If x and y are positive real numbers and xy = 8, then the minimum value of 2x + y is?

Answer: Option D

$$\begin{array}{rl}& xy=8\left(\text{Given}\right)\\ & \text{So, }\left(x,y\right)=\left(1,8\right)\end{array}$$
We have to question the options and check them.
$$\begin{array}{rl}& \left(8,1\right)\\ & \left(2,4\right)\\ & \left(4,2\right)\\ & \therefore 2x+y\\ & =2\times 1+8\\ & =10\\ & 2\times 8+1=11\\ & 2\times 2+4=8\left(\text{Minimum}\right)\\ & 2\times 4+2=10\end{array}$$
Hence, in this question we have all the options.
So, take all the positive factor otherwise we should have to take - ve(negative) values also.
$$\begin{array}{rl}& \left(x,y\right)=\left(1,8\right)\\ & \left(8,1\right)\\ & \left(2,4\right)\\ & \left(4,2\right)\\ & \left(-1,-8\right)\\ & \left(-8,-1\right)\\ & \left(-2,-4\right)\\ & \left(-4,-2\right)\end{array}$$