy = \frac{1}{4}\)
Thus, answer will be (D) \(\frac{1}{4}\) ...
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: If 2^{(x+y)^2} / 2^{(x-y)^2} = 2, what is the value of xy?
[#permalink]
14 Jan 2023, 22:49
14 Jan 2023, 22:49
1
Given that \(\frac{2^{(x+y)^2}}{2^{(x-y)^2}} = 2\) and we need to find the value of xy
\(\frac{2^{(x+y)^2}}{2^{(x-y)^2}} = 2\)
=> \(2^{(x+y)^2 - (x-y)^2} = 2^1\)
=> \((x+y)^2 - (x-y)^2 = 1\)
Using \(a^2 - b^2 = (a+b)*(a-b)\) we get
=> (x + y + x - y) * (x + y -( x - y)) = 1
=> 2x * 2y = 1
=> xy = \(\frac{1}{4}\)
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Exponents
\(\frac{2^{(x+y)^2}}{2^{(x-y)^2}} = 2\)
=> \(2^{(x+y)^2 - (x-y)^2} = 2^1\)
=> \((x+y)^2 - (x-y)^2 = 1\)
Using \(a^2 - b^2 = (a+b)*(a-b)\) we get
=> (x + y + x - y) * (x + y -( x - y)) = 1
=> 2x * 2y = 1
=> xy = \(\frac{1}{4}\)
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Exponents
