Data Sufficiency

Having issue with wording here. can someone help?

#132.

If the integer n>1, is n =2?

1) n has exactly two positive factors

2) the Difference of any two distinct positive factors of n is odd.

the Answer is B. #2 is sufficient
However .. see below

Answer:

1) n is a prime number, but n could be = to 2, 3, 5, etc. Not sufficient.

2) if n is 5.. factors are 5 and 1.. so difference is even. So could be 2. 2-1 = odd number

BUT, what about 6 -- 6-1. odd number. what about 3-2 = odd number. N and 1 are still factors.

Am i missing something in the language in Assumption #2? In #2, we stll dont know that N is a prime number. But the answer is B....

Statement 2 states that the difference of ANY two distinct positive factors of n is odd. That means the difference of ANY 2 positive factors of n must be odd.

The positive factors of 6 are - 1,2,3,6. While 6-1 is odd, 6-2 is even.

Statement 2 rules out all even numbers > 2. It also rules out all non-prime odd numbers (as 1 is a factor of all integers, the difference of an odd number and 1 will be even).

This leaves prime numbers. The factors of all prime numbers are one and itself. However, all prime numbers >2 are odd and the difference between them and 1 will always be even.

Hence, only the integer 2 satisfies ths statement.

So, Statement B is sufficient.