Are X and Y both positive?

[Guest]

Are X and Y both positive?
a)2x+ 2Y =1
b)x/y > 1

The answer is C.

[RonPurewal]

Are X and Y both positive?
(1) 2x+ 2Y =1
(2) x/y > 1

(1)
divide by two, giving x + y = 1/2
this isn't good enough; you could have two positives (such as 1/4 and 1/4) or one positive and one negative (such as -1 and +3/2).
insufficient

(2)
the important aspect of this statement is the fact that x/y must be positive; it's pretty much immaterial that the value is greater than one.**
this means that x and y could be either
* both positive, or
* both negative
insufficient

(together)
from statement (1), the only possibilities for (x, y) are (pos, pos), (pos, neg), or (neg, pos)
from statement (2), the only possibilities are (pos, pos) and (neg, neg)
if both statements are true, then, we must have (pos, pos).
sufficient

**note: always interpret the statements in the context of the problem. because this problem asks whether x and y are positive/negative, you should try to interpret the statements (1) and (2) primarily in those terms.
that's why we interpret statement (2) as 'x/y is positive', and don't concern ourselves unduly with the fact that x/y is greater than one.