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# A certain sum of money is divided among A, B and C such that A gets on

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Manager
Joined: 20 Sep 2008
Posts: 74
A certain sum of money is divided among A, B and C such that A gets on  [#permalink]

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17 Oct 2011, 20:13
2
7
00:00

Difficulty:

75% (hard)

Question Stats:

67% (02:44) correct 33% (02:45) wrong based on 122 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 Joined: 23 Dec 2016 Posts: 62 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 01 Jul 2017, 14:16 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: 175 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 17 Oct 2011, 21:29 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) _________________ ------------------------------------- Intern Joined: 20 Jan 2017 Posts: 13 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 01 Jul 2017, 19:02 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 Joined: 02 Aug 2009 Posts: 7036 A certain sum of money is divided among A, B and C such that A gets on [#permalink] ### Show Tags 01 Jul 2017, 19:42 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
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 29 May 2012
Posts: 37
Re: A certain sum of money is divided among A, B and C such that A gets on  [#permalink]

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28 Sep 2017, 07:18
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
Joined: 19 Aug 2016
Posts: 86
Re: A certain sum of money is divided among A, B and C such that A gets on  [#permalink]

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01 Oct 2017, 22:37
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
Joined: 04 Jan 2015
Posts: 2203
Re: A certain sum of money is divided among A, B and C such that A gets on  [#permalink]

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28 Oct 2018, 13:08

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

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Re: A certain sum of money is divided among A, B and C such that A gets on &nbs [#permalink] 28 Oct 2018, 13:08
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