If n is the product of the integers from 1 to 20 inclusive, : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 06 Dec 2016, 10:12
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.

Close

Request Expert Reply

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is the product of the integers from 1 to 20 inclusive,

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

Hide Tags

Manager
Manager
avatar
Joined: 24 Jun 2009
Posts: 60
Followers: 2

Kudos [?]: 71 [0], given: 2

If n is the product of the integers from 1 to 20 inclusive, [#permalink]

Show Tags

New post 22 Nov 2009, 17:05
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

85% (01:38) correct 15% (01:11) wrong based on 141 sessions

HideShow timer Statistics

If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which \(2^k\) is a factor of n?

A. 10
B. 12
C. 15
D. 18
E. 20
[Reveal] Spoiler: OA
Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 312
Followers: 4

Kudos [?]: 158 [0], given: 37

Re: Number Properties Question [#permalink]

Show Tags

New post 22 Nov 2009, 17:13
shanewyatt wrote:
If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for
which \(2^k\) is a factor of n?
A. 10
B. 12
C. 15
D. 18
E. 20


IMO D

1*2 *3 * 4 * ....20

if we take 2 common out of all even numbers from 1 to 20, we have \(2^{18}\). Hence k=18 because \(2^{18}\)is the max factor in form \(2^K\)
_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35905
Followers: 6846

Kudos [?]: 89982 [1] , given: 10396

Re: Number Properties Question [#permalink]

Show Tags

New post 22 Nov 2009, 17:25
1
This post received
KUDOS
Expert's post
shanewyatt wrote:
If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for
which \(2^k\) is a factor of n?
A. 10
B. 12
C. 15
D. 18
E. 20


\(n=20!\) and we need to find greatest integer \(k\), for which \(2^k*n=20!\). Obviously \(k\) would be highest when \(n=1\). So basically we are asked to determine the highest power of \(2\) in \(20!\).

Finding highest power of prime in \(n!\): everything-about-factorials-on-the-gmat-85592.html

Hence the power of \(2\) in \(20!\) would be: \(\frac{20}{2}+\frac{20}{4}+\frac{20}{8}+\frac{20}{16}=10+5+2+1=18\)

Answer: D.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 19 Nov 2007
Posts: 225
Followers: 1

Kudos [?]: 247 [0], given: 1

Re: Number Properties Question [#permalink]

Show Tags

New post 22 Nov 2009, 20:01
There are 10 numbers divisible by 2
There are 5 numbers divisible by 4
There are 2 numbers divisible by 8
There is 1 number divisible by 16.

Hence the total number of 2’s in 20! are 10+5+2+1=18
Current Student
avatar
Joined: 03 Aug 2012
Posts: 916
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 23

Kudos [?]: 676 [0], given: 322

Premium Member
Re: If n is the product of the integers from 1 to 20 inclusive, [#permalink]

Show Tags

New post 19 Apr 2014, 23:49
n= 20!

And

2^K * A = n = 20!

=> 20! = 2^K * A

Mathematically , we need to find the powers of 2 contained in the factorial given.

2/4/6/8/10/12/14/16/18/20

Total contribution of '2's' is 18

Hence the answer
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12882
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: If n is the product of the integers from 1 to 20 inclusive, [#permalink]

Show Tags

New post 04 Nov 2016, 06:08
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

Math Forum Moderator
User avatar
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2093
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Followers: 81

Kudos [?]: 555 [0], given: 310

GMAT ToolKit User Premium Member CAT Tests
Re: If n is the product of the integers from 1 to 20 inclusive, [#permalink]

Show Tags

New post 04 Nov 2016, 07:32
shanewyatt wrote:
If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which \(2^k\) is a factor of n?

A. 10
B. 12
C. 15
D. 18
E. 20


Product of the integers from 1 to 20 inclusive = 20!

Highest value of \(2^k\) is

20/2 = 10
10/2 = 5
5/2 = 2
2/2 = 1

Hence the value of k will be 10 + 5 + 2 + 1 = 18

So, The correct answer will be (D) 18
_________________

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 )

Re: If n is the product of the integers from 1 to 20 inclusive,   [#permalink] 04 Nov 2016, 07:32
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic If n is the product of all the integers from 5 to 20, inclusive, what MathRevolution 4 11 Nov 2016, 00:26
8 Experts publish their posts in the topic If n is the product of the integers from 1 to 8, inclusive Bunuel 13 09 Jul 2012, 02:31
77 Experts publish their posts in the topic If n is the product of integers from 1 to 20 inclusive ajit257 23 14 Dec 2010, 17:31
29 Experts publish their posts in the topic If p is the product of the integers from 1 to 30, inclusive, gurpreet07 11 16 Sep 2009, 09:54
1 Experts publish their posts in the topic If n is the product of the integers from 1 to 8, inclusive, tinman1412 4 22 Aug 2007, 10:22
Display posts from previous: Sort by

If n is the product of the integers from 1 to 20 inclusive,

  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®.