Question

solve properly and fast please ​

Answer 1

hey mate

The situation looks like

(10n×an+10n−1×an−1+...+a0)−(an+an−1+...+a0)=(10n−1)an+(10n−1−1)an−1+...+(10−1)a1(10n×an+10n−1×an−1+...+a0)−(an+an−1+...+a0)=(10n−1)an+(10n−1−1)an−1+...+(10−1)a1.

To see that this is divisible by 99, look at 10n−110n−1, it consists of a string of 9.....

therefore 9 is the answer.

Alternative ans

Lets say you have a number in the form of a binomial 10x+y10x+y.

Then you add its 2 digits x+yx+y.

Then you subtracted it.

10x+y−(x+y)=10x−x+y−y=9x10x+y−(x+y)=10x−x+y−y=9x

Therefore, the number is divisible by 9 since it contains multiple of 9.