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## Official Guide Explanation:

Problem Solving #81

**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.

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**Solution and Metadata**

**Question****: 81**

Page: 72

Difficulty: **6** (Moderately Difficult)

Category 1: Arithmetic > Descriptive Statistics > Average

Category 2: Word Problems > Other >

**Explanation:** Instead of trying to calculate the averages of Ada's scores and the averages of Paul's scores, focus on the differences. One way to think about this is to say that Paul's scores on all three tests were zero, meaning his average score was zero as well.

If we assume that Paul scored all zeroes, Ada's first score was 10, her second score was 4, and her third score was unknown. Her average was three points lower than Paul's, so it was -3. We can use the average formula to find her third score:

-3 = ((10 + 4 + x)/3)

-9 = 14 + x

-23 = x

Thus, Ada's third score was -23, or 23 points lower than Paul's. Choice (D) is correct.

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