TITLE: Need faster division technique for $4$ digit numbers.
QUESTION [5 upvotes]: I have to divide $2860$ by $3186$. The question gives only $2$ minutes and that division is only half part of question. Now I can't possibly make that division in or less than $2$ minutes by applying traditional methods, which I can't apply on that division anyways.
So anyone can perform below division using faster technique?
$2860/3186$
Thanks for reading, hoping to get some answers. :)
This is a multiple choice question, with answers $6/7$, $7/8$, $8/9$, and $9/10$.

REPLY [2 votes]: This isn't so much a math answer as a test-taking answer: You don't have to compute the fraction, you just have to determine which is the right answer.

2860/3186
This is a multiple choice question, with answers 6/7, 7/8, 8/9 and 9/10.

If you reduce the fraction to get a/b, then b must be a divisor of 3186. This allows you to immediately eliminate some choices. It can't be 9/10 because 10 doesn't divide 3186. You can quickly check that 7 and 8 don't divide 3186, but 9 does, so the only one of the choices that has a shot at being the correct answer is 8/9.
Incidentally, none of those answer is correct; it's not 8/9 either. The furthest you can reduce the fraction is 1430/1593, so you must have an error in your question. Either the fraction is wrong or you're supposed to find the best approximation rather than the actual value.