A number is divisible by 9 if the sum of its digits is divisible by 9. For example, the number 19,836 is divisible by 9 but 19,825 is not.
If D767E89 is divisible by 9, where D and E each represent a single digit, what is the sum of all possible values of the sum D+E?
We look at the current sum of the digits we have(not including D and E).
The sum is 7+6+7+8+9=37. So 37+D+E must be a multiple of 9. Now let's look at the multiples of 9 greater than 37:
45, 54, 63....
However, the greatest that D+E can add up to is 18, so the only possible multiples of 9 would be 45. Since there are no other possible multiples of 9, then the sum of D+E is 45-37=8.