How many different prime numbers are factors of the positive integer n ?

(1) Four different prime numbers are factors of ~$2n$~.
(2) Four different prime numbers are factors of ~$n^2$~.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.