Let $W,X,Y$ and $Z$ be four different digits selected from the set
$\{ 1,2,3,4,5,6,7,8,9\}.$
If the sum $\dfrac{W}{X} + \dfrac{Y}{Z}$ is to be as small as possible, then $\dfrac{W}{X} + \dfrac{Y}{Z}$ must equal
$\text{(A)}\ \dfrac{2}{17} \qquad \text{(B)}\ \dfrac{3}{17} \qquad \text{(C)}\ \dfrac{17}{72} \qquad \text{(D)}\ \dfrac{25}{72} \qquad \text{(E)}\ \dfrac{13}{36}$
\[\frac{W}{X} + \frac{Y}{Z} = \frac{WZ+XY}{XZ}\]
Small fractions have small numerators and large denominators. To maximize the denominator, let $X=8$ and $Z=9$.
\[\frac{9W+8Y}{72}\]
To minimize the numerator, let $W=1$ and $Y=2$.
\[\frac{9+16}{72} = \boxed{\text{(D)}\rightarrow \frac{25}{72}}\]