If x/6 is a positive integer, does x have more than two different posi

From the question stem, we know that \frac{x}{6} is a positive integer. So, the possible values of x = 6, 12, 18, 24, 30, ...
The question stem asks whether x have more than two different positive prime factors. From the previous analysis, we know that the least possible prime factors are 2 and 3 (since the possible values of x are the multiple of 6)

(1) \(\frac{x}{4}\) is a positive integer.
When we consider this statement, it means that x is divisible by 4 and 6. The possible values of x are 12, 24, 36, 48, 60, ...
Let's take a look at some possible values;
x = 12 = \(2^2*3\) --> 2 prime factors
x = 60 = \(2^2*3*5\) --> 3 prime factors
(1) insufficient

(2) \(\frac{x}{9}\) is a positive integer.
When we consider this statement, it means that x is divisible by 6 and 9. The possible values of x are 18, 36, 54, 72, 90 ...
Let's take a look at some possible values;
x = 18 = \(2*3^2\) --> 2 prime factors
x = 90 = \(2*3^2*5\) --> 3 prime factors
(2) insufficient

Consider (1) and (2) together, x must be divisible by 4,6,9. The possible values of x are 36, 72, 108 ... (multiple of 36)
applying the same concept, we will know that both statements is still insufficient e.g. 36 --> 2 prime factors, \(36*5\) --> 3 prime factors

So my answer is "E"