We are given x , y, z > 0, all the variables are positive, we also know that multiplying/dividing each side of an inequality with a positive integer does not change the direction of the inequality. So let's analyze the statements.
Statement (1)
xz > yz z can cancel each other without affecting the direction of inequality
we can deduce
x > y but don't know anything about z in relation to if it is smaller or greater than the other variables. Not Sufficient
Statement (2)
Similarly we can deduce
x > z but we can't place y so Statement 2 alone is not sufficient.. (Be careful NOT to carry over statement 1 on to this one yet!!!)
Now look at:
Statement (1) & (2)
x > y and x > z so now we know is is the greatest but still we don't know whether y > z or y < z
So either of the statements together NOT sufficient.
Answer EBunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf x, y, and z are positive numbers, is x > y > z ?
(1) xz > yz
(2) yx > yz
Data Sufficiency
Question: 69
Category: Algebra Inequalities
Page: 158
Difficulty: 600
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