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## Official Guide Explanation:Data Sufficiency #71

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.

Question: 71
Page: 279
Difficulty: 5 (Moderate)
Category 1: Word Problems > Other >
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: Statement (1) offers an equation: x + y = 42, where x is the length of the shorter route and y is the length of the longer route. That's one linear equation with two variables, so it's not enough to solve for x (the length of the shorter route, which is what the question is asking for).

Statement (2) is also insufficient, but gives us another equation: 2y = 46, or y = 23. On its own, that doesn't tell us anything about the length of the shorter route.

Taken together, the statements are sufficient: if y = 23 and x + y = 42, x + 23 = 42, so x = 19. Choice (C) is correct.

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