Hi yoonsiklim1, nicasc
The problem is that you are both assuming that the quantity by which each part of the ratio is "scaled" is the same. That is not correct. In doing so, you are using an additional constraint not described in the original problem. Look at the following example.
Sara's income (S) could be 40000, but could also be 20000. If S = 20000, according to the first statement, Mary's income (M) = 3*S/4. Then, if S = 20000, M = 15000.
\frac{S}{M} = \frac{20000}{15000} = \frac{4}{3}*\frac{5000}{5000} where that
5000 is the number you called x.
In this case, the spending of Sara (z) is 11000 and the spending of Mary (y) is 9000 (you can get these numbers using all the information given by the statements). Therefore,
\frac{(S - z)}{(M - y)} = \frac{(20000 - 11000)}{(15000 - 9000)} = \frac{9000}{6000} = \frac{3}{2} * \frac{3000}{3000}where that
3000 is ALSO the number you called x.
The
red numbers are the quantities by which each part of the ratio is multiplied in order to obtain the actual incomes, spendings, and savings (
Manhattan GMAT defines this quantity as the "Unknown Multiplier"). You can see that they are different. It happens, however, that in the case of S = 40000 and M = 30000 (the one you described) these quantities (your x´s) are both equal to 10000.
_________________
Francisco
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