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jose.mario.amaya
- Junior | Next Rank: 30 Posts
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Is |x+y| > |x-y|?Is |x+y|>|x-y|?
a) |x|>|y|
b) |x-y|<|x|
When there is absolute value notation on each side, we can square the inequality.
(x+y)² > (x-y)²
x² + 2xy + y² > x² - 2xy + y²
4xy > 0
xy > 0.
Question rephrased: Do x and y have the same sign?
Statement 1: |x| > |y|
Here, x and y could have the same sign or different signs.
INSUFFICIENT.
Statement 2: |x-y| < |x|
Squaring both sides, we get:
(x-y)² < x²
x² - 2xy + y² < x²
y² < 2xy
xy > y²/2.
Since the square of a value cannot be negative, y²/2 cannot be negative.
Thus, xy>0, implying that x and y have the same sign.
SUFFICIENT.
The correct answer is B.
