stonecold wrote:

How many positive factors does positive integer \(N\) have?

1) \(N^2\) has three positive factors

2) \(2N\) has four positive factors

Source->

Magoosh From Statement 1:

It is only possible when N is a prime number, hence sufficient.

From Statment 2 we'll have 2 cases possible:

Case 1: N is a prime number other than 2

Take N = 5, 2N = 10 = 2*5 ==> 2N has 4 factors, and N has 2 factors.

Case 2: N is a non-prime number

Take N = 4 , 2N = 8 = 2^3 => 2N has 4 factors, and N has 3 factors.

So no unique answer is possible. NOT sufficient.

Thanks.