1. ## largest remainder.

Good morning,
having trouble with this one.

what is the largest possible remainder when a two-digit number
is divided by the sum of its digits?
a)13, b)14, C)15, D)16, E)17

How would I approach this one please?
algebra? explanation if possible
Thanks
Cody, Perth

2. The largest sum is 18 for the number 99. The largest remainder can be 17, but in fact the remainder is 9: $\displaystyle 99=18*5+9$

For the numbers 98 and 89 the sum is 17 and the remainders are 13 and 5.

For 79 the sum is 16 and the remainder is 15. This is the largest remainder that can be obtained.

3. Thank you Red Dog,