"And, technically, after you see that options A and C each have a 2-digit repeater... you know E must be right without trying it, b/c there's only one right answer - A and C can't both be it. But you should probably still try E just to be sure."
That is the best answer in this thread. GMAT, much like SAT, tests simple math in tricky ways. That includes in ways a person won't have seen in class work. It tests reasoning using math as a medium.
As Stacey mentioned, the key to GMAT math is using your noodle. Identify the problem type, set up the problem (that's a key for this type), make sure all the work you've written is correct and you know what the problem asks, then complete it and double check the answer.
With problems that appear to be long series, including fraction problems of this nature, finding the first 3-5 digits or numbers will generally reveal the pattern.
For example, this problem someone mentioned: "Last week manhattan GMAT challenging problem was to find the 18th number in 1/37 on which I wasted 2 mins. or some. then too wrong answer. I should have simply multiplied 27 to numerator & denominator. I would hv got
027/999 = .027027027027027027"
1 divided by 37, in long division after 5 digits you suspect it keeps repeating, after 6 you know it repeats. Then it's an easy matter to count to 18 to know a 7 will be in that place.
The only reason long division takes people more time is that they don't practice with it. In a problem like this it's likely a 6th grader, who is constantly working long division, would solve it quickly. That's the first thing he would try and he's pretty quick with it.
