18) In a large office, there are 84 employees, each of whom knows at least one language between English and German; furthermore, the $20 \%$ of those who speak English also speak German, and the $80 \%$ of those who speak German also speak English. How many employees in that office know both languages?

(A) 12, (B) 14, (C) 15, (D) 16, (E) 18.
18. The answer is (D). Let $I$ be the number of employees who speak English, $T$ be the number of employees who speak German, and $B$ be the number of employees who speak both languages. The data in the problem tells us that $20\%$ of $I$, which is $\frac{1}{5} I$, is equal to $B$, and also $80\%$ of $T$, which is $\frac{4}{5} T$, is equal to $B$; therefore, $\frac{1}{5} I = \frac{4}{5} T$ or $I = 4T$. The total number of employees, which is 84, is the sum of the number of employees who speak English and the number of employees who speak German minus the number of employees who speak both languages (otherwise they would be counted twice): $84 = I + T - B = I + T - \frac{4}{5} T = I + \frac{1}{5} T = 4T + \frac{1}{5} T = \frac{21}{5} T$. Therefore, $T = 84 \frac{5}{21} = 20$ and $B = \frac{4}{5} T = 16$.