South African Mathematics Olympiad

15

The smallest value of $n$ is 20 (for which $\frac{1}{2}n$ is 10) and the largest value of $n$ is 49 (for which $2n$ is 98). From 20 to 49 inclusive represents 30 integers, half of which are even (so that $\frac{1}{2}n$ is an integer).