GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2018, 10:44

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.

Close

Request Expert Reply

Confirm Cancel

If k > 1, which of the following must be equal to

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 16 Jun 2015, 03:11
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (01:16) correct 26% (01:57) wrong based on 232 sessions

HideShow timer Statistics

If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\)?

A. 2

B. \(2\sqrt{2k}\)

C. \(2\sqrt{k+1}+\sqrt{k-1}\)

D. \(\frac{\sqrt{k+1}}{\sqrt{k-1}}\)

E. \(\sqrt{k+1}-\sqrt{k-1}\)

Kudos for a correct solution.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 28 Jan 2013
Posts: 31
Location: United States
Concentration: General Management, International Business
GPA: 3.1
WE: Information Technology (Consulting)
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 16 Jun 2015, 05:32
1
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k−1}}\)?

\(\frac{2}{\sqrt{k+1}+\sqrt{k−1}}\)
Rationalizing the denominator

We get
\(\sqrt{k+1}-\sqrt{k−1}\)

Ans : E
CEO
CEO
User avatar
P
Joined: 08 Jul 2010
Posts: 2559
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 16 Jun 2015, 09:13
Bunuel wrote:
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\)?

A. 2

B. \(2\sqrt{2k}\)

C. \(2\sqrt{k+1}+\sqrt{k-1}\)

D. \(\frac{\sqrt{k+1}}{\sqrt{k-1}}\)

E. \(\sqrt{k+1}-\sqrt{k-1}\)

Kudos for a correct solution.


Rationalization is one of the methods, Second is here

Since k>1 , \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\)

Let's Substitute k = 2 in the expression, the expression now becomes

\(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\) = \(\frac{2}{\sqrt{2+1}+\sqrt{2-1}}\)
i.e. \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\) = \(\frac{2}{\sqrt{3}+1}\) = 2/(1.732+1)
i.e. \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\) = 2/(2.732) = approx 0.74

Check option with k=2

A. 2 > 0.74INCORRECT

B. \(2\sqrt{2k}\) = \(2\sqrt{4}\) = 4 > 0.74 INCORRECT

C. \(2\sqrt{k+1}+\sqrt{k-1}\) = \(2\sqrt{3}+\sqrt{2-1}\)>0.74 INCORRECT

D. \(\frac{\sqrt{k+1}}{\sqrt{k-1}}\) = \(\frac{\sqrt{2+1}}{\sqrt{2-1}}\)= 1.7 > 0.74 INCORRECT

E. \(\sqrt{k+1}-\sqrt{k-1}\) = \(\sqrt{2+1}-\sqrt{2-1}\)= 1.73-1 = 0.73 CORRECT

Answer: option
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
User avatar
Joined: 26 Dec 2011
Posts: 114
Schools: HBS '18, IIMA
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 16 Jun 2015, 10:21
1
1
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\)?

Solution -

Divide the numerator and denominator with \(\sqrt{k+1}-\sqrt{k-1}\) in the above equation and solve the equation.

Results, \(\sqrt{k+1}-\sqrt{k-1}\).

ANS E.

Thanks,

Kudos please.
_________________

Thanks,
Kudos Please

Current Student
avatar
Joined: 18 Mar 2015
Posts: 21
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 730 Q50 V38
GPA: 4
WE: Engineering (Computer Software)
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 16 Jun 2015, 10:57
1
Bunuel wrote:
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\)?

A. 2

B. \(2\sqrt{2k}\)

C. \(2\sqrt{k+1}+\sqrt{k-1}\)

D. \(\frac{\sqrt{k+1}}{\sqrt{k-1}}\)

E. \(\sqrt{k+1}-\sqrt{k-1}\)

Kudos for a correct solution.


This one can be easily solved by rationalizing the expression \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\).

So multiplying and dividing the expression by \(\sqrt{k+1}-\sqrt{k-1}\).

We get, \(\frac{2}{[k+1]-[k-1]}\) * \(\sqrt{k+1}-\sqrt{k-1}\).

=\(\frac{2}{2}\) * \(\sqrt{k+1}-\sqrt{k-1}\)

that is \(\sqrt{k+1}-\sqrt{k-1}\).
Hence E.
Queens MBA Thread Master
avatar
Joined: 24 Oct 2012
Posts: 170
Concentration: Leadership, General Management
If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 18 Jun 2015, 04:13
Bunuel wrote:
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\)?

A. 2

B. \(2\sqrt{2k}\)

C. \(2\sqrt{k+1}+\sqrt{k-1}\)

D. \(\frac{\sqrt{k+1}}{\sqrt{k-1}}\)

E. \(\sqrt{k+1}-\sqrt{k-1}\)

Kudos for a correct solution.


Solution :
Rationalizing denominator by multiplying Numerator and denominator by \({\sqrt{k+1}-\sqrt{k-1}}\)

So we get \(\sqrt{k+1}-\sqrt{k-1}\) in numerator

Option E
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12676
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 18 Jun 2015, 17:36
2
Hi All,

This question has an interesting 'quirk' to it.... Even though the question tells us that K > 1, if K = 1 then you'll still end up with the correct answer....

TESTing K = 1 in the prompt gives us...

2/(√2 + √0) =
2/(√2) =

Now we have to multiply both the numerator and denominator by (√2), which simplifies to...

2(√2)/2 =
√2

So we're looking for an answer that equals √2 when K = 1....

Answer A: 2 NOT a match
Answer B: 2√2 NOT a match
Answer C: 2√2 + 0 NOT a match
Answer D: √2/0 = undefined NOT a match
Answer E: √2 - 0 This IS a MATCH

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Director
Director
avatar
G
Joined: 21 May 2013
Posts: 651
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 20 Jun 2015, 10:49
1
Bunuel wrote:
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\)?

A. 2

B. \(2\sqrt{2k}\)

C. \(2\sqrt{k+1}+\sqrt{k-1}\)

D. \(\frac{\sqrt{k+1}}{\sqrt{k-1}}\)

E. \(\sqrt{k+1}-\sqrt{k-1}\)

Kudos for a correct solution.


Let us try this by taking values
Let k=3
Equation becomes=2/2+\sqrt{2}
=\sqrt{2}/\sqrt{2}+1
=2-\sqrt{2}

Now put k=3 in the given options.
Only Option E gives the value as 2-\sqrt{2}
Answer E
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 22 Jun 2015, 07:25
Bunuel wrote:
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}\)?

A. 2

B. \(2\sqrt{2k}\)

C. \(2\sqrt{k+1}+\sqrt{k-1}\)

D. \(\frac{\sqrt{k+1}}{\sqrt{k-1}}\)

E. \(\sqrt{k+1}-\sqrt{k-1}\)

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Since there are variables in the answer choices (VIC), we should pick a number and test the choices. If k = 2, then \(\frac{2}{\sqrt{k+1}+\sqrt{k-1}}=\frac{2}{\sqrt{2+1}+\sqrt{2-1}}=\frac{2}{\sqrt{3}+\sqrt{1}}\approx{\frac{1}{1.7+1}}=\frac{2}{2.7}\) which is less than 1. Now test the answer choices and try to match the target:
Image

The correct answer is E.

Attachment:
2015-06-22_1824.png
2015-06-22_1824.png [ 60.23 KiB | Viewed 2401 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 19 Nov 2014
Posts: 72
Location: India
Concentration: Technology, General Management
Schools: ISB '18
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 04 Oct 2015, 08:51
multiply both numerator and denominator by sqrt(K+1) - sqrt(k-1) ;
and u will get the answer
_________________

KUDOS pls if you like My Post

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8461
Premium Member
Re: If k > 1, which of the following must be equal to  [#permalink]

Show Tags

New post 06 Oct 2018, 00:44
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If k > 1, which of the following must be equal to &nbs [#permalink] 06 Oct 2018, 00:44
Display posts from previous: Sort by

If k > 1, which of the following must be equal to

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.