20. Let $N$ be the smallest positive integer such that the sum of its digits is 2021 . What is the sum of the digits of $N+2021$ ?
A 10
B 12
C 19
D 28
E 2021
Solution
A

For $N$ to be the smallest integer with digit sum 2021, it must have the least number of digits possible, hence it has as many digits 9 as possible. $2021=9 \times 224+5$ so $N$ is the 225 -digit number $599 \ldots 999$. Thus $N+2021$ is the 225 -digit number $600 \ldots 002020$ which has digit $\operatorname{sum} 6+2+2=10$.