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Math Expert V
Joined: 02 Sep 2009
Posts: 58449

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Difficulty:   65% (hard)

Question Stats: 70% (02:45) correct 30% (03:38) wrong based on 74 sessions

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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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Math Expert V
Joined: 02 Sep 2009
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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 _________________ Intern  Joined: 23 Jul 2014 Posts: 2 Re: M07-17 [#permalink] Show Tags 2 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 Math Expert V Joined: 02 Sep 2009 Posts: 58449 Re: M07-17 [#permalink] Show Tags 5 6 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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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 Intern  Joined: 01 Jan 2015 Posts: 1 Re: M07-17 [#permalink] Show Tags 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 Math Expert V Joined: 02 Sep 2009 Posts: 58449 Re: M07-17 [#permalink] Show Tags 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 _________________ Senior Manager  Joined: 12 Aug 2015 Posts: 280 Concentration: General Management, Operations GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27 GPA: 3.3 WE: Management Consulting (Consulting) M07-17 [#permalink] Show Tags 19 4 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 _________________ KUDO me plenty Originally posted by shasadou on 24 Nov 2015, 03:19. Last edited by shasadou on 24 Feb 2016, 03:32, edited 1 time in total. Intern  Joined: 15 Sep 2015 Posts: 1 Re: M07-17 [#permalink] Show Tags 9 1 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 Intern  Joined: 02 Dec 2015 Posts: 4 Re: M07-17 [#permalink] Show Tags 14 2 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
Intern  Joined: 22 Jun 2014
Posts: 21
Concentration: General Management, Finance
GMAT 1: 700 Q50 V34 GRE 1: Q800 V600 GPA: 3.68

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For those who want the theory behind the shortcut, please search 'componendo dividendo' in google.. There is your answer.
Intern  B
Joined: 29 Sep 2015
Posts: 2
Schools: Booth '19, Duke '19
GMAT 1: 660 Q49 V31 Show Tags

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??
Math Expert V
Joined: 02 Sep 2009
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Triangled wrote:
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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I think this is a high-quality question and I agree with explanation.
Intern  Joined: 13 Jun 2016
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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.
Manager  S
Joined: 21 Apr 2016
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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)
Intern  Joined: 25 Jul 2016
Posts: 7
GMAT 1: 740 Q50 V40 Show Tags

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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 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.
Intern  B
Joined: 21 Aug 2017
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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 * T

I hope this helps. Intern  B
Joined: 25 Aug 2017
Posts: 31

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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

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).
Intern  B
Joined: 26 Aug 2017
Posts: 10

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xnthic wrote:
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.

YES! THANK. YOU.

I wish all posts were this straightforward Re: M07-17   [#permalink] 16 Aug 2018, 16:17

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