If n is positive, which of the following is equal to : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 22:35

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If n is positive, which of the following is equal to

Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Nov 2008
Posts: 6
Followers: 0

Kudos [?]: 37 [1] , given: 0

If n is positive, which of the following is equal to [#permalink]

### Show Tags

05 Nov 2008, 20:26
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

82% (01:23) correct 18% (01:04) wrong based on 117 sessions

### HideShow timer Statistics

If n is positive, which of the following is equal to $$\frac{1}{\sqrt{n+1}-\sqrt{n}}$$

A. 1

B. $$\sqrt{2n+1}$$

C. $$\frac{\sqrt{n+1}}{\sqrt{n}}$$

D. $$\sqrt{n+1}-\sqrt{n}$$

E. $$\sqrt{n+1}+\sqrt{n}$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-positive-which-of-the-following-is-equal-to-31236.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Jul 2013, 09:39, edited 1 time in total.
Edited the question, added the OA and moved to PS forum.
Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7073

Kudos [?]: 93052 [1] , given: 10541

### Show Tags

31 Jul 2013, 09:40
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Abakup wrote:
domleon wrote:
freshina
cant that be smiplified to and hence be answer A ?

cheers

A also works for me.

Why E?

If n is positive, which of the following is equal to $$\frac{1}{\sqrt{n+1}-\sqrt{n}}$$

A. 1

B. $$\sqrt{2n+1}$$

C. $$\frac{\sqrt{n+1}}{\sqrt{n}}$$

D. $$\sqrt{n+1}-\sqrt{n}$$

E. $$\sqrt{n+1}+\sqrt{n}$$

This question is dealing with rationalisation of a fraction. Rationalisation is performed to eliminate irrational expression in the denominator. For this particular case we can do this by applying the following rule: $$(a-b)(a+b)=a^2-b^2$$.

Multiple both numerator and denominator by $$\sqrt{n+1}+\sqrt{n}$$: $$\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1}-\sqrt{n})(\sqrt{n+1}+\sqrt{n})}=\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1})^2-(\sqrt{n})^2)}=\frac{\sqrt{n+1}+\sqrt{n}}{n+1-n}=\sqrt{n+1}+\sqrt{n}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-positive-which-of-the-following-is-equal-to-31236.html
_________________
Current Student
Joined: 28 Dec 2004
Posts: 3384
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 282 [0], given: 2

### Show Tags

05 Nov 2008, 21:01
just multiple numerator and denominator with sqrt(n+1)+sqrt(n)

E it is..
Manager
Joined: 14 Jun 2007
Posts: 170
Location: Vienna, Austria
Followers: 1

Kudos [?]: 7 [0], given: 0

### Show Tags

05 Nov 2008, 23:33
freshina
cant that be smiplified to and hence be answer A ?

cheers
Director
Joined: 14 Aug 2007
Posts: 733
Followers: 10

Kudos [?]: 180 [0], given: 0

### Show Tags

06 Nov 2008, 05:35
fresinha12 wrote:
just multiple numerator and denominator with sqrt(n+1)+sqrt(n)

E it is..

agree with E, same approach
Intern
Joined: 17 Dec 2012
Posts: 7
Concentration: Entrepreneurship, Finance
GMAT Date: 12-13-2013
GPA: 3.81
WE: Management Consulting (Consulting)
Followers: 0

Kudos [?]: 2 [0], given: 9

### Show Tags

31 Jul 2013, 09:31
domleon wrote:
freshina
cant that be smiplified to and hence be answer A ?

cheers

A also works for me.

Why E?
Re: question--30   [#permalink] 31 Jul 2013, 09:31
Similar topics Replies Last post
Similar
Topics:
3 If n is the square of a positive integer, which of the following must 5 09 Nov 2015, 21:59
18 For all positive integers n and m, the function A(n) equals the follow 7 24 Apr 2015, 01:58
7 If n is a positive integer, which of the following must be d 4 29 Jun 2014, 12:09
If n + xy = n and x is not equal to 0, which of the follow 1 19 Nov 2013, 02:25
39 If the positive integer N is a perfect square, which of the following 30 25 Sep 2010, 10:37
Display posts from previous: Sort by