Official Guide Explanation:
Data Sufficiency #78




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Solution and Metadata

Question: 78
Page: 279
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Interest Problems > Simple

Explanation: Call the amount that earned x percent interest a. That means the amount that earned y percent interest is 60,000 - a. Thus, the total amount of interest earned is:

a(((x)/100)) + (60,000 - a)(((y)/100))

We know that's equal to $4,080, and we're looking for x.

Statement (1) is insufficient. It gives us a relationship between the two interest rates, but that isn't enough to solve for any of the variables. The equation given by the question has three variables (a, x, and y), and between the question and (1), we only have two equations.

Statement (2) is also insufficient. It tells us that the ratio between a and 60,000 - a is (3/2):

((a)/(60,000 - a)) = (3/2)

That's another equation, but as with (1), it's only a second equation, even though we're dealing with a total of three variables. To solve for three variables, we need three distinct equations.

Taken together, the statements are sufficient. The question gives us one equation, (1) gives us another, and (2) gives us the third. As you can probably tell from the complexity of some of the equations and the unfriendliness of the numbers, it isn't a good idea to try to solve; instead, recognize that you have three variables and three equations, and select choice (C).

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