Explanation

Since 33m + 22n = 11(3m + 2n), divisibility by 121 is equivalent to 11 | (3m + 2n). For m + n = 2 or 3, the value 3m + 2n is 5, 7 or 8 — never a multiple of 11. At m + n = 4, (m, n) = (3, 1) gives 3·3 + 2·1 = 11. Hence the minimum m + n is 4 (B).