B

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.

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Anyone who has never made a mistake has never tried anything new. -Albert Einstein.