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UKMT Senior Mathematical Challenge, 2019

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

Lucy is asked to choose $p$ , $q$ , $r$ and $s$ to be the numbers $1$ , $2$ , $3$ and $4$ , in some order, so as to make the value of $\frac{p}{q} + \frac{r}{s}$ as small as possible. What is the smallest value Lucy can achieve in this way?

(A) $\frac{7}{12}$ (B) $\frac{2}{3}$ (C) $\frac{3}{4}$ (D) $\frac{5}{6}$ (E) $\frac{11}{12}$

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