How many different prime factors does N have?
(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.
Lets look at (1).
2N has 4 different prime factors
=> If N is odd, then N has 3 prime factors(Example N = 3x5x7)
If N is even, then N has 4 prime factors.(Example N = 2x3x5x7)
Therefor (1) is not sufficient by itself.
Lets look at (2)
N ^2 has 4 different prime factors.
Any number N, can be written as product of prime factors(not all distinct).
N = p1 x p2 x ..... x pm
=> N^2 = p1^2 x p2^2 x p3^2 x ..........x pm ^2
You can see that N^2 will have the same set of prime factors, only repeated twice. Therefore if N^2 has 4 distinct prime factors, N will also have 4 distinct prime factors.
Anyone who has never made a mistake has never tried anything new. -Albert Einstein.