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Clue 1 - 2x-2y = 1 ==> 2(x-y) = 1 => x - y = 1/2. Ex - x = 1/4, y = -1/4 one is positive and another another is negative. x = 3/4, y = 1/4 = both are positive, x = -1/4 and y = -3/4, one is negative and another is positive. Cannot say whether x and y are positive.

Clue 2 - x / y > 1 ==> x > y - Cannot say whether x and y are positive.

Even if you combine both the clues, also you cannot say that x and y are positive.

I'll go with C. from 1 we have : x= y + 1/2 insuf from 2 : x/y > 1 insuf 1&2: x/y= (y+1/2)/y = (1+ 1/2y) > 1 then 1/2y > 0 or y must be greater than 0. So we can see that both x and y are greater than 0.

1) can be simplified to x-y = 1/2 => x = y + 1/2. This is equation of line which passes through 1st , 2nd as well as 3rd quadrant. so x and y both may not be positive. insuff

2) this represents area around the line x=y (as shown in attached fig). which passes through 1st and 3rd quadrant. so again x and y can both be positive or both be negative.insuff.

together, (y+1/2)/y > 1 1 + 1/2y > 1 1/2y > 0 i.e y > 0, from 2 it implies that if y>0, x must also be >0

Suff.

C

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Last edited by alpha_plus_gamma on 10 Dec 2008, 20:39, edited 2 times in total.