In a class there are 18 boys who are over 160 cm tall. If these boys constitute three-fourths of the boys and the total number of boys is two-thirds of the number of students in the class, then what is the number of girls in the class?
(a)6
(b)12
(c)18
(d)24
Answer
Answer (as printed): B
Explanation
Let the total number of students in the class be $x$. Then, number of boys $=\frac{2 x}{3}$; number of girls $=\frac{x}{3}$. Number of boys who are over 160 cm tall $=\left(\frac{3}{4} \times \frac{2 x}{3}\right)=\frac{x}{2}$. So, $\frac{x}{2}=18 \quad$ or $\quad x=36$. $$\therefore \quad \text { Number of girls }=\frac{36}{3}=12 .$$
Explanation as extracted from the printed page; notation may be imperfect.