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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?

 Jun 23, 2020
 #1
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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.

 Jun 23, 2020
edited by gwenspooner85  Jun 23, 2020
 #2
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Except 45 - 37 = 8 not 18. So, you could have: 1+7 =8, 2+6 =8, 3+5 =8, 4+4 =8, 5+3 =8, 6+2 =8, 7+1 =8, 9+8 =17, 8+9 =17,
Grand Total =[8 x 7] + [17 x 2] =90

Guest Jun 23, 2020

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