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## Official Guide Explanation:

Data Sufficiency #8

**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.

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

**Solution and Metadata**

**Question****: 8**

Page: 273

Difficulty: **4** (Moderately Easy)

Category 1: Algebra > Linear Equations-Two Unk >

**Explanation:** This question gives us a very common GMAT setup. If we call the number of orange crates shipped r and the number of grapefruit crates shipped g, the grower's receipts are given by:

x = 15r + 18g

Statement (1) gives us another equation:

r = 2g + 20

It provides a relationship between the number of orange crates and the number of grapefruit crates, but we still have two equations with three variables (r, g, and x). Not sufficient.

Statement (2) is also insufficient. It tells us that x, the total receipts, is $38,700. That isn't enough to identify r or g, though.

Taken together, the statements are sufficient. We can combine the formula from the question with (2):

38,700 = 15r + 18g

We also have the formula from (1):

r = 2g + 20

Two variables, two equations. That's enough to find r. Of course, we don't need to solve; simply recognize that we have the necessary information to solve. Choice (C) is correct.

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