Data Sufficiency

Is |x| > |y|?

(1) x^2 > y^2
(2) x > y

Please explain....

dferm wrote:Is |x| > |y|?

(1) x^2 > y^2
(2) x > y

Please explain....

One way we can simplify absolute values is to square both sides.

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).