OA follows after few more responsesm&m wrote:I think the answer is surprisingly E (I've never had a "none of the above" on a GMAT question)
to get sum of 1, it's essentially all the factors of 10..i ie 1, 10, 100, 1000, 10000, etc.
there are 2006 terms
to get sum of 2, we could have form where 2 is leading ie, 2, 20, 200, 2000, etc. as above so 2006 terms
OR
we could have 11,110,101,1001,1010,1100, etc. which has even MORE than 2006 terms
so m-n must be Very negative since n >> m hence E
What's OA?
Good job Uri. OA is 1. After every 9 terms, total 1s and 2 the same. There are 10^2006 numbers. (10^2006)/9 has remainder of 1. To see it,Uri wrote:i think the answer is 1
1.....2......3......4.....5.......6......7......8........9
10...11....12....13....14....15....16.....17......18
19...20....21....22....23....24....25.....26......27
observe that all the numbers in the same column produce the same integer when their constituent digits are summed up. if we continue this way, we will find that ultimately 100 comes just below 1. so, 10^any number will also come just below 1. until that final number, the total number of 1's and 2's will be same. so when that final number (10^2006 in this question) is taken into account, we will have one more 1 than we will have 2.
