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

It is currently 25 Apr 2019, 18:57

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 the closest to 11*1020–9*1010?

  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: 7252
GMAT 1: 760 Q51 V42
GPA: 3.82
Which of the following is the closest to 11*1020–9*1010?  [#permalink]

Show Tags

New post 23 Aug 2017, 01:24
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (01:23) correct 39% (01:29) wrong based on 146 sessions

HideShow timer Statistics

Which of the following is the closest to \(11*10^{20}–9*10^{10}\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^{10}\)
D. \(10^{20}\)
E. \(10^{21}\)

_________________
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: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
Which of the following is the closest to 11*1020–9*1010?  [#permalink]

Show Tags

New post 23 Aug 2017, 02:34
1
MathRevolution wrote:
Which of the following is the closest to \(11*10^{20}–9*10^{10}\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^{10}\)
D. \(10^{20}\)
E. \(10^{21}\)

\(11*10^{20}–9*10^{10}\)

We can use approximate value. Hence we can use \(10\) in place of \(11\) and \(10\) in place of \(9\).

\((10*10^{20}) – (10*10^{10})\)

\(10^{(20+1)}–10^{(10+1)}\)

\(10^{21}–10^{11}\)

\(10^{11}(10^{10}–1)\)

\(1\) is very small value compared to \(10^{10}\). Hence \(1\) can be ignored. Therefore \((10^{10}–1) =\) approximately \(= 10^{10}\)

\((10^{11})(10^{10})\)

\(10^{(11+10)}\) \(= 10^{21}\)

Answer (E)...

_________________
Please Press "+1 Kudos" to appreciate. :-)
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Which of the following is the closest to 11*1020–9*1010?  [#permalink]

Show Tags

New post 23 Aug 2017, 05:39
We have been asked to find the value of the expression \(11*10^{20}–9*10^{10}\)

\(11*10^{20}–9*10^{10}\)
= \(11*10^{10}*10^{10} – 9*10^{10}\)
= \(10^{10}(11*10^{10} – 9)\)

Since we need an approximate value and the overall expression has extremely large numbers,
we can assume both 11 and 9 to be equal to 10

The expression now becomes \(10^{10}(10*10^{10} – 10) = 10^{10}*10^1(10^{10} – 1) = 10^{10+1}(10^{10} – 1)\) = \(10^{11}(10^{10})\)

Since a difference of 1 does not influence the value of the expression to that extent, the value must be \(10^{21}\) approximately (Option E)
_________________
You've got what it takes, but it will take everything you've got
Manager
Manager
User avatar
G
Joined: 27 Dec 2016
Posts: 232
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Reviews Badge
Which of the following is the closest to 11*1020–9*1010?  [#permalink]

Show Tags

New post 23 Aug 2017, 19:26
MathRevolution wrote:
Which of the following is the closest to \(11*10^{20}–9*10^{10}\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^{10}\)
D. \(10^{20}\)
E. \(10^{21}\)


1. Factoring \(10^{10}\) out = \(10^{10} (11*10^{10} - 9)\)
2. Since we are asked about approximation, so we can use our estimation.
3. 11 and 10 is closest to 10, so I can change them to 10 --> \(10^{10} (10^1*10^{10} - 10^1)\) --> \(10^{10} (10^{11} - 10^1)\)
4. Difference between \(10^{11}\) and \(10^{10}\) is so HUGE, so can we can IGNORED this subtraction by \(10^1\).
5. Therefore, \(10^{10} * 10^{11} = 10^{21}\).

E.
_________________
There's an app for that - Steve Jobs.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7252
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Which of the following is the closest to 11*1020–9*1010?  [#permalink]

Show Tags

New post 25 Aug 2017, 01:13
=> \(9*10^{10}\) is a relatively small number compared with \(11*10^{20}\).
\(11*10^{20}–9*10^{10}\) is approximate to \(11*10^{20}\), which is similar to \(10^{21}\).

Ans: E
_________________
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"
Manager
Manager
avatar
G
Joined: 30 Dec 2016
Posts: 235
GMAT 1: 650 Q42 V37
GPA: 4
WE: Business Development (Other)
Premium Member Reviews Badge
Re: Which of the following is the closest to 11*1020–9*1010?  [#permalink]

Show Tags

New post 28 Aug 2017, 09:01
1
i did it this way.

Factor out 10^20 .

10^20 ( 11 - 9 * 10^-10 )
Now,
10^20 ( 11 - 0.000000009) we know from here that ( 11 - 0.000000009 ) will be 10.something .

So,
10^20 * 10.something = 10^21 .

Regards

SandySilva
_________________
Regards
SandySilva


____________
Please appreciate the efforts by pressing +1 KUDOS (:
Manager
Manager
avatar
B
Joined: 02 Nov 2015
Posts: 163
GMAT 1: 640 Q49 V29
Re: Which of the following is the closest to 11*1020–9*1010?  [#permalink]

Show Tags

New post 28 Aug 2017, 09:04
1
sandysilva wrote:
i did it this way.

Factor out 10^20 .

10^20 ( 11 - 9 * 10^-10 )
Now,
10^20 ( 11 - 0.000000009) we know from here that ( 11 - 0.000000009 ) will be 10.something .

So,
10^20 * 10.something = 10^21 .

Regards

SandySilva

Great one !!!!

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5870
Location: United States (CA)
Re: Which of the following is the closest to 11*1020–9*1010?  [#permalink]

Show Tags

New post 29 Aug 2017, 17:21
MathRevolution wrote:
Which of the following is the closest to \(11*10^{20}–9*10^{10}\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^{10}\)
D. \(10^{20}\)
E. \(10^{21}\)


Since 9 x 10^10 is much smaller than 11 x 10^20, magnitude-wise, subtracting it from 11 x 10^20 would still be about 11 x 10^20. Since 11 is close to 10, 11 x 10^20 is approximately 10 x 10^20, magnitude-wise, and we have:

10 x 10^20 = 10^21

Answer: E
_________________

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

GMAT Club Bot
Re: Which of the following is the closest to 11*1020–9*1010?   [#permalink] 29 Aug 2017, 17:21
Display posts from previous: Sort by

Which of the following is the closest to 11*1020–9*1010?

  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®.