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

It is currently 15 Jan 2019, 21:54

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 in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     January 15, 2019

     January 15, 2019

     10:00 PM PST

     11:00 PM PST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.

(7+43+7-43)2 is equal to which of the following?

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

Hide Tags

 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6799
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
(7+43+7-43)2 is equal to which of the following?  [#permalink]

Show Tags

New post 09 Jan 2019, 23:33
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:00) correct 26% (01:16) wrong based on 38 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

\((\sqrt{7+4√3}+\sqrt{7-4√3})^2\) is equal to which of the following?

\(A. 32\)
\(B. 30\)
\(C. 24\)
\(D. 16\)
\(E. 12\)

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Director
Director
User avatar
V
Joined: 06 Jan 2015
Posts: 562
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Premium Member
(7+43+7-43)2 is equal to which of the following?  [#permalink]

Show Tags

New post Updated on: 11 Jan 2019, 07:11
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\((\sqrt{7+4√3}+\sqrt{7-4√3})^2\) is equal to which of the following?

\(A. 32\)
\(B. 30\)
\(C. 24\)
\(D. 16\)
\(E. 12\)


\((\sqrt{7+4√3}+\sqrt{7-4√3})^2\) ==> \(a^2+b^2+2ab\)

=\(7+4√3+7-4√3+2((\sqrt{7+4√3})(\sqrt{7-4√3})\)

=\((a+b)(a-b)=a^2-b^2\)

=7+7+2(7^2-(√3*16)^2)

=14+2

=16

Hence D
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution


Originally posted by NandishSS on 10 Jan 2019, 00:52.
Last edited by NandishSS on 11 Jan 2019, 07:11, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 16 Jul 2018
Posts: 3
Re: (7+43+7-43)2 is equal to which of the following?  [#permalink]

Show Tags

New post 11 Jan 2019, 07:03
NandishSS wrote:

=7+7+2(7^2-√3*16)

=14+2



NandishSS Can you please explain how you reduced 2(7^2-√3*16) to 2?
Director
Director
User avatar
V
Joined: 06 Jan 2015
Posts: 562
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Premium Member
Re: (7+43+7-43)2 is equal to which of the following?  [#permalink]

Show Tags

New post 11 Jan 2019, 07:11
1
jedijodes wrote:
NandishSS wrote:

=7+7+2(7^2-√3*16)

=14+2



NandishSS Can you please explain how you reduced 2(7^2-√3*16) to 2?


(7^2-(√3*16)^2)

49-48=1

There was a typo so edited.
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Intern
Intern
User avatar
B
Joined: 20 Mar 2018
Posts: 37
Location: Ghana
Concentration: Finance, Real Estate
(7+43+7-43)2 is equal to which of the following?  [#permalink]

Show Tags

New post 11 Jan 2019, 08:10
1
((7+4(3)^1/2)^1/2 + ((7-4(3)^1/2)^1/2)^2 is in the form (x+y)^2
Where x= (7+4(3)^1/2)^1/2 and y= (7-4(3)^1/2)^1/2
(x+y)^2 = x^2+y^2 +2(XY)
(7+4(3)^1/2)+(7-4(3)^1/2)+2((7+4(3)^1/2)(7-4(3)^1/2))
(4(3)^1/2) crosses out
Now we have 7+7+2(difference of squares)
Diff of squares =((7)^2-(4(3)^1/2)^2)^1/2) =(49-16(3))^1/2 =1
Now 7+7+2(1)=16 Ans is D

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 09 Mar 2018
Posts: 162
Location: India
Re: (7+43+7-43)2 is equal to which of the following?  [#permalink]

Show Tags

New post 11 Jan 2019, 10:04
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\((\sqrt{7+4√3}+\sqrt{7-4√3})^2\) is equal to which of the following?

\(A. 32\)
\(B. 30\)
\(C. 24\)
\(D. 16\)
\(E. 12\)


just a question of \((a+b)^2\) and a\(^2 - b ^2\) = (a-b) (a+b)

= 7+4√3+7-4√3 + 2 *\(\sqrt{7+4√3}\) * \(\sqrt{7-4√3}\)
= 14 + 2

Ans D.
_________________

Currently taking a holistic approach towards GMAT.

Be a good critique, If you don't like my approach.

Manager
Manager
avatar
B
Joined: 18 Oct 2018
Posts: 51
Location: India
Concentration: Finance, International Business
GPA: 4
WE: Business Development (Retail Banking)
Re: (7+43+7-43)2 is equal to which of the following?  [#permalink]

Show Tags

New post 11 Jan 2019, 10:10
((7+4(3)^1/2)^1/2 + ((7-4(3)^1/2)^1/2)^2
(a+b)^2= a^2+b^2+2*a*b
Thus (7+4(3)^1/2)+(7-4(3)^1/2)+2((7+4(3)^1/2)(7-4(3)^1/2
Diff of squares =((7)^2-(4(3)^1/2)^2)^1/2) =(49-16(3))^1/2 =1
Now 7+7+2(1)=16
Ans is D
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6799
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: (7+43+7-43)2 is equal to which of the following?  [#permalink]

Show Tags

New post 13 Jan 2019, 17:03
=>

You should recall two properties about nested radicals:
\(\sqrt{a+b+2√ab}= √a+√b,\)
\(\sqrt{a+b-2√ab}= √a-√b,\) where \(a > b.\)

Together, these yield
\((\sqrt{7+4√3}+\sqrt{7-4√3})^2\)
\(= (\sqrt{7+2√12}+\sqrt{7-2√12})^2\)
\(= (√4+√3+√4-√3)^2\)
\(= (2√4)^2\)
\(= 16\)

Therefore, the answer is D.
Answer: D
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

GMAT Club Bot
Re: (7+43+7-43)2 is equal to which of the following? &nbs [#permalink] 13 Jan 2019, 17:03
Display posts from previous: Sort by

(7+43+7-43)2 is equal to which of the following?

  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®.