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to Abby, Bill, and Carla

by sanju09 » Tue Jul 27, 2010 12:55 am
A total of j dollars is given to Abby, Bill, and Carla and divided equally among them. Then Abby gives Bill k dollars, Bill gives Carla 2k dollars, and Carla gives Abby 3kdollars. Afterwards, Abby has exactly half of all the dollars given to the three people. In terms of k, how much money was given originally to Abby, Bill, and Carla?

A. 4k
B. 6k
C. 8k
D. 12k
E. 16k

[spoiler]Source: Manhattan GMAT Challenge Problem of the Week - 19 July 2010[/spoiler]
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by 4GMAT_Mumbai » Tue Jul 27, 2010 1:21 am
Hi,

Guessing from answers worked well.

When j = 12k, A = B = C = 4K

After 1st transaction, A = 3K, B = 5K, C = 4K

After 2nd transaction, A = 3K, B = 3K, C = 6K

After 3rd transaction, A = 6K, B = 3K, C = 3K

Hence, j = 12K.

--------------------------

In direct terms, if j = x, A initially has x/3.

(x/3) - k + 3k = x/2

(x/3) - (x/2) = -2k

-x / 6 = -2k

Hence, x = 12k.

Hope this helps. Thanks.
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by saurabhmahajan » Tue Jul 27, 2010 2:16 am
total of J dollars given to A,B n C.therefore each have J/3 amount
1) A gives B k dollars,so B has J+2k/3
2) B gave C 2k dollars,so C has j+6k/3
3) C gave A 3k dollars,so A has j+9k/3

total of 2k+6k+9k =18 dollars
but total of k+2k+3k=6k where exchanged.so 18k-6k= 12k
Thanks and regards,
Saurabh Mahajan

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by outreach » Tue Jul 27, 2010 4:36 am
a-abby
b-bill
c-carla
a=b=c=j/3
Abby gives Bill k dollars
a=j/3-k and b=j/3+k
Bill gives Carla 2k dollars
b=j/3+k-2k and c=j/3+2k
Carla gives Abby 3kdollars
c=j/3+2k-3k and a= j/3-k+3k

a =1/2(j)
j/3+2k=(j/2)
j=12k

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