Given that x is a positive integer, what is the greatest

[Gmat_mission]

Given that x is a positive integer, what is the greatest common divisor (GCD) of the two positive integers, (x+m) and (x-m)?

(1) m^2 - 10m + 16 = 0
(2) x + 26 is a prime number.

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

[deloitte247]

Question=> what is the greatest common division (GCD) of the two positive integers (x+m) and (x-m)?
$$Statement 1=>m^2-10m+16=0$$
$$\left(m-8\right)\left(m-2\right)=0$$
$$m=8\ or\ 2\ \ \ \left(Value\ of\ m\ is\ unknown\right)$$
$$STATEMENT\ 1\ IS\ INSUFFICIENT$$

$$Statement 2=>x+26\ is\ a\ prime\ number$$
This means that the value of x must be a prime number or odd number, but the value of m is unknown. Hence, STATEMENT 2 IS INSUFFICIENT

Combining the two statements together;
m=8 or m=2
x+26= prime number; x is an odd number

odd + m (2 or 8) => ODD
odd - m (2 or 8) => ODD