What is the quickest way to solve this division problem:



10^8 - 10^2/ 10^7 - 10^3

You can take 10^2 common out from numerator and 10^3 common out from denominator as given below:-
(10^2(10^6-1))/(10^3(10^4-1))

Since number 1 is negligible in comparision to 10^6 and 10^4 hence it can be neglected as given below:-
(10^2(10^6))/(10^3(10^4))
=10^8/10^7
=10
Hence answer should be 10.

What is OA?

wait, so this was a gmatprep problem? if so, where are the answer choices?

i'm going to assume that there are supposed to be parentheses around the first two terms, and also around the last two terms (so that the problem involves division of one binomial by another binomial). if not, then the problem has an incredibly ugly answer (and is not gmat-like at all).

you can factor out 10^2 from both top and bottom:
top = (10^2)(10^6 - 1)
bottom = (10^2)(10^5 - 10)
these cancel, leaving you with (10^6 - 1)/(10^5 - 10). (if you don't see how this is done, imagine x's in place of all the 10's.)

at that point, you may as well just evaluate the expression = 999,999 / 99,990 = 10,101 / 1010, which is as far as it reduces.

you cannot, as the other poster says, just pull 1's out because they're smaller than other terms - unless the problem asks you to approximate, in which case that's exactly what they want you to do.

in retrospect, this problem may be easiest by resorting to exact numbers asap: just evaluating the top and bottom right off the bat gives 999,999,900 / 9,999,000, after which knocking off 2 zeros gives what we have above (with less blood, sweat, and tears).

--

if you happened to mis-transcribe the problem, and it was supposed to say (10^8 - 10^3) / (10^7 - 10^2), then the value of that expression is exactly 10.

the question did ask us to approximate -- it says "closest to"
the way that I though about it is that...the 1's are so small that they become irrelevant to the calculation...then one can pretty quickly simplify/approximate down to 10 -- the answer.

ok, guys -- what are the answer choices to this problem?

someone please post the answer choices, per the forum rules -- thanks.
if this is not done in a few weeks, we'll delete the thread.

I got this question too on my GMAC practice exam. The solution to this answer is best explained here: http://www.beatthegmat.com/10-8-10-2-10 ... 18534.html

Basically you factor out 10^2 from Numerator; 10^3 from Denominator so you are left with (10^6)/(10^5) which is equal to 10 (the answer).

OK, people -- this is a final request: Per the forum rules, please post the full problem, with all answer choices. If this is not done in the next week or two, we will delete this thread.
Thanks.

the ANSWERS are
a. 1
b. 10
c. 10^2
d. 10^3
e. 10^4

:)

thanks. see Ron's analysis for a full explanation of the problem, and please in the future make sure to post the ENTIRE problem with ALL answer choices or we will be unable to help you. please note, as Ron initially pointed out, that the original question posted would never be asked on the GMAT; the most important part (the approximation) was left out initially, and without you giving us the full problem and answer choices there is often not much we can do to help..

_________________
Tim Sanders
Manhattan GMAT Instructor