A total of j dollars is given to Abby, Bill, and Carla and divided equ

Question

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  3k  dollars. 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

vindyman · Answer

After dividing j dollars among A, B and C, each has j/3 dollars.
--A gives B k $, 
A has j/3 - k
B has j/3 + k

--B gives C 2k $,
B has j/3 + k - 2k
C has j/3 + 2k

--C gives A 3k $,
C has j/3 + 2k - 3k
A has j/3 - k + 3k

Abby has exactly half of all the dollars given to the three people
j/3 - k + 3k = j/2
2k = j/2 - j/3
2k = j/6

Ultimately, j = 12k

If 'how much money was given originally to Abby, Bill, and Carla' doesn't mean money given to each, then its 12k, else its 4k
 My answer - D

rajarams · Answer

J dollars split equally across three. So, Abby (A), Bill (B) and Clara (C) each have j/3  dollars.

Abby gives Bill  k dollars:
 A -> j/3 -k 
 B -> j/3 + k 
 C -> j/3

Bill gives Carla 2k dollars
 A-> j/3-k 
 B-> j/3 + k - 2k => j/3 -k 
 C-> j/3 + 2k

Carla gives Abby 3k dollars
 A-> j/3+2k 
 B-> j/3 -k 
 C-> j/3 -k

Abby has exactly half of all the dollars given to the three people

All the dollars given to people => j 
=> Abby has  j/2

j/2 = j/3 + 2k 
 j/2-j/3 = 2k 
 j/6 = 2k 
 j/3 = 4k 
 j = 12k

Hence, D is the correct answer

If the question meant how much money was given each to A, B and C, then 4k (A).

PareshGmat · Answer

Abby ............ Bill ............... Carla ............. Total

\frac{j}{3}  ..............  \frac{j}{3}  ..................  \frac{j}{3}  ................... j

Abby gives Bill k dollars

\frac{j}{3}  -  k  ..............  \frac{j}{3}  +  k  ..................  \frac{j}{3}  ................... j

Bill gives Carla 2k dollars

\frac{j}{3}  - k ..............  \frac{j}{3}  + k -  2k  ..................  \frac{j}{3}  +  2k  ................... j

Carla gives Abby 3k dollars

\frac{j}{3}  - k +  3k  ..............  \frac{j}{3}  - k ..................  \frac{j}{3}  + 2k -  3k  ................... j

Abby has exactly half of all the dollars given to the three people

\frac{j}{2} = \frac{j}{3} + 2k

\frac{j}{6} = 2k

j = 12k

Answer = D

Bunuel · Answer

Official Solution:

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  3k  dollars. 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

Taking a "direct algebra" approach, we can see that each of the three people receives  \frac{j}{3}  dollars. During the swaps, Abby gives away  k  dollars but receives  3k  dollars, so her total increases by  2k  dollars. Her final total is half of the original amount of money, or  \frac{j}{2} . Now we can write an equation:
  \frac{j}{3} + 2k = \frac{j}{2} 
 
Now solve for  j  in terms of  k . First, multiply through by 6 to eliminate fractions:
  2j + 12k = 3j 
  12k = j 
 
This is our answer. We can also solve by picking a number for  j , but realize that we cannot separately pick numbers for  j  and  k  - after all, that would determine the very relationship the question is asking us for. Moreover, it's difficult to know ahead of time what would be a good test number for  j . Seeing 2 and 3 as coefficients within the problem, we might pick $6 as the total. Then each of the people receives $2. Abby has to wind up with $3 (half of $6) when all is said and done, so she has to increase her total by $1. Since she gives away  k  dollars but receives  3k  dollars, she increases her total by  2k  dollars. This tells us that  k  is $0.50, so  j  is 12 times bigger. However, this reasoning doesn't save us a whole lot of work. Direct algebra is just as fast.

Answer: D.

law258 · Answer

This question is all about keeping track of monetary movement. Below should be what you arrived at for the main information given in the problem.

Abby --> (j/3)-k+3k 
Bill --> (j/3)+k-2k
Carla --> (j/3)+2k-3k

Lastly, we find out Abby has J/2, so we set her amount equal to this and solve.

(j/3)-k+3k =(j/2) 
j/6 = 2k
j =  12k

Ved22 · Answer

No need to indulge in such complex solvings. Just take option D and start back solving . post adjustments >>> abhay will have 6k thats half of option D : 12k

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A total of j dollars is given to Abby, Bill, and Carla and divided equ

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A total of j dollars is given to Abby, Bill, and Carla and divided equ

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards