Number Prop

[heshamelaziry]

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 B

[Brent@GMATPrepNow]

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]

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

[Brent@GMATPrepNow]

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.

[heshamelaziry]

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

Brent wrote x could equal 4 (1+2+4=7) insuffecient. why this is wrong ?

B says any 2 positive factors " The sum of any two distinct positive factors of x is odd" this applies to 4 . B does not say prime numbers only. I don't understand

[okigbo]

2+4=6 which is not odd so 4 cannot be the answer. No other number except for 2 will have ANY two factors be an odd number.

[Abdulla]

Good questions Hesham, keep it up.

[palvarez]

The sum of any two distinct +ve factors = odd

odd = even + odd or odd + even

Can we have a set of factors such that the sum of any two distinct +ve factors is odd?

Yes, it is a 2-member set that consists of "even and odd". It is {1,2}. Such a number is 2.