Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Taking a “direct algebra” approach, we can see that each of the three people receives 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 j/2. Now we can write an equation:
j/3 + 2k = 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.
The correct answer is (D).