GMAT Prep

IMO C

from 1, x-y=.5

Picking nos x-=-.5 and y=-1 or x=1 and y=.5 Hence not sufficient

from 2, x/y>1 => sign of both x and y are same and |x|>|y|
picking no, x=-3, y=-2 or x=3,y=2, both satisfy, hence not sufficient

combining, since x-y=+ve no, hence x>y so we cannot have both nos as negative and there diff as positive, when |x|>|y|

Therefore x and y have to be +ve, hence C

Statement 1:
2x-2y = 1
so, x=1/2+y
not sufficient

Statement 2:
x/y>1
x and y can be both positive or negative
not sufficient

suppose y is positive then x>y from statement 2
suppose y is negative then x<y from statement 2

from statement 1 we know that x is greater than y...
and from statement 2 we know x is greater than y only when y is positive..
and since x is also greater than y, x is also positive
So the answer is C

from (1) x-y=0.5

we only know X>Y (x & y can be either +ve or -ve) hence not sufficient.

from (2) we know for the ratio x/y>1, the value of X should be greater than y i.e |x|>|y| so not sufficient either

but combining both:
for |x|>|y| & X>Y, only possibility is x must be +ve

if x is +ve then from (2) y has to be +ve