Here's my solution. I only have 1 minute so please let me know if the logic is not correct.
We want to know if 1/(a-b)<b-a
In other words if (b-a)-1/(a-b)>0
or if (-(a-b)^2-1)/(a-b)>0
We can see that the numerator is definitely negative. So the only thing we need to know is if a-b>0
1) answers it. Therefore sufficient.
2) a-b could be negative or positive. Thus insufficent.
Therefore the answer is A.
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.