Question

The sum of digits of the result of the subtraction 10<sup>99 – 99 is

872 . 873. 874. 876

​​</sup>

Answer 1

1. Realize that 10^99 is just 1 followed by 99 zeros.
2. When you subtract 99, from 100000....00, you must borrow from every column all the way to the left.
3. So now, every 0 changes into a 9, except the last zero, which is 10 after the borrow. That means you have 98 nines. And the 1 in the front becomes a 0.
4. Perform the subtraction in the one's place: 10 - 9 = 1.
5. Perform the subtraction in the ten's place 9 - 9 = 0.
6. Perform the subtraction all the way across: 9 - 0 = 9 (same thing 97 times)
7. Sum up 1 + 0 + 97*9. You get 874.