Data Sufficiency

shrey2287 wrote:Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

c

(1) 2x - 2y = 1
x and y both positive means that point (x, y) is in the first quadrant.
2x - 2y = 1 implies y = x - 1/2, and it's an equation of a line and the question asks whether this line is only in first quadrant, which is not possible; NOT sufficient.

(2) x/y > 1
x and y have the same sign. But we don't know whether they are both positive or both negative; NOT sufficient.

Combining (1) and (2), 2x - 2y = 1 implies x = y + 1/2
x/y > 1 implies (x - y)/y > 0
Substituting the value of x, 1/y > 0 implies y is positive and since x = y + 1/2, so x is also positive; SUFFICIENT.

The correct answer is C.