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## Official Guide Explanation:

Data Sufficiency #1

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 1**

Page: 153

Difficulty: **5** (Moderate)

Category 1: Arithmetic > Descriptive Statistics > Average

Category 2: Algebra > Linear Equations-Two Unk >

**Explanation:** To find the average of x and y, we simply need the sum of x and y. (To find the average, we'd divide by 2, but for Data Sufficiency, we don't need the exact average.)

Statement (1) is insufficient. It tells us that ((x + 2y)/2) = 10. There's no way to get from there to the value of x + y.

Statement (2) is also insufficient. This one tells us that ((2x + 7y)/2) = 32. Again, no way to get to x + y from there.

Taken together, the statements are sufficient. We can simplify the equations from each of the statements to get the equations:

x + 2y = 20 and

2x + 7y = 64

Those are two linear equations with two variables. No need to solve, just recognize that we can. Choice (C) is correct.

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