Official Guide Explanation:
Data Sufficiency #69

Background

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Solution and Metadata

Question: 69
Page: 158
Difficulty: 5 (Moderate)
Category 1: Algebra > Inequalities > other

Explanation: Statement (1) is insufficient: since z is positive, we can simplify by dividing both sides by z, leaving x > y, which says nothing about z. Statement (2) is also insufficient: since y is positive, we can simplify by dividing both sides by y, leaving x > z, which says nothing about y.

Taken together, the statements are still not sufficient. If x is greater than y and x is greater than z, x must be the largest of the three numbers, but it is not clear whether y is greater than z. Choice (E) is correct.

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