It is currently 12 Dec 2018, 10:23
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:
1 KUDOS received
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 5150
Followers: 77

Kudos [?]: 1031 [1] , given: 4640

CAT Tests
What is the least integer n such that [#permalink] New post 17 Feb 2017, 02:58
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

82% (00:55) correct 17% (01:08) wrong based on 41 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

3 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1657 [3] , given: 396

CAT Tests
Re: What is the least integer n such that [#permalink] New post 21 Feb 2017, 17:01
3
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: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1657 [1] , given: 396

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: 758
Followers: 6

Kudos [?]: 512 [1] , given: 94

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: 1232
Followers: 45

Kudos [?]: 1115 [1] , given: 7

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: 2

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: 1232
Followers: 45

Kudos [?]: 1115 [1] , given: 7

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

Manager
Manager
Joined: 09 Nov 2018
Posts: 75
Followers: 0

Kudos [?]: 5 [0], given: 1

CAT Tests
Re: What is the least integer n such that [#permalink] New post 20 Nov 2018, 15:27
sandy wrote:
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.

Please explain, is it n>=10 or n>10. How do we sure that n=10, because the question says 1/2^n<1/10^3?
Manager
Manager
Joined: 09 Nov 2018
Posts: 75
Followers: 0

Kudos [?]: 5 [0], given: 1

CAT Tests
Re: What is the least integer n such that [#permalink] New post 20 Nov 2018, 15:30
GreenlightTestPrep wrote:
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:

So, Is The answer A or B?
1 KUDOS received
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 5150
Followers: 77

Kudos [?]: 1031 [1] , given: 4640

CAT Tests
Re: What is the least integer n such that [#permalink] New post 20 Nov 2018, 16:48
1
This post received
KUDOS
Expert's post
Dear An,

the answer is A. Sandy pointed out that n=10 which is \(2^{10}\) still holds, simply because considering that the stem tells us the least AND that does not exist a number as a result of \(2^n = 1000\), we must have that \(2^{10} = 1024\), we could say that \(n > = 10\)

But these are nuances that you do know and acquire with practice. You develop a sort of instinct.

Be flexible in your approach. You can gain only benefits.

Regards
_________________

Get the 2 FREE GREPrepclub Tests

Manager
Manager
Joined: 09 Nov 2018
Posts: 75
Followers: 0

Kudos [?]: 5 [0], given: 1

CAT Tests
Re: What is the least integer n such that [#permalink] New post 21 Nov 2018, 16:52
Carcass wrote:
Dear An,

the answer is A. Sandy pointed out that n=10 which is \(2^{10}\) still holds, simply because considering that the stem tells us the least AND that does not exist a number as a result of \(2^n = 1000\), we must have that \(2^{10} = 1024\), we could say that \(n > = 10\)

But these are nuances that you do know and acquire with practice. You develop a sort of instinct.

Be flexible in your approach. You can gain only benefits.

Regards


I got it now. I was confused with this basic thing.

1024 > 1000
so
1/1024 < 1/1000
Intern
Intern
Joined: 07 Aug 2016
Posts: 42
Followers: 0

Kudos [?]: 12 [0], given: 0

CAT Tests
Re: What is the least integer n such that [#permalink] New post 23 Nov 2018, 13:02
Carcass wrote:


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


0.001 means 10^-3 means 1/1,000

So anything larger than 1,000

2^10 = 1,024

Answer choice A
Manager
Manager
Joined: 23 Oct 2018
Posts: 58
Followers: 0

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

CAT Tests
Re: What is the least integer n such that [#permalink] New post 27 Nov 2018, 21:37
it was one of questions in the exam
Intern
Intern
User avatar
Joined: 30 Nov 2018
Posts: 12
GRE 1: Q164 V164
Followers: 0

Kudos [?]: 8 [0], given: 12

Re: What is the least integer n such that [#permalink] New post 03 Dec 2018, 05:07
Alternative solution. I multiplied by 1000 in the beginning so:

1000 / 2^n < 1
8*125 / 2^n < 1 ( factoring the 2s out of 1000 )
=>
2^n > 8*125 ( the denomenator should be > numerator ) then divide all by 8=2^3
2^(n-3) > 125
=>
2^7 > 128
=>
n-3 = 7
=>
n = 10
Re: What is the least integer n such that   [#permalink] 03 Dec 2018, 05:07
Display posts from previous: Sort by

What is the least integer n such that

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.