Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Aug 2016, 15:18
GMAT Club 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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is the greatest positive integer for which 2n is a fact

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 21 Jul 2012
Posts: 11
Followers: 0

Kudos [?]: 6 [1] , given: 17

If n is the greatest positive integer for which 2n is a fact [#permalink]

Show Tags

New post 25 Dec 2012, 10:05
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

82% (01:31) correct 18% (00:28) wrong based on 207 sessions

HideShow timer Statistics

If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!
[Reveal] Spoiler: OA
1 KUDOS received
VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 170

Kudos [?]: 1169 [1] , given: 62

GMAT ToolKit User Premium Member
Re: If n is the greatest positive integer for which 2n is a fact [#permalink]

Show Tags

New post 25 Dec 2012, 10:18
1
This post received
KUDOS
In the questions where you are supposed to find out the maximum power of a prime factor which is a factor of n!, keep one only on thing in mind:
Let the prime number you are looking for be x, then:
\(n/x + n/x^2 + n/x^3.........n/x^k\) where \(x^k\) <=n.
If you apply this rule here,
\(10/2 +10/2^2 +10/2^3\) or 5+2+1=8.
Hence maximum power of 2 in \(10!\) will be 8.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34393
Followers: 6244

Kudos [?]: 79304 [0], given: 10016

Re: If n is the greatest positive integer for which 2n is a fact [#permalink]

Show Tags

New post 26 Dec 2012, 03:49
Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 273
Location: India
Followers: 0

Kudos [?]: 76 [0], given: 29

Re: If n is the greatest positive integer for which 2n is a fact [#permalink]

Show Tags

New post 09 Jan 2014, 10:44
We can count the total number of powers of 2 in 10!
There are 8 of them.So answer D.

Posted from my mobile device Image
1 KUDOS received
Manager
Manager
User avatar
Status: In pursuit of excellence...
Joined: 26 Oct 2013
Posts: 154
Location: India
Schools: ISB '16 (M)
GMAT 1: 610 Q46 V28
GMAT 2: 720 Q49 V40
WE: Project Management (Other)
Followers: 5

Kudos [?]: 53 [1] , given: 175

Reviews Badge
Re: If n is the greatest positive integer for which 2n is a fact [#permalink]

Show Tags

New post 09 Jan 2014, 13:22
1
This post received
KUDOS
1
This post was
BOOKMARKED
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10


Solution:
On a closer look this Qs is asking how many 2s are there in multiplication of 10!
Now, as we know 10! can be written as -- 10.9.8.7.6.5.4.3.2.1

As this is a small multiplication ( To review , not to do), we can check how many 2s we have in this..,
So, 10-1 (no.of 2s), 8-3(no.of 2s), 6-1(no.of 2s),4-2(no.of 2s),2-1(no.of 2s)

Adding all, we'll have 1+3+1+2+1=8

Hence, ans. D.

Hope this helps
Dj. :wink:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11029
Followers: 509

Kudos [?]: 133 [0], given: 0

Premium Member
Re: If n is the greatest positive integer for which 2n is a fact [#permalink]

Show Tags

New post 14 May 2015, 15:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7136
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 310

Kudos [?]: 2118 [1] , given: 161

Re: If n is the greatest positive integer for which 2n is a fact [#permalink]

Show Tags

New post 14 May 2015, 23:06
1
This post received
KUDOS
Expert's post
Hi All,

Many Test Takers get these types of questions wrong because they move too quickly through the work and don't do enough work on their pads. It's a relatively straight-forward prompt though...

We're essentially asked to find all the "2"s inside 10!

The 'key' to this question is to realize that some values have MORE THAN ONE 2 in them....

10! = (10)(9)(8)(7)(6)(5)(4)(3)(2)(1)

10 = 5x2 --> one 2
8 = 2x2x2 --> three 2s
6 = 3x2 --> one 2
4 = 2x2 --> two 2s
2 = 1x2 --> one 2

1+3+1+2+1 = eight 2s

Final Answer:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Math Forum Moderator
User avatar
Status: Moving Towards Perfection Now
Joined: 11 Jun 2011
Posts: 1186
Location: India
Concentration: International Business, Finance
Schools: ISB
WE: Corporate Finance (Commercial Banking)
Followers: 32

Kudos [?]: 296 [0], given: 209

GMAT ToolKit User Premium Member CAT Tests
Re: If n is the greatest positive integer for which 2n is a fact [#permalink]

Show Tags

New post 24 Mar 2016, 10:23
curtis0063 wrote:
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?

A. 2
B. 4
C. 6
D. 8
E. 10

Is any one can provide a solution for this question?It's from GWD. Thanks!


\(\frac{10}{2}\) = 5
\(\frac{5}{2}\) = 2
\(\frac{2}{2}\) = 1

Now, 5+2+1 = 8

Hence the highest power of 2 that will divide 10! is 8
_________________

Abhishek....

Re: If n is the greatest positive integer for which 2n is a fact   [#permalink] 24 Mar 2016, 10:23
    Similar topics Author Replies Last post
Similar
Topics:
27 Experts publish their posts in the topic If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to lpetroski 19 28 Mar 2016, 10:27
3 Experts publish their posts in the topic There is a sequence ni such, in which i is a positive integer, ni+1=2n MathRevolution 3 21 Mar 2016, 04:29
If m and n are positive integers and m^2 + n^2 = 40, what is gmatbull 3 01 Nov 2012, 07:56
6 Experts publish their posts in the topic What is greatest positive integer n such that 2^n is a factor of 12^10 aselfmademan 10 27 Oct 2011, 00:06
15 Experts publish their posts in the topic If (n-2)! = (n! + (n-1)!)/99, and n is a positive integer, then n=? gettinit 14 21 Nov 2010, 19:21
Display posts from previous: Sort by

If n is the greatest positive integer for which 2n is a fact

  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 and phpBB SEO

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®.