Last visit was: 29 May 2024, 00:38 It is currently 29 May 2024, 00:38
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93502
Own Kudos [?]: 627497 [9]
Given Kudos: 81989
Send PM
CAT Tests Forum Quiz Mode
If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of [#permalink] If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of   15 May 2024, 01:30
9
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

76% (02:41) correct 24% (02:46) wrong based on 54 sessions
Hide Show timer Statistics
­If \(x > y > 0\) and \(x+y=4+2\sqrt{xy}\), what is the value of \(\frac{\sqrt{2x}+\sqrt{2y}}{x-y}\)?

A. \(-2\)
B. \(-\frac{\sqrt{2}}{2}\)
C. \(\frac{\sqrt{2}}{2}\)
D. \(\sqrt{2}\)
E. \(2\)


­
ShowHide Answer
Official Answer
C
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3134
Own Kudos [?]: 4523 [3]
Given Kudos: 1857
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of [#permalink] If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of   15 May 2024, 02:37
2
Kudos
1
Bookmarks
Bunuel wrote:
­If \(x > y > 0\) and \(x+y=4+2\sqrt{xy}\), what is the value of \(\frac{\sqrt{2x}+\sqrt{2y}}{x-y}\)?

A. -4
B. -2
C. 1
D. 2
E. 4­
­

­
\(x+y=4+2\sqrt{xy}\)

\(x+y-2\sqrt{xy}=4\)

\((\sqrt{x} - \sqrt{y})^2=4\)­

Taking square root on both sides, we get

\(\sqrt{x} - \sqrt{y} = 2\)­

Note: We are ignoring the possibility of -2, as x > y­

\(\frac{\sqrt{2x}+\sqrt{2y}}{x-y}\)

\(\frac{\sqrt{2}(\sqrt{x}+\sqrt{y})}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}\)­

\(\frac{\sqrt{2}}{2}\)­

Option C­
User avatar
S
Purnank
Manager
Manager
Joined: 05 Jan 2024
Posts: 77
Own Kudos [?]: 39 [2]
Given Kudos: 57
Send PM
Re: If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of [#permalink] If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of   15 May 2024, 02:55
2
Kudos
gmatophobia wrote:
Bunuel wrote:
­If \(x > y > 0\) and \(x+y=4+2\sqrt{xy}\), what is the value of \(\frac{\sqrt{2x}+\sqrt{2y}}{x-y}\)?

A. -4
B. -2
C. 1
D. 2
E. 4­
­

­
\(x+y=4+2\sqrt{xy}\)

\(x+y-2\sqrt{xy}=4\)

\((\sqrt{x} - \sqrt{y})^2=4\)­

Taking square root on both sides, we get

\(\sqrt{x} - \sqrt{y} = 2\)­

Note: We are ignoring the possibility of -2, as x > y­

\(\frac{\sqrt{2x}+\sqrt{2y}}{x-y}\)

\(\frac{\sqrt{2}(\sqrt{x}+\sqrt{y})}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}\)­

\(\frac{\sqrt{2}}{2}\)­

Am I missing something ?  :?

­i am also getting same.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93502
Own Kudos [?]: 627497 [1]
Given Kudos: 81989
Send PM
CAT Tests Forum Quiz Mode
Re: If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of [#permalink] If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of   15 May 2024, 03:07
1
Kudos
Expert Reply
Fixed the options. Thank you both!
User avatar
S
Shwarma
Manager
Manager
Joined: 10 Sep 2023
Posts: 60
Own Kudos [?]: 48 [0]
Given Kudos: 53
Send PM
Re: If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of [#permalink] If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of   15 May 2024, 14:06
gmatophobia
your solution is so elegant and faster to do.
I got the same answer
But it was so tedious
When you look at these algebraic equations, how finalise the method to go about it?
how do you decide which method to employ when faced with a question?
User avatar
B
charlie1195
Intern
Intern
Joined: 08 Jan 2024
Posts: 4
Own Kudos [?]: 4 [1]
Given Kudos: 9
Location: India
Send PM
Re: If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of [#permalink] If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of   16 May 2024, 00:23
1
Kudos
Generally when I approach an algebra question, I'd spend 10 seconds to identify if the given expression can be modified to fit a formula like (a-b)^2, a^2-b^2, etc.
99% of the times it will fit into a formula.
But I'd suggest practice a lot to identify that.
GMAT Club Bot
gmatclubot
Re: If x > y > 0 and x + y = 4 + 2(xy)^(1/2), what is the value of [#permalink]
16 May 2024, 00:23
Moderator:
Bunuel
Math Expert
93502 posts