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M17 Q 17

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M17 Q 17 [#permalink] New post 22 Jun 2012, 04:31
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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?

$90,000
$100,000
$120,000
$180,000
$240,000

Fritz owns \frac{2}{3} of the shares of the other three shareholders \right 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 \right 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 \right 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 .


I can't understand how did they come up with the logic that Fritz owns 2/5 of all shares with the given information. Similarly the same for other guys.
[Reveal] Spoiler: OA
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Re: M17 Q 17 [#permalink] New post 22 Jun 2012, 04:34
Expert's post
teal wrote:
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?

$90,000
$100,000
$120,000
$180,000
$240,000

Fritz owns \frac{2}{3} of the shares of the other three shareholders \right 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 \right 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 \right 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 .


I can't understand how did they come up with the logic that Fritz owns 2/5 of all shares with the given information. Similarly the same for other guys.


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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Re: M17 Q 17 [#permalink] New post 07 Jul 2014, 16:14
Bunuel wrote:
teal wrote:
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?

$90,000
$100,000
$120,000
$180,000
$240,000

Fritz owns \frac{2}{3} of the shares of the other three shareholders \right 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 \right 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 \right 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 .


I can't understand how did they come up with the logic that Fritz owns 2/5 of all shares with the given information. Similarly the same for other guys.


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.


Bunuel is their any theory for this law of fractions discussed somewhere?

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Re: M17 Q 17   [#permalink] 07 Jul 2014, 16:14
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