M07-17

Question

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

Show Answer

Official Answer

C

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

Bunuel · Accepted Answer

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

Show Answer

Official Answer

C

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

shasadou · Answer

f= \frac{2}{3} (a+l+w) - this is what the stem provides to us

treat this as a fraction - in a simpler form it is:  \frac{f}{1} = \frac{2 (a+l+w)}{3}

hence  \frac{f}{(a+l+w)} = \frac{2}{3}  - it means there are total 5 parts of a whole, of which f gains 2, hence

f= \frac{2}{5}  of total

szuprio · Answer

For anyone still having doubts,

Remember: The money will be divided as per each person's individual share of the whole. Thus, you need to find  W's  share

Consider total share = 1

Denote share of each guy as:- F,L,A and W. Thus, F+L+A+W = 1

F has  \frac{2}{3}  of the rest of the 3's share combined. "Rest of the 3 means"  (1-F) , so we can write:-

F =  \frac{2(1-F)}{3} Therefore, F = \frac{2}{5}

Now, for the rest:-

L = \frac{3(1-L)}{7} Therefore, L = \frac{3}{9}

A = \frac{4(1-A)}{11} Therefore, A = \frac{4}{15}

So, W's share = 1 - (\frac{2}{5}+\frac{3}{9}+\frac{4}{15}) 
Thus, W has  \frac{1}{30}  of the whole or \frac{1*3,600,000}{30}  =  $120,000

koladecollins · Answer

For those who are still confused.
F=2/3 of (1-F)
F=2/3-2F/3
3F=2-2F
5F=2
hence, F=2/5
This is a longer method and not advised during the exam, just for clarity

Bunuel · Answer

It's quite simple: A has $2 and B has 3$ --> A has 2/3rd of B's amount and also 2/(2+3)=2/5th of total amount of $5.

Hope it's clear.

scottrsmiley · Answer

How do you get the fraction 2/5th's of the total out of 2/3rd's of the shares of the other 3? Like why do you do 2/2+3? I can't seem to figure out how that computes.... thank you

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

xnthic · Answer

I'm not sure if i am interpreting this question correctly, but for those who are still confused;

"F = 2/3 of the other three shareholders" basically says "F's ratio to the other three is 2:3". Hence "total part" = 5.

AlexBunea · Answer

Other solution: 
I think you can treat this problem as a ratio problem:

Number of shares that Fritz owns is  \frac{2}{3}  of number of the shares of the other three shareholders.
That means: F= \frac{2}{3} (L+A+W). We can re-write this as  \frac{F}{L+A+W} = \frac{2}{3} .
So, the ratio of F to (L+A+W) to Total (=F+L+A+W) is  2:3:5 . That means  \frac{F}{Total} = \frac{2}{5}  <=> F= \frac{2}{5} Total

The same for the others
Please correct me if i'm wrong.

karankhurana04 · Answer

A simple and clear explanation for those who couldn't understand the fraction part -

Given - F = 2/3 * ( L+A+W)

Simplifying : 3/2 * F = L+A+W

Adding "F" to both sides : F + 3/2 * F= F + L + A + W

5/2* F = F + L + A + W = Total (T)

Therefore : F = 2/5 * T

I hope this helps.

leonardBe · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

avikalagarwal · Answer

I think this is a  high-quality  question and I agree with explanation.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

saransh2797 · Answer

Hi Bunuel, I did this questions by assuming 'n' shares in total. Hence, by the last step of your solution, I was down to the following step- W owns n/30 shares. Now what happens to 'n'? For ex, Case 1) W has 10 shares, Case 2) W has 20 shares. Won't this affect the answer choice? I am just confused with the role of Share Price & Number of Shares in this question. Thanks

Bunuel · Answer

n represents 100% because the corporation is fully owned by the four shareholders. Therefore, there is no specific "number" of shares; each shareholder owns a certain percentage of the corporation, with the total ownership equaling 100%.

Premkungg · Answer

I like the solution - it’s helpful.

adarsh2209 · Answer

I like the solution - it’s helpful.

iamdarshitgupta · Answer

I did not quite understand the solution. please guide this solution in other way pls

M07-17

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