Can someone answer this with explanation?

Expert replies

lanefoly: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Mar 23, 2010 5:58 pm

by lanefoly » Tue Mar 30, 2010 4:51 pm

This question is from ManhattanGMAT, they provided an answer and explanation which I don't understand.

X is divisible by 144. If X^1/3 is an integer, then which of the following is X^1/3 definitely divisible by? (choose all that apply)
a) 4
b) 8
c) 9
d) 12
Note : X^1/3 is the cubic root of X.

Thanks in advance.

Source: Beat The GMAT — Problem Solving | Tue Mar 30, 2010 4:51 pm

nitingupta5: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Fri Jul 11, 2008 8:40 am; Thanked: 2 times

by nitingupta5 » Tue Mar 30, 2010 5:50 pm

the answer is 12

el_torero: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Mon Nov 17, 2008 9:07 pm; Thanked: 3 times

by el_torero » Tue Mar 30, 2010 8:57 pm

here's my reasoning:

start by doing a prime factorization of 144: 144 = (2^4)*(3^2)

(1) if X is divisible by 144, then X = M*(2^4)*(3^2) for some positive integer M.
therefore, we're guaranteed that 2 and 3 are two of prime factors of X.

(2) if X^(1/3) is an integer, then X's prime factors must have exponents in multiples of 3.

combining the two pieces of information, we know that 2^6 and 3^3 must be prime factors of X.

so that means 2^2 and 3^1 are factors of X^(1/3), which implies 4 and 12 are factors of X. in fact, 2, 4, 6, 12 are all factors.

hope this helps.

lanefoly: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Mar 23, 2010 5:58 pm

by lanefoly » Thu Apr 01, 2010 10:04 am

Thanks el_torero. This is what I needed.

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