SOFTengCOMPelec has the right answer, and it's based on logic more than algebra. To start with we have only ONE variable: the fraction of the sample that picked Option A is 0.1021. Then there's the logical statement that the ONLY other choice was Option B, and hence the fraction that made that choice is already known.
The point about rounding is crucial. In attempting to answer OP's question we can make an assumption (since the info is not provided) that the results quoted are absolutely precise with NO rounding. The precision of the the result is 4 significant digits, so the possible variability in it is no more than than ± 1 in 10,000. Thus the MINIMUM sample size is 10,000. Now, a larger sample size could also generate exactly that result of 0.1021 (with an infinite number of zeroes after that to indicate absolute precision) ONLY if the sample size is exactly an integer multiple of 10,000. That is, the sample size also could be 20,000, 30,000, 100,000 or 1,000,000, etc. But it cannot be 19,287, for example, because that could not generate that exact result without any rounding. IF we assume that some rounding has been done already, then all bets are off and you can NOT determine a unique minimum sample size.
In terms of mathematics, this type of statistic falls into the realm of a Binary Distribution (that is, there are only two possible choices for an individual observation), an area widely used in studies of the occurence of defects and of reliability or failure of equipment.