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

It is currently 18 Jun 2018, 21:32

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

root[root{96}+2/(5+2*root{6})] lies between

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

Hide Tags

1 KUDOS received
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 840
GMAT ToolKit User
root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 26 Jan 2012, 06:26
1
5
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:04) correct 20% (01:34) wrong based on 577 sessions

HideShow timer Statistics

\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\) lies between

A) 1 & 2
B) 2 & 3
C) 3 & 4
D) 4 & 5
E) 5 & 6
Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46143
Re: Square Root [#permalink]

Show Tags

New post 26 Jan 2012, 06:39
4
2
LM wrote:
\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\) lies between

A) 1 & 2
B) 2 & 3
C) 3 & 4
D) 4 & 5
E) 5 & 6


Multiply both nominator and denominator of \(\frac{2}{5+2*\sqrt{6}}\) by \({5-2*\sqrt{6}}\) and apply \((a+b)(a-b)=a^2-b^2\): \(\frac{2*(5-2*\sqrt{6})}{(5+2*\sqrt{6})(5-2*\sqrt{6})}=\frac{2*(5-2*\sqrt{6})}{25-24}=2*(5-2*\sqrt{6})\).

Now, \(\sqrt{6}\) is a little bit more than 2 (~2.5), hence \(2*(5-2*\sqrt{6})\approx{2(5-2*2.5)}=0\);

So we have: \(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\approx{\sqrt{\sqrt{96}+0}=\sqrt{\sqrt{96}}\) --> \(\sqrt{96}\) is more than 9 but less than 10 (~9.5), hence \(\sqrt{\sqrt{96}}\approx{\sqrt{9.5}}\), which is more than 3 but less than 4.

Answer: C.

Or another way, using the same approximations as above:
\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\approx{\sqrt{9.5+\frac{2}{5+2*2.5}}}=\sqrt{9.5+\frac{1}{5}}\approx{\sqrt{10}}\approx{3.something}\)

Answer: C.

Hope it's clear.
_________________

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46143
Re: root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 05 Jun 2013, 04:30
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on roots problems: math-number-theory-88376.html

All DS roots problems to practice: search.php?search_id=tag&tag_id=49
All PS roots problems to practice: search.php?search_id=tag&tag_id=113

Tough and tricky exponents and roots questions (DS): tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky exponents and roots questions (PS): new-tough-and-tricky-exponents-and-roots-questions-125956.html

_________________

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

5 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1099
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 05 Jun 2013, 07:27
5
LM wrote:
\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\) lies between

A) 1 & 2
B) 2 & 3
C) 3 & 4
D) 4 & 5
E) 5 & 6


\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}=\sqrt{4\sqrt{6}+\frac{2}{5+2*\sqrt{6}}}=\sqrt{2(2*\sqrt{6}+\frac{1}{5+2*\sqrt{6}})}=\sqrt{2(\frac{25+10\sqrt{6}}{5+2*\sqrt{6}})}=\sqrt{2*5(\frac{5+2\sqrt{6}}{5+2*\sqrt{6}})}=\sqrt{2*5}\)

a bit more than \(3\),C
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

3 KUDOS received
Intern
Intern
avatar
B
Joined: 09 Apr 2013
Posts: 40
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 750 Q50 V41
GPA: 3.55
WE: General Management (Non-Profit and Government)
Re: root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 05 Jun 2013, 08:15
3
Here is how I solved this:
1) Follow what Bunuel did up to a point
Bunuel wrote:
LM wrote:
\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\) lies between

A) 1 & 2
B) 2 & 3
C) 3 & 4
D) 4 & 5
E) 5 & 6


Multiply both nominator and denominator of \(\frac{2}{5+2*\sqrt{6}}\) by \({5-2*\sqrt{6}}\) and apply \((a+b)(a-b)=a^2-b^2\): \(\frac{2*(5-2*\sqrt{6})}{(5+2*\sqrt{6})(5-2*\sqrt{6})}=\frac{2*(5-2*\sqrt{6})}{25-24}=2*(5-2*\sqrt{6})\).


2) multiply out \(2(5-2\sqrt{6}) = 10-4\sqrt{6}\)
3) \(\sqrt{96} = 4\sqrt{6}\)
4) \(\sqrt{4\sqrt{6}+10-4\sqrt{6}} = \sqrt{10}\)
5) 3² = 9 and 4² = 16, so \(\sqrt{10}\) is between 3 and 4
Answer is C
1 KUDOS received
Manager
Manager
avatar
Joined: 28 Feb 2012
Posts: 112
Concentration: Strategy, International Business
Schools: INSEAD Jan '13
GPA: 3.9
WE: Marketing (Other)
GMAT ToolKit User
Re: root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 06 Jun 2013, 06:48
1
LM wrote:
\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\) lies between

A) 1 & 2
B) 2 & 3
C) 3 & 4
D) 4 & 5
E) 5 & 6


In approximation questions we can approximate, so:
\(\sqrt{96}\) is between 9 and 10, \(\sqrt{6}\) is between 2 and 3, and the expression \(\frac{2}{5+2*\sqrt{6}}\) is about 1/5 (0.20) which means it does not affect the final answer too much in our case. Since the first number is bigger than 9 and smaller than 10 its square root will be more than 3 but less than 4.

Answer is C.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Manager
Manager
avatar
Joined: 23 May 2013
Posts: 112
GMAT ToolKit User
Re: root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 06 Jun 2013, 07:30
ziko wrote:
LM wrote:
\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\) lies between

A) 1 & 2
B) 2 & 3
C) 3 & 4
D) 4 & 5
E) 5 & 6


In approximation questions we can approximate, so:
\(\sqrt{96}\) is between 9 and 10, \(\sqrt{6}\) is between 2 and 3, and the expression \(\frac{2}{5+2*\sqrt{6}}\) is about 1/5 (0.20) which means it does not affect the final answer too much in our case. Since the first number is bigger than 9 and smaller than 10 its square root will be more than 3 but less than 4.

Answer is C.


No need to solve for the second part. moment we get to know that sqrt of 96 will be approx 9 and sqrt of 9 is 3. So ans should be between 3 and 4
_________________

“Confidence comes not from always being right but from not fearing to be wrong.”

Manager
Manager
avatar
Joined: 21 Oct 2013
Posts: 189
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 16 Dec 2013, 04:49
LM wrote:
\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\) lies between

A) 1 & 2
B) 2 & 3
C) 3 & 4
D) 4 & 5
E) 5 & 6


I used ballparking. root96 rounded up to root100 is 10. root6 rounded down to root4 is 2. so I have 10+ 2/9 which is a little bigger than root9 which is 3.

Thus answer C.
Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 392
Location: India
GMAT 1: 760 Q50 V44
Re: root[root{96}+2/(√+25+2∗6√−−−−−−−−−−−−√ 5+2*root{6})] lies between [#permalink]

Show Tags

New post 01 Oct 2015, 23:58
NOTE: When ever we have an expression which contains a square root in the denominator, always rationalize the denominator.
Example: \(a/b+\sqrt{c}\)
We should multiply both the numerator and the denominator by \(b - \sqrt{c}\)


Coming to the question, first step is to rationalize \(2/(5 + 2*\sqrt{6})\)
Multiplying both numerator and denominator by \(5 - 2*\sqrt{6}\)

The expression becomes:

\((4 \sqrt{6} + 2*( 5 - 2*\sqrt{6)}/(25 - 24))\)^(1/2)
\((4 *\sqrt{6} + 10 - 4* \sqrt{6})\)^(1/2)
\(\sqrt{10} = 3. xx\)

Option C
Intern
Intern
avatar
B
Joined: 28 May 2017
Posts: 6
GMAT 1: 640 Q44 V34
Re: root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 30 Aug 2017, 04:32
No need for any complex calculations.
( 10- + 2/(5+2*2+) )^1/2
= ( 92/9+ )^1/2
= 10-/3+
= between 3 and 4
1 KUDOS received
Manager
Manager
User avatar
G
Joined: 05 Dec 2016
Posts: 114
Re: root[root{96}+2/(5+2*root{6})] lies between [#permalink]

Show Tags

New post 17 Mar 2018, 06:10
1
LM wrote:
\(\sqrt{\sqrt{96}+\frac{2}{5+2*\sqrt{6}}}\) lies between

A) 1 & 2
B) 2 & 3
C) 3 & 4
D) 4 & 5
E) 5 & 6


The fastest way for my is this : we have\(\sqrt{96}=\sqrt{6*8*2}=4*\sqrt{6}\) and \(\frac{2}{(5+2*\sqrt{6})}\) =\(\frac{2*(5-2*sqr(6))}{5^2-2^2*sqr(6)^2}\) = \(10-4*\sqrt{6}\)


so we have \(\sqrt{10}\) which must lie between the closest perfect squares \(\sqrt{9}<\sqrt{10}<\sqrt{12}\) therefore answer is C
_________________

lets all unite to reach our target together

Re: root[root{96}+2/(5+2*root{6})] lies between   [#permalink] 17 Mar 2018, 06:10
Display posts from previous: Sort by

root[root{96}+2/(5+2*root{6})] lies between

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


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®.