One way we can simplify absolute values is to square both sides.dferm wrote:Is |x| > |y|?
(1) x^2 > y^2
(2) x > y
Please explain....
So, we can actually rewrite:
Is |x| > |y|?
As:
Is |x|^2 > |y|^2
or simply:
Is x^2 > y^2?
(1) x^2 > y^2
exactly what we're looking for! Sufficient.
(2) x > y
Sadly, this doesn't tell us about the relative absolute values.
For example, if we pick x = 10 and y = 5, then when we ask:
Is |10| > |5|? We get a "yes" answer.
However, if we pick x = 10 and y = -20 (so x > y, our rule from statement (2), then when we ask:
Is |10| > |-20|? We get a "no" answer.
Since we can get both a yes and a no, (2) is insufficient.
(1) is sufficient, 2 is insufficient: choose (a).
