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S96-13

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:51
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Difficulty:

55% (hard)

Question Stats:

56% (02:21) correct 44% (02:47) wrong based on 52 sessions

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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. $$16k$$

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Posts: 57155

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16 Sep 2014, 01:51
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.

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04 Oct 2016, 22:29
In this question we are asked the individual share that each had or the total sum of money?
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05 Oct 2016, 02:28
sommya wrote:
In this question we are asked the individual share that each had or the total sum of money?

We need to find the total amount of money that was given originally to Abby, Bill, and Carla.
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18 Sep 2018, 13:18
x given to each A, B & C. j=3x

.......................A...............B................C

initial : ..............x...............x...............x
A gives B , K:...x-k.............x+k.............x
B gives C , 2K:.x-k.............x-k.........x+2k
C gives A , 3K:...x+2k.........x-k...........x-k

Now, 2(x+2k) = 3x ==> x=4k ==>j=12k ansD
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Please let me know if I am going in wrong direction.
Thanks in appreciation.
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12 Oct 2018, 21:08
I also found the wording of the question confusing: "how much money was given originally to Abby, Bill, and Carla", I interpreted it as how much money each of them got.
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GMAT Date: 03-15-2015
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21 Nov 2018, 22:26
I think this is a poor-quality question and I agree with explanation. In terms of kk, how much money was given originally to Abby, Bill, and Carla?

No clearity.
Found out j/3
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01 Mar 2019, 10:07
Same here. I find the question vague (is it asking for the total amount given to the three or the individual share?) Based on the answer provided, it seems that it asked for total amount given to Abby, Bill and Carla.

J = divide by 3, let J/3 = X
J=X+X+X = 3x

A= x - K (given to B) +3K (given by C) = x - k + 3k = X + 2k
B= x +K (given by A) -2K (given to C) = x + k - 2k = X - k
C= x +2k (given by B) -3K (given to A) = x + 2k - 3k = x - k

A = x + 2k = exactly half of all the dollars given to the three people
= x + 2k = J/2
= x + 2k = 3x / 2
= 2(x+2K) = 3x
= 2x+4K = 3x
= 4k = 1x or 4k = x

J = 3(X) = 3(4k) =12K
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11 May 2019, 14:42
Hello,

Apologies but I think I may be completely missing something here. Below is how I understood the question:

Since Abby gave Bill k dollars and received 3k from Carla, that means she would have 2k left on her

since she now has half of the dollars distributed amongst the three people, wouldn't the answer simply be 2*2k=4k?

Re: S96-13   [#permalink] 11 May 2019, 14:42
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