Tough nut to crack!!

Guys its been a while that I have been practicing for GMAT, and although I am able to crack the easy to crack nuts, the challenging ones still pose a challenge. Being always on the lookout for tough problems I linger around on forums, especially BeatTheGMAT, I like the way people post questions and there is a good amount of discussion and expert replies..

Say for example.. I am excellent at exponents and good at permutations, but was totally taken aback by this problem of the BeatTheGMAT practice questions.

How many integers between 1 and 10^21 are such that the sum of their digits is 2?

now how do I approach this problem?
should I even care to write 1 and 21 zeroes behind it to have better clarity of the problem.
I guess not.
We can have a case where we have 1+1=2 and 19 zeroes
21C2 which shall give 21*20/2 =210
and another set of numbers which has just the value 2
now this is where I faltered... I calculated the wrong number of zeroes.

If an integers is between 1 and 10^21 so 2* 10^21 is out of question,
there can be only 21 such numbers..
so in effect its 210+21 and not 210+22.
Just when I had thought the tough part in the problem the permutation was over and I kind of relaxed mentally, this problem shook me... I got it wrong!

Well.. while practicing such multi-layered tough problems, I have come to realize a few things...
Firstly... never relax in between a problem
Secondly..They just dont test only the basics in GMAT (as per my past GMAT experience, they try and make problems more and more complex and also try to trick you into making a mistake)
Thirdly.. never give up  ( I was around 720s in practice tests but in the real GMAT I scored a 670)
Finally...practice only on GMAT like material.

The first three points can come as a second nature to you after some practice, but the last point is of importance.Manhattan is great for Sentence Correction and PowerScore cricitical reasoning bible is a must do.But till date I haven't found much success in getting a good theory material for the Math section.
As far as the practice material is concerned there is TONNES of crap material (read 1000 series and similar material) available but its waste of time and energy and is not than useful. I guess OG11 and OG12 is a must.
Among the new materials I am referring to the practice questions of BTG is really good.
(http://practice.beatthegmat.com) especially the RC,SC and Math part.

I am glad to share this news with you all, well I was among the lucky few to win these questions in the 100k challenge. http://www.beatthegmat.com/mba/100k
The thing which sets it apart from other materials is it also give the Avg%Correct and Avg Time.
It gives me an overall idea as to how I fared compared to others, on any question.
Since GMAT also uses the same percentile standing, its good to have such an idea.
I wonder how in the good old days without internet, how people used to manage their studies,
decide when to take the test and know where they stand?