If a = 100, 210 * 90,021, is b > a

a) b = 100, 021 * 90, 210
b) b = 100

Answer is D. But how to prove that answer A is correct. In less time

First, factor out a = 100, 210 * 90,021 = (100k+210)(90k+21) = 100k*90k + 100k*21 + 90k*210 + 210*21

Then, factor out b = 100, 021 * 90, 210 = (100k+21)(90k+210) = 100k*90k + 100k*210 + 90k*21 + 210*21

Eliminating like terms, we obtain what's left:
for a: 100k*21 + 90k*210 = 21*(100k + 90k*10)
for b: 100k*210 + 90k*21 = 21*(100k*10 + 90k)

At this point, we eliminate the like term of 21 and are left with fairly simple numbers to be able to determine that we now know whether b>a or not (I actually don't do the math at this point, and if fact could have stopped at the first step when I factored out a and b, as I know I can come up with an answer that leads to SUFF.).

In hind sight, I suggest that no factoring needs to be performed as we are provided with a numeric equation and thus don't care what the result is, we just need to know that we can obtain a numeric result that will determine whether b>a, which by default leads to SUFF>

Can you please cite the source for this question?

gre power prep

One question. Is necessary to do all this operations?

From 1 we can calculate b, so we can compare b with a. SUF

From 2 we can compare b with a. SUF

Is this reasoning correct?

Absolutely correct. We are given a value for A. It doesn't matter what the value is. We are then given a value for B. Thus, we can compare. One note: this problem could not be a real GMAT problem, as the statements contradict each other.