How would you efficiently work through this question?
Is |x - y| > |x| - |y|?
I. y < x
II. xy < 0
Answer is B
Is |x - y| > |x| - |y|?
I. y < x
II. xy < 0
Answer is B
Hi,
From(1):
if x=4, y=2, |x - y| = |x| - |y|
if x=4, y=-2, |x - y| > |x| - |y|
Not sufficient
From(2):As xy<0, |xy| = -xy
case-1 : |x| - |y| < 0
As |x - y| > 0, |x - y| > |x| - |y| always holds
case-2 : |x| - |y| > 0
|x - y|^2 = x^2 + y^2 - 2xy = x^2 + y^2 + 2|xy|
(|x| - |y|)^2 = x^2 + y^2 - 2|xy|
So, |x - y|^2 > (|x| - |y|)^2
So, |x - y| > |x| - |y|
Sufficient
By picking x and y on the number line or by plugin values also, we can solve this.
Hence, B
