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# M17 Q 17

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M17 Q 17 [#permalink]

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22 Jun 2012, 05:31
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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. Math Expert Joined: 02 Sep 2009 Posts: 39676 Re: M17 Q 17 [#permalink] ### Show Tags 22 Jun 2012, 05:34 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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 Status: Verbal Forum Moderator Joined: 17 Apr 2013 Posts: 612 Location: India GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49 GPA: 3.3 Re: M17 Q 17 [#permalink] ### Show Tags 07 Jul 2014, 17:14 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, 17:14
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# M17 Q 17

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