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

It is currently 01 Oct 2014, 06:30

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 p is the product of the integers from 1 to 30, inclusive,

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 31 Oct 2007
Posts: 115
Location: Frankfurt, Germany
Followers: 1

Kudos [?]: 22 [0], given: 0

If p is the product of the integers from 1 to 30, inclusive, [#permalink] New post 17 Jul 2008, 01:55
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18

Show the quickest way to solve this.
_________________

Jimmy Low, Frankfurt, Germany
Blog: http://mytrainmaster.wordpress.com
GMAT Malaysia: http://gmatmalaysia.blogspot.com

Director
Director
User avatar
Joined: 12 Jul 2008
Posts: 519
Schools: Wharton
Followers: 15

Kudos [?]: 102 [0], given: 0

Re: Math Set 1: Q15 [#permalink] New post 17 Jul 2008, 02:58
jimmylow wrote:
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18

Show the quickest way to solve this.


C

Since 3 is a prime number, the numbers 1 to 30 that are relevant here are only numbers with 3 as a factor, i.e., multiples of 3:

3, 6, 9...27, 30

3 numbers have 3 as a factor multiple times: 9, 18, 27. 7 have 3 as a factor only once.
9 = 3^2
18 = 2*3^2
27 = 3^3

Counting up:
7+2+2+3 = 14
Manager
Manager
User avatar
Joined: 11 Apr 2008
Posts: 129
Location: Chicago
Followers: 1

Kudos [?]: 32 [0], given: 0

Re: Math Set 1: Q15 [#permalink] New post 06 Aug 2008, 16:52
jimmylow wrote:
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18

Show the quickest way to solve this.


Fastest way to solve:

30/3 = 10
10/3 = 3 (with a remainder)
3/3 = 1

Then just add up the quotients: 10 + 3 + 1 = 14
C :)
_________________

Factorials were someone's attempt to make math look exciting!!!

VP
VP
avatar
Joined: 17 Jun 2008
Posts: 1406
Followers: 7

Kudos [?]: 118 [0], given: 0

Re: Math Set 1: Q15 [#permalink] New post 06 Aug 2008, 18:12
jimmylow wrote:
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18

Show the quickest way to solve this.


3,6,9,12,15,18,21,24,27,30 -------> total is 14 => k=14 can be the highest power of 3 to make 3^k a divisor of p
_________________

cheers
Its Now Or Never

Re: Math Set 1: Q15   [#permalink] 06 Aug 2008, 18:12
    Similar topics Author Replies Last post
Similar
Topics:
14 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
If p is the product of the integers from 1 to 30, inclusive, dancinggeometry 5 05 Sep 2008, 23:24
If p is the product of the integers from 1 to 30, inclusive, nakib77 4 11 Nov 2005, 04:22
If p is the product of the integers from 1 to 30, inclusive, mbassmbass04 6 01 Oct 2005, 05:16
If p is the product of the integers from 1 to 30, inclusive, Antmavel 6 16 Oct 2004, 05:56
Display posts from previous: Sort by

If p is the product of the integers from 1 to 30, inclusive,

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.