Angela and Maria’s Salaries

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Angela and Maria each earn a different regular monthly salary. Each of them has a different percentage of that salary withheld every month by her employer. Is Angela's monthly salary after withholding greater than Maria's?

(1) Angela's monthly salary after withholding is 20 percent less than her regular salary; Maria's monthly salary after withholding is 25 percent less than her regular salary.

(2) Angela's monthly salary after withholding is $1000 less than her regular salary; Maria's monthly salary after withholding is $1200 less than her regular salary.

Review: Angela and Maria's Salaries




Explanation

So, just from the question it's maybe not totally obvious what the data statements are going to give us, but we know that we have a salary, a withholding, and a salary after withholding, which we will think of as an "effective" salary and write, . (we figure, why use variables such as x and y when you don't have to, because doing so will only generate the opportunity to forget what the variables stand for later). For Maria, we have the same thing, but, as far as we know, all the variables are different. So we might write Maria's equation as . Very well - on to the data statements, evaluating them separately first, as always.

Statement (1) gives us a couple pieces of comparative information. For Angela, . For Maria, . But we have a situation with four variables and two equations. If we could construct a ratio of and determine whether it was greater or less than 1, that would allow us to answer who has the bigger effective salary, but we have no information about how S and compare. So this statement is insufficient.

Statement (2) is similar--we have way more variables than equations, and no way of establishing a direct comparison such as a ratio. Insufficient.

With the statements together, we may have something, because we believe we have four distinct equations and four variables. We'll confirm this by writing out the equations:









The first and third equation allow us to determine E. The second and fourth equation allow us to determine . We'll then be able to compare them directly. So, together, we have sufficient data to answer the question.

The correct answer is (C).


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