M07-17

Official Solution:

Metropolis Corporation has four shareholders: Fritz, Luis, Alfred, and Werner. The number of shares Fritz owns is \(\frac{2}{3}\) of the total number of shares owned by the other three shareholders combined. Similarly, Luis owns \(\frac{3}{7}\) of the total number of shares owned by the other three shareholders, while Alfred owns \(\frac{4}{11}\) of the total number of shares owned by the other three shareholders. If the company distributed $3,600,000 in dividends among the four shareholders, how much of this amount was received by Werner?

A. $90,000
B. $100,000
C. $120,000
D. $180,000
E. $240,000


Fritz owns \(\frac{2}{3}\) of the shares owned by the other three shareholders. In other words, Fritz owns \(\frac{2}{2+3}=\frac{2}{5}\) of all the shares. To put it more simply, Fritz owns 2 parts, while the other three shareholders together own 3 parts. Thus, Fritz owns 2 parts out of a total of 5 parts.

Luis owns \(\frac{3}{7}\) of the shares owned by the other three shareholders. In other words, Luis owns \(\frac{3}{3+7}=\frac{3}{10}\) of all the shares.

Alfred owns \(\frac{4}{11}\) of the shares owned by the other three shareholders. In other words, Alfred owns \(\frac{4}{4+11}=\frac{4}{15}\) of all the shares.

Combined, these three shareholders own \(\frac{2}{5}+\frac{3}{10}+\frac{4}{15}=\frac{29}{30}\) of all the shares. This implies that Werner owns the remaining shares, which amounts to \(1-\frac{29}{30}=\frac{1}{30}\). Therefore, from the total of $3,600,000, Werner receives \($3,600,000 * \frac{1}{30} = $120,000\).


Answer: C