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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
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16 Sep 2014, 00:35
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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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Re: M0717 [#permalink]
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05 Dec 2014, 12:10
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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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Re: M0717 [#permalink]
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14 Jan 2015, 06:35
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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Re: M0717 [#permalink]
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22 Mar 2015, 02:30
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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Re: M0717 [#permalink]
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22 Mar 2015, 06:15



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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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Re: M0717 [#permalink]
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24 Dec 2015, 00:52
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For those who are still confused. F=2/3 of (1F) F=2/32F/3 3F=22F 5F=2 hence, F=2/5 This is a longer method and not advised during the exam, just for clarity



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Re: M0717 [#permalink]
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09 Jan 2016, 00:07
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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" (1F), so we can write:
F = \(\frac{2(1F)}{3} Therefore, F = \frac{2}{5}\)
Now, for the rest:
\(L = \frac{3(1L)}{7} Therefore, L = \frac{3}{9}\)
\(A = \frac{4(1A)}{11} Therefore, A = \frac{4}{15}\)
\(So, W's share = 1  (\frac{2}{5}+\frac{3}{9}+\frac{4}{15})\) Thus, W has \(\frac{1}{30}\) of the whole or\(\frac{1*3,600,000}{30}\) = $120,000



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Re: M0717 [#permalink]
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12 Jan 2016, 05:06
For those who want the theory behind the shortcut, please search 'componendo dividendo' in google.. There is your answer.



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Re M0717 [#permalink]
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25 Jun 2016, 05:00
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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Re: M0717 [#permalink]
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25 Jun 2016, 05:03



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Re M0717 [#permalink]
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07 Aug 2016, 01:53
I think this is a highquality question and I agree with explanation.



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Re: M0717 [#permalink]
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31 Aug 2016, 02:13
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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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Re: M0717 [#permalink]
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07 Sep 2016, 21:20
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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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 rewrite 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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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 * TI hope this helps.



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Re: M0717 [#permalink]
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17 Oct 2017, 17:30
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koladecollins wrote: For those who are still confused. F=2/3 of (1F) F=2/32F/3 3F=22F 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 (1F).










