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## Official Guide Explanation:

Data Sufficiency #78

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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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