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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.

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: 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:

rx = ((x)/(z))

ry = ((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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