to Abby, Bill, and Carla

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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]

The mind is everything. What you think you become. -Lord Buddha

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Source: Beat The GMAT — Problem Solving | Tue Jul 27, 2010 12:55 am

4GMAT_Mumbai: Master | Next Rank: 500 Posts; Posts: 161; Joined: Mon Apr 05, 2010 9:06 am; Location: Mumbai; Thanked: 37 times

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.

Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai

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saurabhmahajan: Master | Next Rank: 500 Posts; Posts: 250; Joined: Thu Jan 07, 2010 2:21 am; Thanked: 10 times

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

I can understand you not winning,but i will not forgive you for not trying.

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

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

D

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