Official Guide Explanation:
Data Sufficiency #71

Background

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Solution and Metadata

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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