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)
Note : X^1/3 is the cubic root of X.
Thanks in advance.
My take are both A and D.
X is divisible by 144 = 12 squared = 3 * 4 * 3 * 4.
For the cubic root of x to be an integer, consider multiplying a value y to 144 to get x such that cubic root of 3*4*3*4*y is an integer. Basic exponents tells us that until y is another 3*4, it is practically not possible to get a cubic root which is also an integer. Thus after calculating the cube root what remains is a 3*4, certainly divisible by both A and D options given.
I am AWESOME and it's gonna be LEGENDARY!!!