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 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
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. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
16 Mar 2023, 13:55
Kudos
Bookmarks
Dipanjan005
If x = y, say, then the third option will be equal to zero, so will always be less than 1/√(x + y), since that's positive. The third option can even be negative if y > x.
08 Nov 2024, 00:25
Kudos
Bookmarks
KarishmaB could you please share how you would solve this question?
08 Nov 2024, 05:00
Kudos
Bookmarks
study
In comparison, we always need to look for something common. To compare fractions, either numerator or denominator must be the same.
I. \(\frac{\sqrt{x+y}}{2x}\) Let's compare it with our given expression.
\(\frac{1}{\sqrt{x+y}} = \frac{\sqrt{x+y}}{x+y}\) (Dividing and multiply by sqrt(x+y))
Their numerators are same so now we just compare denominators. Is 2x ( = x + x) smaller or greater than (x+y)? That simply depends on whether y is smaller or greater than x. Hence this expression can be greater or smaller than the given expression.
II. \(\frac{\sqrt{x}+\sqrt{y}}{x+y}\) Let's compare it with our given expression.
\(\frac{1}{\sqrt{x+y}} = \frac{\sqrt{x+y}}{x+y}\) (Dividing and multiply by sqrt(x+y))
Here denominator is same so we compare numerators. If you recall that \(\sqrt{x+y} \leq \sqrt{x}+\sqrt{y}\) then great. Equality holds when x or y is 0. Since x and y are positive, this expression will always be greater.
Else try some values. It seems likely. But we still need to convince ourselves that it will work in all cases.
\((\sqrt{x}+\sqrt{y})^2 = x + y + 2\sqrt{xy}\)
\((\sqrt{x+y})^2 = x + y\)
So we see that \(\sqrt{x}+\sqrt{y}\) is greater.
Hence II is greater in all cases.
III. \(\frac{\sqrt{x}-\sqrt{y}}{x+y}\)
Since there is a negative in the numerator, it is easy to eliminate this option. It can be negative. Say if x = 1 and y = 4. Our given expression cannot be negative.
Answer (C)
