Ans:B

(1) x^2 > y ( hope x2 in question means x^2)
If x is positive: 25(=x^2)>(=y)4 ==>5>4 AND 9(=x^2)>4(=y)=> 3<4
but if x is negative -5<4 & -3<4 similarly we can check taking y negative(=-4) ..... insufficient as few cases give us x>y and other give us x<y

(2) x – |y| > 0 ==> x>lyl since mod gives positive value this means x is positive and greater than y no matter y is positive or negative
5>l4l==>5>4 OR 5>l-4l ==> 5>-4 ........sufficient

Stmt I

x=-2 y=2 x^2>y but x<y

x=1000 y=1 x^2>y and x>y

INSUFF

Stmt I

x- |y| >0
x>|y|

Case 1: y is positive

By definition of mod function |y|= y if y is 0 or positive we get x>y

Case 2: y is negative

By definition of mod function |y|= -y if y is negative (which makes |something| always positive or 0

Therefore again x>y

SUFF

Choose B

500 -550 level question

Ans B.

1. X2>y .. In this case x can either be greater than y (x = 4 and y =1) or
x<y (x = 2, y=3 or x=-2 y=3). Insufficient

2. x-|y| >0
x> |y|

So for any values of y (either positive or negative ) x is greater than y. Sufficient

A simple one - but I got screwed never the less .. the modulus got me. I was like x > y when y > 0 and x > -(-y) when y < 0 .. so .. lesson learned

i read the 1st statement as x*2, and thought why on earth is A insuff? ))

B is the answer

was this really posted as a 600-700 level question?

Yes it was. Do you need the screen shot as a proof