Exists a perfect square that divided by 6 equals a prime number?

Question

I recently took a test and a question came up that asked the question:

If n is a prime number, then 6n could NOT be:
A. An even number 
B. An integer 
C. A multiple of 3 
D. A perfect square 
E. A whole number

I was able to rule out all the options except D, but I felt like it was possible for a prime number multiplied by 6 to be a perfect square, but I couldn’t think of any possible cases.

Answer 1

$6n=2\cdot3\cdot n$

For this to be a perfect square, $n$ would need to have $2$ and $3$ as factors because each prime factor needs to occur an even number of times. Since $n$ is prime it could not have both $2$ and $3$ as factors. Therefore, $6n$ cannot be a perfect square.