NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 10:21 It is currently 27 Apr 2024, 10:21
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is greatest positive integer n such that 2^n is a factor of 12^10

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
aselfmademan
Intern
Intern
Joined: 27 Sep 2011
Posts: 11
Own Kudos [?]: 114 [18]
Given Kudos: 9
Send PM
What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   27 Oct 2011, 00:06
2
Kudos
16
Bookmarks
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

82% (00:52) correct 18% (01:10) wrong based on 569 sessions
Hide Show timer Statistics
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60
ShowHide Answer
Official Answer
D
User avatar
g106
Manager
Manager
Joined: 21 Aug 2010
Posts: 130
Own Kudos [?]: 317 [4]
Given Kudos: 141
Location: United States
GMAT 1: 700 Q49 V35
Send PM
GMAT ToolKit User
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   27 Oct 2011, 00:32
2
Kudos
2
Bookmarks
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...


The given number is 12^10
=(2*2*3)^10
=(2^20)*(3^10)

So the greatest possible value for n such that 2^n can be factor of given number is 20.

Posted from my mobile device
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64948 [3]
Given Kudos: 427
Location: Pune, India
Send PM
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   27 Oct 2011, 05:02
3
Kudos
Expert Reply
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...


\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.
User avatar
aselfmademan
Intern
Intern
Joined: 27 Sep 2011
Posts: 11
Own Kudos [?]: 114 [1]
Given Kudos: 9
Send PM
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   27 Oct 2011, 08:03
1
Bookmarks
VeritasPrepKarishma wrote:
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...


\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.


Thank you very much.......... :-D I am very weak in this type of PS math :(
Could you please explain 12! math you have given ?
User avatar
g106
Manager
Manager
Joined: 21 Aug 2010
Posts: 130
Own Kudos [?]: 317 [0]
Given Kudos: 141
Location: United States
GMAT 1: 700 Q49 V35
Send PM
GMAT ToolKit User
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   27 Oct 2011, 20:32
VeritasPrepKarishma wrote:
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...


\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.



n = 10

I just counted the number of 2s till 12 since the 12! is multiplication of all numbers till 12


Do you have any faster method which can be used for bigger factorials?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64948 [2]
Given Kudos: 427
Location: Pune, India
Send PM
What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   Updated on: 11 Oct 2022, 00:49
2
Kudos
Expert Reply
Please check my signature for the link to the relevant blog posts.

Originally posted by KarishmaB on 27 Oct 2011, 20:39.
Last edited by KarishmaB on 11 Oct 2022, 00:49, edited 1 time in total.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92956
Own Kudos [?]: 619436 [0]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   07 Mar 2016, 09:36
Expert Reply
aselfmademan wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60


Similar question to practice: what-is-the-largest-integer-n-such-that-2-n-is-a-factor-of-158297.html
User avatar
D
stonecold
Alum
Joined: 12 Aug 2015
Posts: 2282
Own Kudos [?]: 3133 [0]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Send PM
GMAT ToolKit User
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   14 Mar 2016, 05:57
Nice One.
Here breaking down 12^10 => 2^20 *3^10
so 20 is our answer
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11669 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   02 Feb 2018, 11:28
1
Bookmarks
Expert Reply
Hi All,

This question comes down to exponent rules and how to 'rewrite' a number raised to a power.

12 = (2)(2)(3)

12^2 = (2^2)(2^2)(3^2) = (2^4)(3^2)
12^3 = (2^3)(2^3)(3^3) = (2^6)(3^3)

Seeing this pattern, you should be able to rewrite 12^10...

12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)

So the largest 'power of 2' that is a factor of 12^10 is 20.

Final Answer:
Show Spoiler
D


GMAT assassins aren't born, they're made,
Rich
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16609 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   05 Oct 2020, 01:28
Expert Reply
Lets write \(12^{10} in the prime factors: (2 * 2 * 3)^{10}\)

=> \((2 ^2)^{10} * (3)^{10}\)

=> \((2)^{20} * (3)^{10}\)

The greatest possible value of n = 20

Answer D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32716
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] New post   29 Nov 2022, 11:57
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 Club Bot
gmatclubot
Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink]
29 Nov 2022, 11:57
Moderators:
Bunuel
Math Expert
92954 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions