Official Guide Explanation:
Data Sufficiency #8




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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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