For positive integers x, y, and z, the function x ? y ? z means that

Here's what I've got. Following the notation, it suggests that:

\(\frac{144}{x^{2}}\) is an integer

\(\frac{144}{x^{3}}\) is NOT an integer

Breaking down 144 into its prime factors and we get \(144 = 2^4(3^2)\).

Now, going through the possible answers to check if the number is divisible:
(A) \(144/x^2\) is an int, as \(2^2\) exists in 144. \(144/2^3\) will also be an int, as \(2^3\) exists in 144. Therefore, 2 cannot be a possible answer as we need the second result to not be an integer.
(B) \(144/x^2\) is an int, as \(3^2\) exists in 144. \(144/3^3\) will NOT be an int, as \(3^3\) is not part of 144. 3 is a possible value for x.
(C), (D), (E) follow same approach