GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Oct 2019, 00:23

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

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

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 21 Jul 2012
Posts: 8
If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

Show Tags

New post 25 Dec 2012, 10:05
4
14
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (00:46) correct 16% (01:11) wrong based on 417 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!
Most Helpful Expert Reply
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15262
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

Show Tags

New post 14 May 2015, 23:06
5
2
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:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Most Helpful Community Reply
VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1008
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

Show Tags

New post 25 Dec 2012, 10:18
3
5
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.
_________________
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58368
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

Show Tags

New post 26 Dec 2012, 03:49
Manager
Manager
avatar
Joined: 20 Dec 2013
Posts: 224
Location: India
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#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
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4778
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

Show Tags

New post 24 Mar 2016, 10:23
1
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
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Intern
avatar
B
Joined: 27 Jul 2017
Posts: 47
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

Show Tags

New post 03 Apr 2018, 08:29
The answer must be D, i.e. 2 will be having a total power of 8 in 10!
_________________
Ujjwal
Sharing is Gaining!
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

Show Tags

New post 05 Apr 2018, 17:12
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


Let’s put the even numbers from 2 to 10 in prime factors.

2

4 = 2^2

6 = 2 x 3

8 = 2^3

10 = 2 x 5

We see that there are 8 prime factors of 2 in 10!, so 8 is the value of n.

Alternate Solution:

We know that 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Let’s find all the 2’s in this product.

The number 10 contributes 1 two.

The number 8 contributes 3 twos.

The number 6 contributes 1 two.

The number 4 contributes 2 twos.

The number 2 contributes 1 two.

Thus, we have a total of 8 twos, and so 8 is the value of n..

Answer: D
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13162
Re: If n is the greatest positive integer for which 2^n is a factor of 10!  [#permalink]

Show Tags

New post 02 May 2019, 04:40
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
Re: If n is the greatest positive integer for which 2^n is a factor of 10!   [#permalink] 02 May 2019, 04:40
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne