NEW HERE? LEARN MORE
closeclose
Last visit was: 07 May 2024, 05:52 It is currently 07 May 2024, 05:52
Decision Tracker
My Rewards
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 is positive, then 1/(root(x+1) + root(x)) =

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
registerincog
Intern
Intern
Joined: 16 Nov 2013
Posts: 24
Own Kudos [?]: 439 [7]
Given Kudos: 20
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
Send PM
If x is positive, then 1/(root(x+1) + root(x)) = [#permalink] New post   21 Nov 2013, 02:03
7
Bookmarks
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

82% (00:58) correct 18% (01:51) wrong based on 208 sessions
Hide Show timer Statistics
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\)

A) 1

B) x

C) \(\frac{1}{x}\)

D) \(\sqrt{x+1}-\sqrt{x}\)

E) \(\sqrt{x+1}+\sqrt{x}\)
ShowHide Answer
Official Answer
D
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93072
Own Kudos [?]: 621859 [3]
Given Kudos: 81780
Send PM
CAT Tests Forum Quiz Mode
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink] New post   21 Nov 2013, 02:11
2
Kudos
1
Bookmarks
Expert Reply
registerincog wrote:
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}\)

A) 1
B) x
C) \(\frac{1}{x}\)
D) \(\sqrt{x+1}-\sqrt{x}\)
E) \(\sqrt{x+1}+\sqrt{x}\)


Rationalize the fraction by multiplying it by \(\frac{\sqrt{x+1}-\sqrt{x}}{\sqrt{x+1}-\sqrt{x}}\) and apply \((a+b)(a-b)=a^2-b^2\) to the denominator:

\(\frac{1}{\sqrt{x+1}+\sqrt{x}}*\frac{\sqrt{x+1}-\sqrt{x}}{\sqrt{x+1}-\sqrt{x}}=\frac{\sqrt{x+1}-\sqrt{x}}{x+1-x}=\sqrt{x+1}-\sqrt{x}\).

Answer: D.
avatar
wuhanmatt
Intern
Intern
Joined: 16 Nov 2013
Posts: 13
Own Kudos [?]: 6 [1]
Given Kudos: 1
Location: Australia
GMAT 1: 770 Q51 V42
GPA: 3
Send PM
GMAT ToolKit User Reviews Badge
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink] New post   18 Dec 2013, 05:42
1
Kudos
Am I being stupid, or is the question missing something?

I.e. should there not be a question mark or something at the end, or at least an equal sign.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93072
Own Kudos [?]: 621859 [0]
Given Kudos: 81780
Send PM
CAT Tests Forum Quiz Mode
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink] New post   18 Dec 2013, 06:53
Expert Reply
wuhanmatt wrote:
Am I being stupid, or is the question missing something?

I.e. should there not be a question mark or something at the end, or at least an equal sign.


You are right there should be an equal sign at the end. Edited. Thank you.
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7222 [3]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink] New post   11 Sep 2014, 03:01
3
Kudos
registerincog wrote:
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\)

A) 1
B) x
C) \(\frac{1}{x}\)
D) \(\sqrt{x+1}-\sqrt{x}\)
E) \(\sqrt{x+1}+\sqrt{x}\)


For such type of questions, change the middle sign & reciprocal

For example, \(\frac{1}{\sqrt{6} + \sqrt{5}} = \sqrt{6} - \sqrt{5}\)

Answer = D
User avatar
L
Arro44
Director
Director
Joined: 04 Jun 2018
Posts: 668
Own Kudos [?]: 733 [0]
Given Kudos: 362
Location: United States
Concentration: General Management, Finance
Schools: Sloan '22 (M) Cambridge "21 (A$)
GMAT 1: 730 Q47 V44
GPA: 3.4
Send PM
Reviews Badge
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink] New post   27 Jul 2018, 12:25
PareshGmat wrote:
registerincog wrote:
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\)

A) 1
B) x
C) \(\frac{1}{x}\)
D) \(\sqrt{x+1}-\sqrt{x}\)
E) \(\sqrt{x+1}+\sqrt{x}\)


For such type of questions, change the middle sign & reciprocal

For example, \(\frac{1}{\sqrt{6} + \sqrt{5}} = \sqrt{6} - \sqrt{5}\)

Answer = D


I just encountered this question as part of my daily questions from the log and only got it right by guessing.

Could you elaborate how you get root 5&6?

Thanks and best regards,
Chris
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93072
Own Kudos [?]: 621859 [3]
Given Kudos: 81780
Send PM
CAT Tests Forum Quiz Mode
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink] New post   28 Jul 2018, 04:34
1
Kudos
2
Bookmarks
Expert Reply
Arro44 wrote:
PareshGmat wrote:
registerincog wrote:
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\)

A) 1
B) x
C) \(\frac{1}{x}\)
D) \(\sqrt{x+1}-\sqrt{x}\)
E) \(\sqrt{x+1}+\sqrt{x}\)


For such type of questions, change the middle sign & reciprocal

For example, \(\frac{1}{\sqrt{6} + \sqrt{5}} = \sqrt{6} - \sqrt{5}\)

Answer = D


I just encountered this question as part of my daily questions from the log and only got it right by guessing.

Could you elaborate how you get root 5&6?

Thanks and best regards,
Chris


This is explained HERE.

This algebraic manipulation is called rationalization and is performed to eliminate irrational expression in the denominator.

Questions involving rationalization to practice:
https://gmatclub.com/forum/in-the-given ... 59791.html
https://gmatclub.com/forum/if-x-0-then-106291.html
https://gmatclub.com/forum/if-n-is-posit ... 31236.html
https://gmatclub.com/forum/consider-a-qu ... 31083.html
https://gmatclub.com/forum/in-the-diagra ... 39282.html
https://gmatclub.com/forum/in-the-diagra ... 29962.html
https://gmatclub.com/forum/the-perimeter ... 27049.html
https://gmatclub.com/forum/which-of-the- ... 98531.html
https://gmatclub.com/forum/if-x-is-posit ... 63491.html
https://gmatclub.com/forum/1-2-sqrt3-64378.html
https://gmatclub.com/forum/if-a-square-m ... 99359.html

Hope it helps.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32817
Own Kudos [?]: 827 [0]
Given Kudos: 0
Send PM
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink] New post   01 Oct 2023, 12:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink]
01 Oct 2023, 12:23
Moderators:
Bunuel
Math Expert
93072 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions