well...i think the answer is E (correct me if i am wrong)
and i don't know what approach you followed to arrive at the answer and hence can't say if my approach is shorter than yours. anyways...
Remainder of 10^m + n = 1 + remainder of n/3 (as the remainder of 10^m will always be 1)
Remainder of 10^n + m = 1 + remainder of m/3 (as the remainder of 10^n will always be 1)
so the question is "Is r(n/3) > r(m/3)?"
1) m > n => doesn't say anything much
2) r(n/3) = 2, doesn't talk about m so of no use
1) + 2) also don't help us much..if n = 2, then m can be 3, 4 or 5 with remainder 0, 1 and 2 respectively...so we can't say
Hence the answer is E.
Please note: If the question would have been
Is Is r(n/3) < r(m/3)?
then the answer would be B as r(m/3) can never be greater than 2
HTH
cheers