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## Official Guide Explanation:

Data Sufficiency #44

**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.

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**Solution and Metadata**

**Question****: 44**

Page: 276

Difficulty: **5** (Moderate)

Category 1: Word Problems > Work Problems > 3+ inputs

Category 2: Word Problems > Rate Problems > other

**Explanation:** First, call X's rate x, Y's rate y, and Z's rate z. Thus:

r_{x} = ((x)/(z))

r_{y} = ((y)/(z))

Statement (1) is insufficient. It can be simplified to:

((x)/(z)) < ((y)/(z))

Since rates must be positive, we can multiply both sides by z:

x < y

That gives us some information about the rates, but nothing about how z compares to the other two.

Statement (2) is also insufficient. Again, simplifying:

((y)/(z)) < 1

Multiply both sides by z:

y < z

z is greater than y, but we don't know whether z is greater than x as well.

Taken together, the statements are sufficient. (2) tells us that z is greater than y, and since (1) tells us that y is greater than x, we know that z must be greater than x as well. Choice (C) is correct.

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