Divisibility problem

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daygoballa: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu Feb 26, 2009 10:08 am; Location: San Diego, CA

Divisibility problem

by daygoballa » Sat May 23, 2009 3:47 pm

x is divisible by 144. If cube root of "x" is an integer, then which of the following is cube root of "x" definitely divisible by? (choose all that apply)

a. 4
b. 8
c. 9
d. 12

I simply just don't understand what the problem is asking. Can someone please interpret what the question is asking?

thank you!

Quote

Source: Beat The GMAT — Problem Solving | Sat May 23, 2009 3:47 pm

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Sat May 23, 2009 5:05 pm

I am not sure I am a little weak in these areas but my approach is that if a cube root of x is an integer, then the prime factors of x must occur in sets of 3.

Here x is divisible by 144. 144 has 2*2*2*2*3*3.

2 occurs 4 times and 3 occurs only 2 times. two more 2's are needed to make this two sets of 2's and one more 3 is needed to make it one set of 3.

so 2*2*3 = 12

So I would say x is definitely divisible by 12 and since 4 is also a divisor of 12, it would be divisible by 4 as well.

What is the OA