Solution:
Consider first statement (1) alone.
2x - 2y = 1.
Let x = 1 and y = 1/2.
So 2x - 2y = 1 and x and y are both positive.
Next let x = 1/4 and y = -1/4.
Again 2x - 2y = 1 and x is positive and y is negative.
So we cannot say definitely from statement (1) alone whether x and y are both positive or not.
Next consider statement (2) alone.
It says x/y > 1 or (x-y)/y > 0.
So either case (1) x > y and y > 0
Or case (2) x < y and y < 0.
For example let x = 4 and y = 2, then x/y = 4/2 = 2 > 1.
Here both x and y are positive.
Next let x = -4 and y = -2, then x/y = (-4)/(-2) = 2 >1.
Here both x and y are negative.
So again from statement (2) alone, we cannot say definitely whether x and y are both positive or not.
Next combine both the statements together and check.
On combining we have that x = y + 1/2 .
Since (x-y)/y > 0, we have that (y+1/2 - y)/y > 0.
Or 1/2y > 0.
Or 2y > 0.
Or y > 0.
Also if y > 0, as seen from case (1), x > y and so x > 0.
Or both x and y are positive.
The correct answer is hence (C).
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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