Is xy > 0?
(1) x-y > -2
(2) x-2y < -6
Statement 1: x > y-2
If y=2 and x= 1, is 1*2 > 0? YES.
If y= -1 and x = 1, is (1)(-1) > 0? NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.
Statement 2: x < 2y-6
If y=1 and x = -10, is (1)(-10) > 0? NO.
If y = 10 and x = 1, is 1*10 > 0? YES.
Since the answer is NO in the first case but YES in the second case, INSUFFICIENT.
Statements 1 and 2 combined:
Linking together the two statements, we get:
y-2 < x < 2y-6
y-2 < 2y-6
4 < y
y > 4.
Since y > 4 and x > y-2, we know that x > 2.
Thus, xy > 0.
SUFFICIENT.
The correct answer is
C.
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