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

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Source: — Data Sufficiency |
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by deloitte247 » Wed Apr 10, 2019 7:28 am

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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
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