Question

When 1013 is divided by a 2-digit number N, the remainder is 12. Find the sum of all possible values of N?

Answer 1

Take 12 from 1013=1001=7×11×13. So the 2 digit numbers are 11 and 13. However, the remainder has to be 12 which is bigger than 11, so we must exclude 11 from the set. And 7×11=77 and 7×13=91, two more 2 digit numbers, 91+77=168, so the total of all three is 13+168=181.