At an International Dinner, $\frac{1}{5}$ of the people attending were French men. If the number of French women at the dinner was $\frac{2}{3}$ greater than the number of French men, and there were no other French people at the dinner, then what fraction of the people at the dinner were not French?
(a)$\frac{1}{5}$
(b)$\frac{2}{5}$
(c)$\frac{2}{3}$
(d)$\frac{7}{15}$
Answer
Answer (as printed): D
Explanation
French men $=\frac{1}{5}$; French women $=\left(\frac{1}{5}+\frac{2}{3} \times \frac{1}{5}\right)=\frac{5}{15}=\frac{1}{3}$. French people $=\left(\frac{1}{5}+\frac{1}{3}\right)=\frac{8}{15}$. ∴ Not French $=\left(1-\frac{8}{15}\right)=\frac{7}{15}$.
Explanation as extracted from the printed page; notation may be imperfect.