Metropolis Corporation has 4 Shareholders GMAT Problem Solving

Question: Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number of states that Fritz owns is  \(\frac{2}{3}\) of number of the shares of the other three shareholders, number of the shares that Luis owns is \(\frac{3}{7} \)  of the number of the shares of the other three shareholders and number of the shares that Alfred owns is \(\frac{4}{11}\) of the number of the shares of the other three shareholders. If dividends of $3,600,000 were distributed among the 4 shareholders, how much of this amount did Werner receive?

1. $90,000
2. $100,000
3. $120,000
4. $180,000
5. $240,000

“Metropolis Corporation has 4 shareholders GMAT Problem Solving ”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer

Approach Solution 1

Fritz owns \(\frac{2}{3}\) of the shares of the other three shareholders: Fritz owns \(\frac{2}{2+3}\) = \(\frac{2}{5}\) of the shares;

Luis owns \(\frac{3}{7}\) of the shares of the other three shareholders: Luis owns \(\frac{3}{3+7}\) = \(\frac{3}{10}\) of the shares;

Alfred owns \(\frac{4}{11}\) of the shares of the other three shareholders: Alfred owns \(\frac{4}{4+11}\) = \(\frac{4}{15}\) of the shares;

Together these three own \(\frac{2}{5}+\frac{3}{10}+\frac{4}{15}=\frac{29}{30}\) of all shares, which means that Werner owns 1 – \(\frac{29}{30}\) =\(\frac{1}{30}\)

Hence, from $3,600,000 Werner gets $3,600,000 * \(\frac{1}{30}\) = $120,000

Correct Answer: C

Approach Solution 2

We will write the equation as:

F = \(\frac{2}{3}\) of (1 – F)

F = \(\frac{2}{3}\) – \(\frac{2F}{3}\)

3F = 2 – 2F

5F = 2

Hence, F = \(\frac{2}{5}\)

Correct Answer: C

Approach Solution 3

Given: F = \(\frac{2}{3}\) * (L + A + W)

Simplifying: \(\frac{3}{2}\) * F = L + A + W

Adding “F” to both sides:

F + \(\frac{3}{2}\) * F = F + L + A + W

\(\frac{5}{2}*F\)= F + L + A + W = Total (T)

Therefore, F = \(\frac{2}{5}*T\)

Correct Answer: C

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