venmic wrote:
Is |x – y| < |x| + |y|?
(1) y < x
(2) xy < 0
Bunuel
I searched of this question on gmatclub culd not find a post please explain your method
Useful to remember the so-called "Triangle Inequality " for the absolute value:
For any real numbers \(x,y\) \(\,|x+y|\leq|x|+|y|\).
Equality holds if and only if \(xy\geq{0}\), which means, at least one of the two numbers is 0 or they both have the same sign (both positive or both negative).
Or, strict inequality holds if and only if \(xy<0.\)
In our case, we can see that always \(|x-y|=|x+(-y)|\leq|x|+|y|\), because \(|y|=|-y|\).
The strict inequality will hold if and only if \(x(-y)<0\) or \(xy>0.\)
(1) Either \(x\) or \(y\) can be zero, and in addition, we don't know anything about their signs.
Not sufficient.
(2) Obviously sufficient, because we can state with certainty that the given inequality does not hold.
Answer B
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