A5. Dion and Jaap participated in a running race. The number of runners who finished before Dion is equal to the number of runners who finished after him. The number of runners who finished before Jaap is three times the number of runners who finished after him. In the final ranking, there are 10 other participants between Dion and Jaap. No runners finished at the same time, and everyone finished the race. How many runners participated in this race?
A) 22
B) 23
C) 41
D) 43
E) 45
A5. E) 45 Let the number of participants be $n$. The number of participants who finished before Dion is $\frac{1}{2}(n-1)$ (half of all participants except Dion). The number of participants who finished before Jaap is $\frac{3}{4}(n-1)$. Since exactly 10 participants finished between Dion and Jaap, it follows that $\frac{3}{4}(n-1)-\frac{1}{2}(n-1)$ is equal to 11 (Dion himself and the 10 participants between Dion and Jaap). It follows that $\frac{1}{4}(n-1)=11$, so $n=4 \times 11+1=45$. The number of participants was therefore 45.