It is currently 17 Nov 2017, 16:41

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

Events & Promotions in June
Open Detailed Calendar

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

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4314

Kudos [?]: 3033 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Which of the following is the closest to 11*1020–9*1010? [#permalink]

Show Tags

New post 23 Aug 2017, 01:24
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (00:56) correct 39% (01:00) wrong based on 123 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. \(10^{21}\)
[Reveal] Spoiler: OA

_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3033 [0], given: 0

1 KUDOS received
Director
Director
User avatar
P
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 315 [1], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User CAT Tests
Which of the following is the closest to 11*1020–9*1010? [#permalink]

Show Tags

New post 23 Aug 2017, 02:34
1
This post received
KUDOS
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. :-)

Kudos [?]: 315 [1], given: 261

BSchool Forum Moderator
User avatar
D
Joined: 26 Feb 2016
Posts: 1594

Kudos [?]: 667 [0], given: 17

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
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)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 667 [0], given: 17

Manager
Manager
User avatar
S
Joined: 27 Dec 2016
Posts: 171

Kudos [?]: 44 [0], given: 202

Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)
Premium Member CAT Tests
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.

Kudos [?]: 44 [0], given: 202

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4314

Kudos [?]: 3033 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3033 [0], given: 0

1 KUDOS received
Intern
Intern
avatar
B
Joined: 30 Dec 2016
Posts: 48

Kudos [?]: 13 [1], given: 60

CAT Tests
Re: Which of the following is the closest to 11*1020–9*1010? [#permalink]

Show Tags

New post 28 Aug 2017, 09:01
1
This post received
KUDOS
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


____________
Hit kudos if my post helped (:

Kudos [?]: 13 [1], given: 60

1 KUDOS received
Manager
Manager
avatar
B
Joined: 02 Nov 2015
Posts: 176

Kudos [?]: 26 [1], given: 121

GMAT 1: 640 Q49 V29
Premium Member CAT Tests
Re: Which of the following is the closest to 11*1020–9*1010? [#permalink]

Show Tags

New post 28 Aug 2017, 09:04
1
This post received
KUDOS
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

Kudos [?]: 26 [1], given: 121

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1806

Kudos [?]: 919 [0], given: 3

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

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 919 [0], given: 3

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  


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.