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Is x^2>y^2 ?
--> Is (x-y)(x+y)>0 ?
--> Are both (x-y) and (x+y) of the same sign ?

(1) x > y > 0
We know from statement (1) as follows:
a. x > y --> x - y > 0 --> (x-y) is positive
b. x > 0 and y > 0 both positive --> (x+y) is positive
--> Both (x-y) and (x+y) are of the same sign. Thus, x^2>y^2 must be true
SUFFICIENT

(2) x > 1 > y
We know from statement (2) as follows:
a. x > y --> x - y > 0 --> (x-y) is positive
b. x>1 is positive. However, y<1 could be positive or negative of zero --> (x+y) could be positive or negative or zero
--> Both (x-y) and (x+y) could be of either the same sign or the opposite sign. Thus, x^2>y^2 could be either true of false.
NOT SUFFICIENT

Answer is (A)

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