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Manager  Joined: 20 Sep 2008
Posts: 72
A certain sum of money is divided among A, B and C such that A gets on  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 66% (03:05) correct 34% (03:42) wrong based on 131 sessions

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A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $12.4 more than that received by B, find the total amount shared by A, B and C. A.$345.20
B. $386.40 C.$520.30
D. $446.40 E. None Most Helpful Community Reply Manager  S Joined: 24 Dec 2016 Posts: 59 Location: United States Concentration: Statistics Schools: Duke Fuqua GMAT 1: 720 Q49 V40 GPA: 3.38 A certain sum of money is divided among A, B and C such that A gets on [#permalink] Show Tags 10 4 D The problem is not hard at all, if you get the logic of it If A has $$\frac{1}{3}$$ of B and C, this means that B and C together have $$\frac{3}{3}$$ . So A has 1 peace, B and C have 3 peaces, overall A has $$\frac{1}{4}$$ of the total share. If we apply similar logic to B, B has$$\frac{2}{9}$$. Now we can make an equality. $$\frac{1}{4}$$x - $$\frac{1}{9}$$x = 12.4 $$\frac{(9-8)}{36}$$x = 12.4 $$\frac{1}{36}$$x = 12.4 x= 12.4*36=446.4 Hope that helped _________________ If you find my solution useful, hit the "Kudos" button General Discussion Manager  Joined: 21 Aug 2010 Posts: 173 Location: United States GMAT 1: 700 Q49 V35 Re: A certain sum of money is divided among A, B and C such that A gets on [#permalink] Show Tags stoy4o wrote: A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is$12.4 more than that received by B, find the total amount shared by A, B and C.

A. $345.20 B.$386.40
C. $520.30 D.$446.40
E. None

Can someone give me a short-cut on how to get to an answer?

A = 1/3 (B+C) => C = 3A - B ---(1)
B = 2/7 (A+C) => C = 3.5 B - A --(B)
A-B = $12.4 A = 12.4+B (1)===> C = (37.2)+3B - B = 2B+37.2 ==> 2B-C = -37.2 ---(3) (2)===> C = 3.5 B - B-12.4 = 2.5B-12.4==>2.5B-C = 12.4 ---(4) from (4) and (3) 0.5B = 49.6 B =$99.2
A= $111.6 C =334.8-99.2=$235.6

Ans $446.4 (D) _________________ ------------------------------------- Current Student B Joined: 20 Jan 2017 Posts: 12 Location: Armenia Concentration: Finance, Statistics Schools: Duke Fuqua (A) GMAT 1: 730 Q51 V38 GPA: 3.92 WE: Consulting (Consulting) A certain sum of money is divided among A, B and C such that A gets on [#permalink] Show Tags D Just need to get an equation. A = $$\frac{(B+C)}{3}$$ = $$\frac{(total - A)}{3}$$ B = $$\frac{2(A+C)}{7}$$ = $$\frac{2(total - B)}{7}$$ A - B = 12.4 $$\frac{(total - A)}{3}$$ - $$\frac{2(total - B)}{7}$$ = 12.4 $$\frac{(7Total - 7A - 6Total + 6B)}{21}$$ = 12.4 (Total - 7A + 6B)= 21*12.4 A + B + C - 7A + 6B = 21*12.4 B + C - 6A + 6B = 21*12.4 B + C - 6(A-B) = 21*12.4 B + C = 21*12.4 + 6*12.4 B + C = 27*12.4 => A = 9*12.4 A + B + C = 36*12.4 = 446.4 Math Expert V Joined: 02 Aug 2009 Posts: 7757 A certain sum of money is divided among A, B and C such that A gets on [#permalink] Show Tags stoy4o wrote: A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is$12.4 more than that received by B, find the total amount shared by A, B and C.

A. $345.20 B.$386.40
C. $520.30 D.$446.40
E. None

Hi,

Since the method with equation is given, I will touch on an alternate method.

A bit of quick thinking at times can save you a lot of time
B gets $$\frac{2}{7}$$ of (B+C), so total= A+B+C=$$\frac{2}{7}$$*(B+C)+B+C=$$\frac{9}{7}$$*(B+C)..
Here B+C=TOTAL*$$\frac{7}{9}$$..
So answer should be div by 9, only D is left.

If there are two three choices fitting in, one more calculation can get you to answer.
Best if you are clueless on making equations and the choices does not have None in choices
_________________
Intern  B
Joined: 29 May 2012
Posts: 34
Re: A certain sum of money is divided among A, B and C such that A gets on  [#permalink]

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Vardan95 wrote:
D
The problem is not hard at all, if you get the logic of it
If A has $$\frac{1}{3}$$ of B and C, this means that B and C together have $$\frac{3}{3}$$ . So A has 1 peace, B and C have 3 peaces, overall A has $$\frac{1}{4}$$ of the total share. If we apply similar logic to B, B has$$\frac{2}{9}$$. Now we can make an equality.

$$\frac{1}{4}$$x - $$\frac{1}{9}$$x = 12.4

$$\frac{(9-8)}{36}$$x = 12.4

$$\frac{1}{36}$$x = 12.4

x= 12.4*36=446.4

Hope that helped

This is brilliant. Thanks! Kudos to you.
Manager  B
Joined: 19 Aug 2016
Posts: 82
Re: A certain sum of money is divided among A, B and C such that A gets on  [#permalink]

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Vardan95 wrote:
D
The problem is not hard at all, if you get the logic of it
If A has $$\frac{1}{3}$$ of B and C, this means that B and C together have $$\frac{3}{3}$$ . So A has 1 peace, B and C have 3 peaces, overall A has $$\frac{1}{4}$$ of the total share. If we apply similar logic to B, B has$$\frac{2}{9}$$. Now we can make an equality.

$$\frac{1}{4}$$x - $$\frac{1}{9}$$x = 12.4

$$\frac{(9-8)}{36}$$x = 12.4

$$\frac{1}{36}$$x = 12.4

x= 12.4*36=446.4

Hope that helped

Just a small correction...

1/4x-2/9x=12.4
e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2888
Re: A certain sum of money is divided among A, B and C such that A gets on  [#permalink]

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Solution

Given:

• A certain sum of money is divided among A, B and C.
• A gets one-third of what B and C together get.
• B gets two-seventh of what A and C together get.
• Amount received by A is \$12.4 more than that received by B

To find:
• Find the total amount shared by A, B and C.

Approach and Working

A gets one-third of what B and C together get.
• Thus, if A gets ‘a’ then B+C= 3a
o A+B+C = 4a

B gets two-seventh of what A and C together get.
• Thus, B gets 2b, then A+C = 7b
o A+B+C = 9b

Now, A+B+C is equal to 4a as well as 9b.
• Therefore, we can assume A+B+C= 36k.
o Hence, A= 9k, B= 8k, c= 19k
• 9k= 8k+12.4
o k= 12.4
• Therefore, total amount shared by A, B, and C= 9k=446.4

_________________ Re: A certain sum of money is divided among A, B and C such that A gets on   [#permalink] 28 Oct 2018, 14:08
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