Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
GMAT 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.
Nov 3011:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
Nov 2112:00 PM EST
-11:59 PM EST
Don’t miss Target Test Prep’s biggest sale of the year! Grab 25% off any Target Test Prep GMAT plan during our Black Friday sale. Just enter the coupon code BLACKFRIDAY25 at checkout to save up to $400.
Nov 2310:00 AM EST
-11:59 PM EST
Don't miss Manhattan Prep's biggest sale of the year! Use code SALE25 to save 25% on GMAT prep.
Nov 2907:30 AM PST
-08:30 AM PST
Deciding between an MBA in India and an MBA in Europe? In this video, Shruti Parashar, seasoned MBA expert and founder of GoalISB consulting, explores the risks, opportunities, and rewards of pursuing your MBA in these regions.
Nov 3001:00 PM EST
-02:00 PM EST
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of how students should study. So, it's no wonder that more and more Target Test Prep students are scoring super high on the GMAT.- Dec 01
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
24 Apr 2017, 03:31
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:16) correct
31%
(02:46)
wrong
based on 359
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x^2 + y^2 = a\) and \(x^2 − y^2 = b\), then \((2xy)^2=\)
A. (a^2 + b^2)/2
B. (a^2 − b^2)/2
C. a^2 + b^2
D. a^2 − b^2
E. 4a^2*b^2
A. (a^2 + b^2)/2
B. (a^2 − b^2)/2
C. a^2 + b^2
D. a^2 − b^2
E. 4a^2*b^2
24 Apr 2017, 04:28
Kudos
Bookmarks
(x^2 + y^2) = a ------------ (1)
(x^2 - y^2) = b ------------ (2)
Add 1 and 2:
2(x^2) = a+b ------------ (3)
Subtract 1 and 2:
2(y^2) = a-b ------------ (4)
multiplying 3 and 4,
(2xy)^2 = (a+b) (a-b) = a^2 - b^2
Hence, D will be the answer.
(x^2 - y^2) = b ------------ (2)
Add 1 and 2:
2(x^2) = a+b ------------ (3)
Subtract 1 and 2:
2(y^2) = a-b ------------ (4)
multiplying 3 and 4,
(2xy)^2 = (a+b) (a-b) = a^2 - b^2
Hence, D will be the answer.
General Discussion
27 Apr 2017, 17:10
Kudos
Bookmarks
Bunuel
If \(x^2 + y^2 = a\) and \(x^2 − y^2 = b\), then \((2xy)^2=\)
A. (a^2 + b^2)/2
B. (a^2 − b^2)/2
C. a^2 + b^2
D. a^2 − b^2
E. 4a^2*b^2
A. (a^2 + b^2)/2
B. (a^2 − b^2)/2
C. a^2 + b^2
D. a^2 − b^2
E. 4a^2*b^2
We are given that x^2 + y^2 = a and that x^2 - y^2 = b.
Observing that every answer choice involves a^2 and b^2, let’s find each in terms of x and y:
a^2 = (x^2 + y^2)^2 = x^4 + 2(x^2y^2) + y^4
b^2 = (x^2 - y^2)^2 = x^4 - 2(x^2y^2) + y^4
Let’s subtract the two equations above:
a^2 - b^2 = x^4 + 2(x^2y^2) + y^4 - (x^4 - 2(x^2y^2) + y^4) = x^4 + 2(x^2y^2) + y^4 - x^4 + 2(x^2y^2) - y^4
= 4(x^2y^2)
= (2xy)^2
Answer: D
