formula: (x^2)^1/2 = |x|

therefore if we know x^2 > y^2 ---> |x| >|y|

statement 2 is insufficient becos
let
x = 2, y = -3
x>y but |x| is not > |y|

hope it answers your query!

Choice 1 tells us that x^2 > y^2

Lets test theories: lets say x = -6; y = 5

(-6)^2 = 36; (5)^2 = 25

36 > 25

|-6| = 6; |5| = 5

so is 6>5 ?---> yes.

As long as you satisfy the first condition, you can plug any number irregardless of the sign, and |x| will always be greater than |y|

Choice 1 works.


Choice 2 will not work. Lets take 2 examples.

x = 5; y = 3

|5| > |3| ? ---> yes

if x = -3; y = -5

-3 > -5? yes

|-3| > |-5| ? ----> No

Choice 2 does not work. Therefore it is (A)