Not sure, but judging by the pattern of multiplying the first 3 or 4 101s, I would say E
gmatnub, lets try ur mathod. I belive finding pattern is the best method on GMAT. lets see.
101^2= 10201 and 10201 - 1 = 10200. ( can't be divided by (E)100,000,00)
101^3= 1030301 and 1030301 - 1 = 1030300 ( again E is not the correct option )
there is a rule i.e. if (a-b) is divided by n then (a^k - b^k) too is divided by n. for all k>=1
However I am not sure if this rules holds true for finding the greatest divisor.
so lets try
if the highest divisor that will divide (101 - 1) is 100 then 100 will also be the highest divisor for (101^100 - 1).....Option A
even if we try the pattern mathod, as we tried above for 101^2 and 101^3 then too 100 will be the highest divisor.
So, answer IMO is A