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

It is currently 20 May 2019, 00:12

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

Which of the following is closest to the value of (√21 - √7)^2?

  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: 55172
Which of the following is closest to the value of (√21 - √7)^2?  [#permalink]

Show Tags

New post 30 Jun 2018, 23:53
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (01:23) correct 40% (01:28) wrong based on 243 sessions

HideShow timer Statistics

Intern
Intern
avatar
Joined: 26 Mar 2015
Posts: 10
Re: Which of the following is closest to the value of (√21 - √7)^2?  [#permalink]

Show Tags

New post 01 Jul 2018, 00:07
this is of the form a2-2ab+b2
so we have (sqrt21)^2 - 2 sqrt(21*7) + sqrt7^2
= 21 - 2(sqrt 147) + 7
=28- 2 (sumthin more little more than 12) as 12 sqare is 144
=28-24 = 4 , now ans should be littler less than 4 as we have srt 147 , which is little more than 12

so ans 3
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Which of the following is closest to the value of (√21 - √7)^2?  [#permalink]

Show Tags

New post 01 Jul 2018, 02:43
1
Bunuel wrote:
Which of the following is closest to the value of \((\sqrt{21}-\sqrt{7})^2\)?

A. 4
B. 5
C. 7
D. 16
E. 196


21 lies between \(16(4^2)\) and \(25(5^2)\) and the square root of 21 is little over 4.5 \((4.5^2 = 20.25)\)
Similarly, 7 lies between \(4(2^2)\) and \(9(3^2)\) and the square root of 7 is a little over 2.6 \((2.6^2 = 6.76)\)

Therefore, the value closest to \((\sqrt{21}-\sqrt{7})^2\) is \((4.5 - 2.6)^2 = (1.9)^2\) = approximately 4(Option A)
_________________
You've got what it takes, but it will take everything you've got
Intern
Intern
avatar
B
Joined: 27 May 2017
Posts: 5
GMAT 1: 490 Q39 V19
GPA: 4
Reviews Badge CAT Tests
Re: Which of the following is closest to the value of (√21 - √7)^2?  [#permalink]

Show Tags

New post 01 Jul 2018, 04:23
= 21+ 7- 2*sqrt21* sqrt 7
=28 - 2* sqrt(3*7*7)
=28 - 2* 7*sqrt3
=28 - 14*sqrt3
=28 - (14* 1.73)
=28- 24.24 = 3.76 ~ 4
So answer is A
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7672
Which of the following is closest to the value of (√21 - √7)^2?  [#permalink]

Show Tags

New post 01 Jul 2018, 05:22
Bunuel wrote:
Which of the following is closest to the value of \((\sqrt{21}-\sqrt{7})^2\)?

A. 4
B. 5
C. 7
D. 16
E. 196


Of course GMAT won't require to know square roots of anything more than 5 apart from perfect squares

\((\sqrt{21}-\sqrt{7})^2=√21^2+√7^2-2*√21*√7=21+7-2*√3*√7*√7=28-14√3=28-14*1.73=14(2-1.73)=14*0.27\)
So slightly less than 14*0.3=4.2
So closest is 4

A
_________________
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6152
Location: United States (CA)
Re: Which of the following is closest to the value of (√21 - √7)^2?  [#permalink]

Show Tags

New post 04 Jul 2018, 19:08
Bunuel wrote:
Which of the following is closest to the value of \((\sqrt{21}-\sqrt{7})^2\)?

A. 4
B. 5
C. 7
D. 16
E. 196


Foiling we have:

(√21)^2 + (√7)^2 - 2(√21)(√7) = 21 + 7 - 2√147

Since √147 is a little more than 12, we have:

21 + 7 - 2(12) = 28 - 24 = 4

Alternate Solution:

We can use approximation to solve this problem quickly. We see that √21 is close to 5, and √7 is close to 3. Therefore (5 - 3)^2 = 4.

Alternate Solution:

We note that √21 = √(7*3) = (√7)*(√3). Then,

(√21 - √7)^2 = (√7*√3 - √7)^2 = [(√7)^2][√3 - 1]^2 = 7*(√3 - 1)^2

We note that √3 is approximately 1.7; thus we can approximate as

(√21 - √7)^2 ≈ 7 * (1.7 - 1)^2

(√21 - √7)^2 ≈ 7 * (0.7)^2

(√21 - √7)^2 ≈ 7 * (0.49) = 3.43

The closest value among the choices is A.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
User avatar
G
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 248
Re: Which of the following is closest to the value of (√21 - √7)^2?  [#permalink]

Show Tags

New post 10 Mar 2019, 14:14
Here's the calculation if you estimate square roots:

(√3*√7 - √7)² = (1.7*2.65 - 2.65)² ...estimate 2.65 to 3 here... (3*[1.7 - 1])² = (3*.7)² = 2.1² ≈ 4, A
GMAT Club Bot
Re: Which of the following is closest to the value of (√21 - √7)^2?   [#permalink] 10 Mar 2019, 14:14
Display posts from previous: Sort by

Which of the following is closest to the value of (√21 - √7)^2?

  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®.