Let n 34d42718 For what values of the digit d is n divisibl

Let n = 34d42718. For what value(s) of the digit d is n divisible by 3, but not 9?

Solution

A number is divisible by 3 if the sum of its digits is divisible by 3

So if d =1 the sum =30 is divisible by 3

d = 4, 7 then the sum is divisible by 3

Hence for d= 1, 4 , 7

A number is divisible by 9 if the sum of its digits is evenly divisible by 9.

If d= 0 , 1 , 2, 3 ,4,5,6, 8,9 the sum is not divisible by 9

Hence d = 0 , 1 ,2, 3, 4, 5 ,6 ,8 and 9