11. There were five teams entered in a competition. Each team consisted of either only boys or only girls. The number of team members was $9,15,17,19$ and 21. After one team of girls had been knocked out of the competition, the number of girls still competing was three times the number of boys. How many girls were in the team that was eliminated?
A 9
B 15
C 17
D 19
E 21
Solution
E

The total number of team members is $9+15+17+19+21=81$. Let $x$ be the number of girls in the team eliminated. Then the number of remaining players is $81-x$ and a quarter of these must be boys (since there remains three times as many girls as boys). The values of $\frac{81-x}{4}$ for $x=9,15,17,19$ and 21 are $18,16.5,16,15.5$ and 15 respectively. The only one of the latter list which equals the number of members of a team is 15 (when $x=21$ ) and none of the latter list can be made by a combination of two or more of $9,15,17,19$ and 21 . Therefore the team eliminated consisted of 21 girls. This left a team of 15 boys and teams of 9,17 and 19 girls. The total number of girls left was 45 and this was three times the number of boys.