15. There are twenty students in a class. Some of them sit in pairs so that exactly one third of the boys sit with a girl, and exactly one half of the girls sit with a boy. How many boys are there in the class?
A 9
B 12
C 15
D 16
E 18
15. B Let the number of boys in the class be $x$ and let the number of girls be $y$. Since one third of the boys sit with a girl and one half of the girls sit with a boy, we have $\frac{1}{3} x=\frac{1}{2} y$ and hence $\frac{2}{3} x=y$. The total number of students in the class is 20 . Therefore $x+\frac{2}{3} x=20$. Hence $\frac{5}{3} x=20$, which has solution $x=12$. Therefore there are 12 boys in the class.