Number Prop

heshamelaziry wrote:If the integer x is greater than 1, does x = 2?

A) x is evenly divisible by exactly two positive integers.
B) The sum of any two distinct positive factors of x is odd.

OA C

(A) This tells us that x is prime (it's actually the definition of a prime number)
So, x could equal 2, but it could also equal 3, 5, 7 etc --> INSUFFICIENT

(B) Factor sum is odd. So, x could equal 2 (1+2=3) or x could equal 4 (1+2+4=7)--> INSUFFICIENT

(A&B): (A) tells us that x is a prime number. Now most prime numbers (except 2) are odd, which means the two factors will be odd (1 and the prime number itself), so the sum of the factors will always be even (e.g., x=7 --> factors are 1 and 7 --> sum=8)
However, the two factors of 2 (1 and 2) add to be an odd number (3). So, x must equal 2, which means(A)&(B) are sufficient.
Answer = C

okigbo wrote:Are you sure its C? I think its B. 2 is the only even prime number that ANY factor sums will be odd...

You're absolutely right. I read it as the sum of ALL factors. I guess every word plays its role in the question
The answer is, indeed, B.