Need simpler logic!

Expert replies

vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Wed Sep 18, 2013 2:39 am

If k^3 is divisible by 240 what is the least possible value of integer K?

A. 12
B. 30
C. 60
D. 90
E. 120

The earlier answers were not understandable

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

Like this post

Source: Beat The GMAT — Problem Solving | Wed Sep 18, 2013 2:39 am

vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Wed Sep 18, 2013 2:45 am

k^3/2*2*2*2*3*5
k must have two 2 one 3 and one 5, hence smallest value = 60

Like this post

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Sep 18, 2013 2:57 am

240= 2 x 3 x 2 x 2 x 5 x 2 == 2 ^ 4 x 3 x 5

hence, we would need a number that contains .. atleast TWO 2, one 3 and one 5.

The reason for TWO 2's is that if there were only one Two than cubing "k" would create only 2^3; but we need at least 2^4

So, Answer = 60 [C]

Hope this solution is understandable; feel free to ask if you have any doubts!!

Njoy!

vinay1983 wrote:If k^3 is divisible by 240 what is the least possible value of integer K?

A. 12
B. 30
C. 60
D. 90
E. 120

The earlier answers were not understandable

Last edited by theCodeToGMAT on Wed Sep 18, 2013 2:59 am, edited 1 time in total.

Like this post

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Sep 18, 2013 2:58 am

vinay1983 wrote:If k^3 is divisible by 240 what is the least possible value of integer K?

A. 12
B. 30
C. 60
D. 90
E. 120

The earlier answers were not understandable

240 = 2^4 times 3^1 times 5^1, and the smallest cube number divisible by 240 must have 2 more 2s, 2 more 3s, and 2 more 5s to become 2^6 times 3^3 times 5^3, whose cube root (k here) is [spoiler]2^2 times 3^1 times 5^1 = 60.

Pick C[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 18, 2013 7:00 am

vinay1983 wrote:If k^3 is divisible by 240 what is the least possible value of integer K?

A. 12
B. 30
C. 60
D. 90
E. 120

The approach shown by vipulgoyal and rahulmittal87 is perfect, but if you didn't spot that approach, don't forget that we can also test the answer choices.

k^3 is divisible by 240
Since 240 = (2)(2)(2)(2)(3)(5), we know that k^3 MUST HAVE at least four 2's, one 3 and one 5 in its prime factorization.

Now check the answer choices.

A) k = 12 = (2)(2)(3)
Since there's no 5 in the prime factorization of k, k^3 cannot have at least one 5 in its prime factorization
ELIMINATE A.

B) k = 15 = (2)(3)(5)
So, k^3 = (2)(3)(5)(2)(3)(5)(2)(3)(5)
As we can see, k^3 does not have at least four 2's in its prime factorization
ELIMINATE B.

C) k = 30 = (2)(2)(3)(5)
So, k^3 = (2)(2)(3)(5)(2)(2)(3)(5)(2)(2)(3)(5)
Perfect! k^3 has at least four 2's, one 3 and one 5 in its prime factorization

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review