Max@Math Revolution wrote:[GMAT math practice question]
Is x > 0?
1) |x| + |y| > |x + y|
2) |y| > y
Note:
|a|² = a²
|a+b|² = (a+b)²
Statement 1:
Since an absolute value cannot be negative, both sides of the inequality must be nonnegative, allowing us to safely square it:
(|x| + |y|)² > |x + y|²
|x|² + |y|² + 2|x||y| > (x+y)²
x² + y² + 2|x||y| > x² + y² + 2xy
|x||y| > xy
The resulting inequality requires that x and y have DIFFERENT SIGNS.
Thus:
If y<0, then x>0, with the result that the answer to the question stem is YES.
If y>0, then x<0, with the result that the answer to the question stem is NO.
INSUFFICIENT.
Statement 2:
The inequality requires that y<0.
No information about x.
INSUFFICIENT.
Statements combined:
Since y<0 and x and y must have different signs, x>0.
Thus, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is
C.
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