math

What is the sum of all possible digits that could fill in the blank
in 47_021 so that the resulting five digit number is divisible by 3?

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  1. A number is divisible by 3 if the sum of all the digits in the number is divisible by 3

    eg. 25632 divides evenly by 3
    because 2+5+6+3+2 = 18 which divides by 3
    but 25631 has digits that add up to 17
    so 25631 does not evenly divide by 3

    so let the missing digit in your number be x
    then 17X021 has a sum of 1+7+x+0+2+1 = x+11

    it is easy to see that x+11 evenly divides by 3 when
    x = 1, 4, or 7

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