Bunuel
What is the smallest positive number that should be added to 27452 to make it exactly divisible by 9?
A. 1
B. 2
C. 7
D. 8
E. 9
Divisibility by 9 is checked by dividing the sum of the digits by 9 or simply, as we keep getting a sum of 9, we keep ignoring those digits.
27452
2+7 is 9 so ignore these digits.
4+5 = 9 so ignore these digits too.
We are left with 2.
To be divisible by 9, we need another 7. So if we add 7 to this number, it will become 27459 which gives 2+7, 4+ 5 and 9. All divisible by 9.
Try the same for a greater number 2647530919
2+6 = 8.
8 + 4 = 12 which is 3 more than 9. Just consider 3 now.
3+7 = 10 which is 1 more than 9.
1+5+3 = 9 ignore all digits till now.
Both 9s and 0 are divisible by 9. We are left with 1. When we divide this number by 9, we get remainder 1. So we should add another 8 to it to make it divisible by 9.