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# M17 Q 17

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Manager
Joined: 13 May 2010
Posts: 125
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Kudos [?]: 7 [0], given: 4

M17 Q 17 [#permalink]  22 Jun 2012, 04:31
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. Math Expert Joined: 02 Sep 2009 Posts: 25927 Followers: 4004 Kudos [?]: 36805 [0], given: 4533 Re: M17 Q 17 [#permalink] 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. _________________ Director Joined: 17 Apr 2013 Posts: 596 Concentration: Entrepreneurship, Leadership Schools: HBS '16 GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GPA: 3.3 Followers: 8 Kudos [?]: 106 [0], given: 272 Re: M17 Q 17 [#permalink] 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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# M17 Q 17

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