11. The numbers $a, b, c$ and $d$ are distinct positive integers chosen from 1 to 10 inclusive. What is the least possible value $\frac{a}{b}+\frac{c}{d}$ could have?
A $\frac{2}{10}$
B $\frac{3}{19}$
C $\frac{14}{45}$
D $\frac{29}{90}$
E $\frac{25}{72}$
11. C To obtain the smallest value, the numerators should be as small as possible, so 1 or 2 , and the denominators should be as large as possible, so 9 or 10 . The two possible candidates are $\frac{1}{10}+\frac{2}{9}$ and $\frac{1}{9}+\frac{2}{10}$. The first gives $\frac{9}{90}+\frac{20}{90}=\frac{29}{90}$, and the second gives $\frac{10}{90}+\frac{18}{90}=\frac{28}{90}=\frac{14}{45}$, which is smaller.