Number properties problem

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Troika: Master | Next Rank: 500 Posts; Posts: 136; Joined: Wed Apr 08, 2009 12:09 pm; Thanked: 4 times; Followed by:1 members

Number properties problem

by Troika » Mon Apr 09, 2012 5:51 pm

If p is the product of 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

OA: C

Source: OG 12, #110

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Source: Beat The GMAT — Problem Solving | Mon Apr 09, 2012 5:51 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Mon Apr 09, 2012 6:38 pm

I posted a solution here:

https://www.beatthegmat.com/product-of-t ... 94247.html

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Mon Apr 09, 2012 6:42 pm

p=30! and in there select 3,6,9,12,15,18,21,24,27,30 all the multiples of 3. Then rewrite them as the primes 3,3*2,3*3,3*2*2,3*5,3*3*2,3*7,3*2*2*2,3*3*3,3*2*5. If you noticed we have exactly 14 repeating 3s, hence the greatest factor of p will be 3^k where k=14

c

HG10 wrote:If p is the product of 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

OA: C

Source: OG 12, #110

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