25. A rugby team scored 24 points, 17 points and 25 points in the seventh, eighth and ninth games of their season. Their mean points-per-game was higher after 9 games than it was after their first 6 games. What is the smallest number of points that they could score in their 10th game for their mean number of points-per-game to exceed 22 ?
A 22
B 23
C 24
D 25
E 26
SOLUTION
$\mathbf{C}$

Let $X$ be the total number of points scored after 6 games and let $y$ be the number of points scored in the 10 th game. Since the mean score after 9 games is greater than the mean score after 6 games, we have $\frac{X}{6}22$ and hence $X+66+y>220$ and so $X+y>154$.

Therefore $X \leq 131$ and $X+y \geq 155$. Hence the smallest number of points they could score in the 10 th game is $155-131=24$.