Problem 1
You can rephrase the question stem as follows:
1/(x-y) < y-x ?
1/(x-y) < -(x-y) ?
1/(x-y) + x-y < 0 ?
[(x-y)^2 + 1] / (x-y) < 0 ?
In a case such as this where we have the form a/b < 0, a and b must have opposite signs in order for the quotient to be negative. That is, either the numerator or the denominator is positive and the other is negative.
(x-y)^2 + 1 is always positive, so (x-y) must be negative for this inequality to hold true.
x-y < 0 ?
Is x less than y?
Statement 1) x is not given. x could be greater or less than y even with a positive value of y, depending on x. Insufficient.
Statement 2) y is not given. x could be greater or less than y even with a negative value of x, depending on y. Insufficient.
Combined) x is negative and y is positive, therefore x < y. Sufficient.
C
Problem 2
Is the product of x and y greater than 9? Testing extreme values for problems like this seems to work best.
Statement 1) x<=4 and y>=2. With x=1 and y=100, xy=100 and satisfies, but with x=-1 and y=100, xy=-100. Insufficient.
Statement 2) x>=2 and y<=4. Same as statement 1 but with the variables reversed. Insufficient.
Combined) 2<=x<=4 and 2<=y<=4. With x=2, y=2 we have xy=4, but with x=4, y=4 we have xy=16. Insufficient.
E
