BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Which of the following numbers is closest to 100*(11-sqrt(

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

Which of the following numbers is closest to 100*(11-sqrt(

by fskilnik@GMATH » Thu Feb 14, 2019 12:50 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

GMATH practice exercise (Quant Class 12)

Image

Answer: [spoiler]____(B)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Feb 14, 2019 2:42 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 12)

Image

Answer: [spoiler]____(B)__[/spoiler]
100(11 - √119)(11 + √119) = 100(11² - √119²) = 100(121-119) = 100*2 = 200.

When the correct answer is multiplied by 11+√119, the result must be as close as possible to 200.
11+√119 = 11 + (a bit less than 11) = a bit less than 22.
Since 9*22 = 198, multiplying 9.2 by a bit less than 22 will yield a product close to 200.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Thu Feb 14, 2019 5:01 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 12)

Image
$$?\,\,\,:\,\,\,\,100\left( {11 - \sqrt {119} } \right)\,\,\,{\rm{approx}}{\rm{.}}$$

$$\left( {11 - \sqrt {119} } \right)\left( {11 + \sqrt {119} } \right) = {11^2} - 119 = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,11 - \sqrt {119} = {2 \over {11 + \sqrt {119} }}$$
$$100 < 119 < 121\,\,\,\, \Rightarrow \,\,\,\,10 < \sqrt {119} < 11\,\,\,\,\mathop \Rightarrow \limits^{ + 11} \,\,\,\,21 < 11 + \sqrt {119} < 22\,\,\,\, \Rightarrow \,\,\,\,{1 \over {22}} < {1 \over {11 + \sqrt {119} }} < {1 \over {21}}$$

$${2 \over {22}} < {2 \over {11 + \sqrt {119} }} < {2 \over {21}}\,\,\,\,\, \Rightarrow \,\,\,\,100 \cdot {1 \over {11}} < \underbrace {100\left( {11 - \sqrt {119} } \right)}_{{\rm{focus}}\,{\rm{!}}} < 100 \cdot {2 \over {21}}$$

$$\left. \matrix{
{{100} \over {11}} = {{99 + 1} \over {11}} = 9{1 \over {11}}\,\, \cong \,\,9.1 \hfill \cr
{{200} \over {21}} = {{210 - 10} \over {21}} = 10 - {{10} \over {21}} = 9{{11} \over {21}}\,\, \cong \,\,9.5 \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{B}} \right)$$


The correct answer is (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Post new topic Post Reply
• Page 1 of 1