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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Is x + y > 0 ?
Source: Beat The GMAT — Data Sufficiency |
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Statement 1: x² > y² + 1eitijan wrote:Is x + y > 0 ?
(1) x² - y² > 1
(2) x/y + 1 > 0
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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