Register    Login    Search    Rss Feeds

Forums Home » Ask An Instructor » GMAT Math » Manhattan GMAT Math Strategy Guides


 Page 1 of 1 [ 3 posts ] 



  Print view Print view Previous topic Previous topic | Next topic Next topic
 

Divisibility: Advanced Strategy pg. 124

Author Message
omalkin20
 Post subject: Divisibility: Advanced Strategy pg. 124
 Post Posted: Sun Aug 28, 2011 9:50 pm 
Offline
Course Students


Posts: 1
My question comes from Strategy Guide 1, pg. 124. The answer is not clear to me for the questions, "If k^3 is divisible by 240, what is the least possible value of integar k?". I picked (B) 30 because 30 contains the factors 2,3,5, which 240 also contains. How do we know there should be 2 2s in the prime box and not just 1? Thanks, appreciate a clearer explanation.
Top 
mithunsam
 Post subject: Re: Divisibility: Advanced Strategy pg. 124
 Post Posted: Mon Aug 29, 2011 11:01 am 
Offline
Course Students


Posts: 76
240 = 2^4 * 3 * 5

For k^3 to be a multiple of 240, k^3 should contain four 2s, one 3 and one 5.

if you take k = 2*3*5, then k^3 will be 2^3 * 3^3 * 5^3, which is not a multiple of 240 (still short of one 2).

[If you want to test it... 2^3 * 3^3 * 5^3 = (2^3 * 3 * 5) * 3^2 * 5^2 = (120) * 3^2 * 5^2]

Since we are short of 2, we have to increase the power of 2 in k. Now try k = 2^2 * 3 * 4

Now, k^3 = (2^2 * 3 * 4)^3 = 2^6 * 3^3 * 4^3, which satisfies the minimum criteria of four 2s, one 3 and one 5.

[If you want to try it... 2^6 * 3^3 * 4^3 = (2^4 * 3 * 5) * 2^2 * 3^2 * 5^2 = (240) * 2^2 * 3^2 * 5^2]
Top 
jnelson0612
 Post subject: Re: Divisibility: Advanced Strategy pg. 124
 Post Posted: Sat Sep 17, 2011 11:07 pm 
Offline
ManhattanGMAT Staff


Posts: 1857
mithunsam, once again, great job! Thanks!

_________________
Jamie Nelson
ManhattanGMAT Instructor
Top 
Display posts from previous:  Sort by  
 
 Page 1 of 1 [ 3 posts ] 





Who is online

Users browsing this forum: No registered users and 0 guests

 
 

 
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to: