NEW HERE? LEARN MORE
closeclose
Last visit was: 13 May 2024, 00:29 It is currently 13 May 2024, 00:29
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

M11-18

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93187
Own Kudos [?]: 623303 [26]
Given Kudos: 81850
Send PM
CAT Tests Forum Quiz Mode
M11-18 [#permalink] New post   16 Sep 2014, 00:44
2
Kudos
24
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

59% (01:35) correct 41% (01:59) wrong based on 155 sessions
Hide Show timer Statistics
\(\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?\)

A. 1
B. 1.7
C. 2
D. 2.4
E. 3
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93187
Own Kudos [?]: 623303 [11]
Given Kudos: 81850
Send PM
CAT Tests Forum Quiz Mode
M11-18 [#permalink] New post   16 Sep 2014, 00:44
3
Kudos
8
Bookmarks
Expert Reply
Official Solution:

\(\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?\)

A. 1
B. 1.7
C. 2
D. 2.4
E. 3


First, let's simplify the expression: \(\sqrt{7 + \sqrt{48}} - \sqrt{3} = \sqrt{7 + \sqrt{16*3}} - \sqrt{3} = \sqrt{7 + 4\sqrt{3}} - \sqrt{3}\). Observe that the answer choices are all rational numbers, so irrational parts in the expression must somehow cancel each other out. This observation should be a hint that we might be able to rewrite \(7 + 4\sqrt{3}\) in a way that makes it the square of something, which would allow us to extract the square root and simplify the expression. Bearing this hint in mind, we rewrite the expression as \(4 + 4\sqrt{3} + 3\). Upon examining the expression \(4 + 4\sqrt{3} + 3\), we notice that \(4 + 4\sqrt{3} + 3 = (2 + \sqrt{3})^2\).

Therefore:

\(\sqrt{7 + \sqrt{48}} - \sqrt{3} = \)

\(=\sqrt{7 + \sqrt{16*3}} - \sqrt{3}=\)

\(=\sqrt{7 + 4\sqrt{3}} - \sqrt{3}=\)

\(=\sqrt{4 + 4\sqrt{3} + 3} - \sqrt{3}=\)

\(=\sqrt{(2 + \sqrt{3})^2} - \sqrt{3} = \)

\(=(2 + \sqrt{3}) - \sqrt{3} = 2\).

Answer: C­
avatar
Magsy
Intern
Intern
Joined: 13 Feb 2016
Posts: 6
Own Kudos [?]: 13 [8]
Given Kudos: 5
Location: United States
Schools: INSEAD Jan '17 (WD)
GMAT 1: 710 Q48 V41
GMAT 2: 760 Q49 V45
Send PM
Reviews Badge
Re: M11-18 [#permalink] New post   27 Apr 2016, 11:38
2
Kudos
6
Bookmarks
For square roots:

1. Find the nearest perfect square

\(\sqrt{14}\) would be \(\sqrt{16}=4\).


2. Divide the original number by the answer

\(14/4=3.5\)


3. Find average of square root of perfect square and your answer in part 2 above

\((3.5+4)/2=3.75\)

This approximation is accurate enough for any GMAT level questions I have come across.

For the example above. Simplify to

\(\sqrt{14} - \sqrt{3} = 3.75-1.7\)

Round down as the original question should have been slightly lower than \(\sqrt{14}\).

Answer = 2.0 (c)
General Discussion
User avatar
Harley1980
Retired Moderator
Joined: 06 Jul 2014
Posts: 1010
Own Kudos [?]: 6351 [2]
Given Kudos: 178
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Send PM
GMAT ToolKit User
Re: M11-18 [#permalink] New post   05 Apr 2015, 13:23
1
Kudos
Bunuel wrote:
\(\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?\)

A. 1.0
B. 1.7
C. 2.0
D. 2.4
E. 3.0


This question can a be a little harder if answers will not be so diverse.
Because now we can calculate roughly
\(\sqrt{48}= 6.9\)

\(\sqrt{7 + 6.9}= 3.8\)

\(3.8-\sqrt{3}=2.1\)

So nearest answer is C.
IMHO if there will be answer with 2.1 and 1.9 than rough calculation will be imposible and task will be more useful.
User avatar
Zhenek
Manager
Manager
Joined: 17 Mar 2015
Posts: 106
Own Kudos [?]: 212 [7]
Given Kudos: 4
Send PM
Re: M11-18 [#permalink] New post   03 May 2015, 02:40
4
Kudos
3
Bookmarks
Another smart way of doing this is like this:
\(\sqrt{7 + \sqrt{48}} - \sqrt{3} = X\)
\(\sqrt{7 + \sqrt{48}} = X + \sqrt{3}\)
\(7 + \sqrt{48} = 7 + 4*\sqrt{3} = (X^2+3) + 2*X*\sqrt{3}\)
Its not hard to figure out that X = 2
avatar
S
redfield
Current Student
Joined: 18 Aug 2014
Posts: 303
Own Kudos [?]: 271 [0]
Given Kudos: 80
Send PM
GMAT ToolKit User Reviews Badge
Re: M11-18 [#permalink] New post   27 Apr 2016, 10:21
Harley1980 wrote:
\(\sqrt{7 + 6.9}= 3.8\)


I have approximate for root 3 memorized but should I know roughly square root of higher numbers like 14 as well?
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11237
Own Kudos [?]: 32475 [1]
Given Kudos: 301
Send PM
Reviews Badge Forum Quiz Mode
Re: M11-18 [#permalink] New post   27 Apr 2016, 10:56
1
Bookmarks
Expert Reply
redfield wrote:
Harley1980 wrote:
\(\sqrt{7 + 6.9}= 3.8\)


I have approximate for root 3 memorized but should I know roughly square root of higher numbers like 14 as well?


Hi,
No you don't have to, whenever you encounter something of this sort, there would be better ways to do it, as GMAT is not likely to test you \(\sqrt{14}\) etc..

But say you get this kind of problems, you can always approximate..
\(\sqrt{14}=\sqrt{3}*\sqrt{5}\) = 1.7*2.2 = 3.8
so you can work with lower numbers too to get the answer
User avatar
nikhiljd
Intern
Intern
Joined: 01 Apr 2014
Posts: 37
Own Kudos [?]: 19 [0]
Given Kudos: 93
Schools: ISB '17
GMAT 1: 530 Q35 V28
GPA: 2.5
Send PM
Reviews Badge
Re: M11-18 [#permalink] New post   08 Jun 2016, 22:09
I think this is a high-quality question and I agree with explanation.
User avatar
123mba123
Intern
Intern
Joined: 14 Mar 2015
Posts: 8
Own Kudos [?]: 40 [2]
Given Kudos: 8
Location: India
Concentration: General Management, Strategy
Schools: IIMA ISB '18 IIMB
GPA: 3.53
WE:Engineering (Other)
Send PM
Re: M11-18 [#permalink] New post   02 Jul 2016, 08:08
1
Kudos
1
Bookmarks
Great question. Could not figure out that the way Bunuel has solved it.
I guessed the answer in following way though -
48 is close to 49 which is square of 7
Now sqrt of 48 will be around 7
Now it becomes sqrt of (7+7) which srt of 14. It is close to sqrt of 16 which is equal to 4.
Now 4 - sqrt of 3 = 4-1.7 = 2.3

Now answer will be slightly smaller than 2.3 as we considered sqrt of 16 rather than original sqrt of 14.
So answer will be smaller than 2.3 and within given answers, it will be equal to 2.

The way Bunual has solved it is very good. New learning. Thanks.
avatar
mbabubble
Intern
Intern
Joined: 02 Jan 2015
Posts: 5
Own Kudos [?]: [0]
Given Kudos: 3
Send PM
Re: M11-18 [#permalink] New post   08 Nov 2016, 02:47
I think this is a high-quality question and I agree with explanation. Pretty innovative question, and very close options!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93187
Own Kudos [?]: 623303 [0]
Given Kudos: 81850
Send PM
CAT Tests Forum Quiz Mode
Re: M11-18 [#permalink] New post   25 Aug 2023, 01:13
Expert Reply
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
GMAT Club Bot
gmatclubot
Re: M11-18 [#permalink]
25 Aug 2023, 01:13
Moderator:
Bunuel
Math Expert
93186 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