These ones can get a bit nasty.

(1) From the statement, it says four different prime numbers are factors of 2n. But it is not clear whether 2 is one of these prime numbers. Because if n is even, the presence of 2n would not add a prime factor. But in case of odd n, 2 would act as a supplement prime factor. So the number of prime factors change with even or odd n.

For Example.

If n = 2 * 3 * 5 * 7 (here n has 4 prime factors), then 2n = 2 * 2 * 3 * 5 * 7. Here 2n has 4 prime factors.

If n = 3 * 5 * 7 (here n has 3 prime factors), then 2n = 2 * 3 * 5 * 7. Here 2n has 4 prime factors.

From the above examples, it can be seen that number of different prime numbers may vary; NOT sufficient.

(2) Four different prime numbers are factors of n² implies four different prime numbers are factors of n as well; SUFFICIENT.

## Please log in or register to add a comment.