karthikpandian19 wrote:Are x and y positive?
1. 2x-2y=1
2.x/y >1
(1) 2x - 2y = 1
Implies (x - y) = 1/2. This means the only case that is not possible is x negative and y positive. In that case the LHS will be negative always! So the possible cases are (with examples),
(1) x positive, y positive (x = 4.5, y = 4)
(2) x positive, y negative (x = 0.25, y = -0.25)
(3) x = 0.5, y = 0
(4) x = 0 , y = -0.5
(5) x negative, y negative (x = -4, y = -4.5)
(Note : In each case there is also some constraints. Like in the 1st case, not for all positive x, y the relation will hold! x must be equal to (y + 0.5) etc.) ; NOT sufficient.
(2) (x/y) > 1
Again this implies any one of the following two cases,
(1) Both of them are positive and x > y
(2) Both of them are negative and x < y; NOT sufficient.
Combining (1) and (2) together, (2) limits the number of possible cases to two. So, let's analyze them again with the help of statement 1.
(1) Both of them are positive and x > y => (x - y) = 0.5 is possible.
(2) Both of them are negative and x < y => (x - y) will be always negative. Not possible.
Thus, x and y are both positive; SUFFICIENT.
The correct answer is
C.
