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.
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Answer B
Statement1 2n has 4 different prime factors.
2n could be 2*3*5*7(i.e. for n 3 diff prime factors) OR 2n could be 2*2*3*5*7(i.e. 4 different prime factors for 2n and 4 different prime factors for n)
Thus INSUFF
Statement 2
n^2 has 4 different prime factors i.e.(2*3*5*7)^2 thus n will always have 4 different prime factors.
thus SUFF
hence answer is B.
Statement1 2n has 4 different prime factors.
2n could be 2*3*5*7(i.e. for n 3 diff prime factors) OR 2n could be 2*2*3*5*7(i.e. 4 different prime factors for 2n and 4 different prime factors for n)
Thus INSUFF
Statement 2
n^2 has 4 different prime factors i.e.(2*3*5*7)^2 thus n will always have 4 different prime factors.
thus SUFF
hence answer is B.
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