It is currently 15 Nov 2018, 07:31
My Tests

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.

What is the least integer n such that

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 4876
Followers: 74

Kudos [?]: 973 [0], given: 4479

CAT Tests
What is the least integer n such that [#permalink] New post 17 Feb 2017, 02:58
Expert's post
00:00

Question Stats:

84% (00:55) correct 15% (01:17) wrong based on 32 sessions


What is the least integer n such that \(\frac{1}{2^n}\) \(< 0.001\) ?

A) 10

B) 11

C) 500

D) 501

E) There is no such least integer
[Reveal] Spoiler: OA

_________________

Get the 2 FREE GREPrepclub Tests

2 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [2] , given: 375

CAT Tests
Re: What is the least integer n such that [#permalink] New post 21 Feb 2017, 17:01
2
This post received
KUDOS
Expert's post
Explanation

We rewrite 0.001 as \(\frac{1}{1000}\) .

So if \(\frac{1}{2^n} < \frac{1}{1000}\).

Cross multiplying we can rewrite \(1000 < 2^n\).

So we know \(2^1 = 2, 2^2 =4 ....... 2^1^0 = 1024\).

So if \(n \geq 10\) then the inequality proposed in the question holds.

Hence A is the right answer.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Intern
Joined: 10 Sep 2017
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: What is the least integer n such that [#permalink] New post 18 Sep 2017, 15:53
How are we supposed to know that 2^10 = 1024??

Is there a shortcut? Thanks!
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [1] , given: 375

CAT Tests
Re: What is the least integer n such that [#permalink] New post 18 Sep 2017, 17:07
1
This post received
KUDOS
Expert's post
clausen8657 wrote:
How are we supposed to know that 2^10 = 1024??

Is there a shortcut? Thanks!


I remember with Megabyte Gigabyte relation.

1 Gigabyte is \(2^{10}\) Megabyte or 1024
.5 Gigabyte is \(2^9\) Mb or 512

I remember these nubers because these are all multiples of RAM of a computer or cellphone.

Other wise remember \(2^5\) is 32. And \(2^{10}\) is \(32^2\).
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Intern
Joined: 12 May 2016
Posts: 12
Followers: 0

Kudos [?]: 9 [0], given: 3

Re: What is the least integer n such that [#permalink] New post 21 Sep 2017, 14:15
how does cross multiplying 2^(1/n) becomes 2^n
1 KUDOS received
Director
Director
Joined: 20 Apr 2016
Posts: 743
Followers: 6

Kudos [?]: 498 [1] , given: 86

CAT Tests
Re: What is the least integer n such that [#permalink] New post 21 Sep 2017, 20:22
1
This post received
KUDOS
saumya17lc wrote:
how does cross multiplying 2^(1/n) becomes 2^n



it is \(\frac{1}{2^n}\) and not \(2^(1/n)\)
_________________

If you found this post useful, please let me know by pressing the Kudos Button

1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1175
Followers: 44

Kudos [?]: 1048 [1] , given: 6

CAT Tests
Re: What is the least integer n such that [#permalink] New post 15 Oct 2017, 15:07
1
This post received
KUDOS
Expert's post
clausen8657 wrote:
How are we supposed to know that 2^10 = 1024??

Is there a shortcut? Thanks!


It's not a bad idea to memorize powers of 2 up to 2^7
From there, you can keep multiplying by 2 to get bigger powers.

2^7 = 128
2^8 = 256
2^9 = 512
2^10 = 1024



Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Intern
Intern
Joined: 22 May 2018
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: What is the least integer n such that [#permalink] New post 20 Jun 2018, 03:32
how did you cross multiply? please explain
1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1175
Followers: 44

Kudos [?]: 1048 [1] , given: 6

CAT Tests
Re: What is the least integer n such that [#permalink] New post 20 Jun 2018, 04:56
1
This post received
KUDOS
Expert's post
Ronaksingh wrote:
how did you cross multiply? please explain


Let's do this in steps...

We have the inequality: 1/(2^n) < 1/1000
Since 2^n is always POSITIVE, we can multiply both sides by 2^n to get: 1 < (2^n)/1000
Also, since 1000 is POSITIVE, we can multiply both sides by 1000 to get: 1000 < 2^n

Here's a video on dealing with inequalities like this:

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Re: What is the least integer n such that   [#permalink] 20 Jun 2018, 04:56
Display posts from previous: Sort by

What is the least integer n such that

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.