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Divisibility problem

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Junior | Next Rank: 30 Posts
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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!
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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
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Junior | Next Rank: 30 Posts
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by daygoballa » Sun May 24, 2009 1:34 am
the answer is 4 and 12...thank you!
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by alexdallas » Sat Aug 15, 2009 4:54 pm
tks baws
best explanation ive seen on this problem.
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