Source: Exemplar

Given that 0 < p < q < r < sandandp, q, r, s$ are integers, which of the following is the smallest?

Options

Option A is correct

p+qr+s\frac{p+q}{r+s}

Option B

p+sq+r\frac{p+s}{q+r}

Option C

q+sp+r\frac{q+s}{p+r}

Option D

r+sp+q\frac{r+s}{p+q}

Explanation

To make a fraction smallest, its numerator should be as small as possible and its denominator as large as possible. Given 0 < p < q < r < s, the sum p+qp+q is the smallest possible numerator among the options, and r+sr+s is the largest possible denominator. Therefore, p+qr+s\frac{p+q}{r+s} will be the smallest.