Official Guide Explanation:
Data Sufficiency #44




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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:

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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