Question : Are x & y both positive
There is nothing in the question stem that can be rephrased. So directly attack the statements
Picking numbers would be the best approach to solve this question.
Statement 1:
2x - 2y = 1
=> x - y = 1/2
Let x = 0
0 - y = 1/2
=> y = -1/2
Both x & y are not positive . Ans NO

let x = 1
1 - y = 1/2
=> y = 1/2
Both x & y are positive . Ans Yes

Since we got both yes & no for an answer, the statement is insufficient

Statement 2:

x/y > 1

From this statement we know that
1) Either both x & y are positive or both x & y are negative
2) If both are positive then x>y and if both are negative than x<y

let x= 2

2/y > 1
=> 0 < y < 2
Both x & y are positive. Ans Yes

let x = -2
-2/y > 1
=> -2 < y < 0
Both x & y are not positive . Ans No

Since we got both yes & no for an answer, the statement is insufficient

Combining both the statements

Let x = 1
Using statement 1: 1 - y = 1/2 => y = 1/2
This also satisfies statement 2 : x/y > 1
Both are positive

Now let x = -1/2
Using statement 1: -1/2 -y = 1/2 => y = -1
This doesn't satisfy statement 2: As in this case x/y = 1/2 < 1
You can also check for a couple of more negative numbers, both statements will never satisfy.
So both cannot be negative.

Hence both statements are together sufficient

The correct answer is C

Given that,

(1) 2(x-y) =1
Therefore, x-y = 1/2
INSUFFICIENT

(2) x/y > 1

There can be two possibilities,
x>y when y > 0
x<y when y< 0

INSUFFICIENT, since we cannot get enough details from this

Combined,
From (1) we get, x-y=1/2
Thus, x>y when y>0
Thus, x>0

Therefore, combined we get a solution.
Option: C

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Thank you for confirming the correct approach. Can you share your comments for GMATPrep SC question at https://www.beatthegmat.com/sc-question- ... 17146.html