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Is x + y > 0 ?

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Source: — Data Sufficiency |
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by MartyMurray » Fri Apr 08, 2016 9:57 pm
Statement 1: x² - y² > 1

This tells us that the absolute value of x is greater than the absolute value of y, but because both are squared, it does not provide information on whether either x or y is negative or positive. So x + y could be positive or negative.

Statement 2: x/y + 1 > 0

Your first inclination may be to multiply both sides by y, but since you don't know whether y is positive or negative you don't know whether multiplying by y would change the direction of the inequality.

If x and y are both negative or both positive, x/y > 0 and x/y + 1 > 0. So x + y could be positive or negative.

Insufficient.

Given Statement 2, x and y could be both positive, both negative or both 0. Statement 1 works as long as the absolute value of x is sufficiently greater than that of y such that x² - y² > 1. So given both statements, x and y could have a variety of values and could clearly be both positive or both negative. So x + y could be negative or positive.

Insufficient.

The correct answer is E.
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by GMATGuruNY » Sat Apr 09, 2016 2:19 am
eitijan wrote:Is x + y > 0 ?

(1) x² - y² > 1

(2) x/y + 1 > 0
Statement 1: x² > y² + 1
Case 1: y=1, x=2
In this case, x + y > 0, so the answer to the question stem is YES.
Case 2: y=-1, x=-2
In this case, x + y < 0, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Cases 1 and 2 satisfy BOTH STATEMENTS.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
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