Official Guide Explanation:
Data Sufficiency #89




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Solution and Metadata

Question: 89
Page: 159
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other

Explanation: Statement (1) is insufficient. To translate the statement into something resembling plain English: "z is more than one greater than x + y." In that case, z could be greater than 1, but if it is, say, (3/4), x + y could be -(1/2), for a sum of (1/4), which is greater than 0.

Statement (2) is sufficient. x + y + 1 < 0 is equivalent to x + y< - 1. If x + y is less than -1 and x + y + z is greater than 0, z must be greater than 1. This is easiest to see by rewriting the initial inequality:

x + y + z > 0

z>-(x + y)

z>-(something less than -1)

z > (something greater than 1)

Choice (B) is correct.

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