Three Categories of Spending

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Last year, if a company spent a total of $1,200,000 on marketing, salaries, and administrative costs, how much did it spend on salaries?

(1) Last year, the total amount that the company spent on salaries and administrative costs was 50 percent of the amount that it spent on marketing.

(2) Last year, the amount that the company spent on salaries was 25 percent of the total amount it spent on marketing and administrative costs.

Review: Three Categories of Spending




Explanation

We go ahead and sling an equation onto our note board when we read the question: . We need to find S. We might do it by getting two more independent equations involving these variables, to satisfy the n variables, n equations. Or, we could find S by learning the value of . Let's turn to the statements, separately first.

Statement (1) tells us that . We have only two equations, so by the rule we don't have enough to solve exhaustively. We will check for fortuitous algebra. That would involve finding . However, in an attempt to isolate on one side of this statement we end up with . Substituting that yields nothing helpful. Therefore, Statement (1) is insufficient.

Statement (2) says that . Again, we have only two equations for three variables. But fortuitous algebra is afoot. We can rewrite this statement as



and substitute in the order equation to obtain



from which we can solve for S. We can answer the question definitively, so Statement (2) is sufficient.

The correct answer is (B).


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