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M07-17

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Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number of shares 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 number of the shares of the other three shareholders and number of the shares that Alfred owns is \(\frac{4}{11}\) of 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?

A. $90,000
B. $100,000
C. $120,000
D. $180,000
E. $240,000
[Reveal] Spoiler: OA

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Official Solution:

Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number of shares 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 number of the shares of the other three shareholders and number of the shares that Alfred owns is \(\frac{4}{11}\) of 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?

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


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

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

Alfred owns \(\frac{4}{11}\) of the shares of the other three shareholders: Alfred owns \(\frac{4}{4+11}=\frac{4}{15}\) of all 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 \($3,600,000*\frac{1}{30}=$120,000\).


Answer: C
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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

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scottrsmiley wrote:
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


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.
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New post 14 Jan 2015, 05:35
Bunuel wrote:
scottrsmiley wrote:
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


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.




Had the same doubt

Now its clear

Thanks Bunuel

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New post 22 Mar 2015, 01:30
even i have the same doubt
"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."

i did not understand the solution posted above
please explain a little more in detail.

thanks a lot

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New post 22 Mar 2015, 05:15
samko wrote:
even i have the same doubt
"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."

i did not understand the solution posted above
please explain a little more in detail.

thanks a lot


Please read this post: m07-183751.html#p1451999
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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
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Last edited by shasadou on 24 Feb 2016, 02:32, edited 1 time in total.

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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

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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

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Re: M07-17 [#permalink]

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New post 12 Jan 2016, 04:06
For those who want the theory behind the shortcut, please search 'componendo dividendo' in google.. There is your answer.

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I think this the explanation isn't clear enough, please elaborate. Please explain solution in detail.
How did you arrive that own share of Fritz is 2/2+3=2/5 pf all??

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New post 07 Aug 2016, 00:53
I think this is a high-quality question and I agree with explanation.

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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.

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New post 07 Sep 2016, 20:20
To understand how 2/3 of others shares becomes 2/5 of one's share:

Let others share amount equal x

this makes ones share = 2/3 (others) = 2x/3

So total shares = x+2x/3 = (2+3)x/3

Ones share will be ( 2x/3 ) / ( Total )

=> 2/(2+3)

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New post 18 Jan 2017, 00:40
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.

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New post 09 Oct 2017, 10:30
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. :-)

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koladecollins wrote:
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


Thanks for this explanation. I think the confusion stems from how the question is worded. It's clear once you take 2/3 of (1-F).

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Re: M07-17   [#permalink] 17 Oct 2017, 16:30
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