Two variables

IMO - E

what is OA ?

Official answer is E.

Examples:

1. x = 0, y = 1 satisfies (1) and (2) and yields "No"
2. x = 3, y = 4 satisfies (1) and (2) and yields "Yes"

Obviously this is true, but can anyone think of a way to solve this without a) graphing all inequalities or 2) trial and error?

TrebleMaker85 wrote:Is x² - y > 1/y² where y is non-zero?

(1) x < y
(2) x² < y²

Thoughts?

Let's start by simplifying the original by multiplying both sides by y² (we can safely do so because we know that y² is positive):

Is x²y² - y^3 > 1

(arg, can't seem to cut and paste superscripted numbers!)

(1) x < y

If x and y are big positive numbers, y^3 will dominate x²y² and the left side will be negative; if x and y are big negative numbers, x²y² and (-y^3) will both be positive and the left side will be a big positive number: insufficient.

(2) x² < y²

Tells us that |x| < |y|, but nothing about the signs of x and y. If we pick really big values with different signs we can generate both "yes" and "no" answers.

Together: combining doesn't help us at all, since we have the same generalizations from both: choose E.

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Moral of the story: there are lots of DS number property questions on which you can reason out the correct answer, but picking numbers is often quicker. To get a 700+ score on the GMAT you must be able to effectively pick numbers, there just isn't time to apply esoteric principles to every question.