SOLUTION: If X is a digit such that 35*64 is divisible by 3, find the possible values of X.

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Question 811284: If X is a digit such that 35*64 is divisible by 3, find the possible values of X.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean the number 35X64 with X as the middle digit is divisible by 3?

A number is divisible by 3 if, and only if the sum of its digits is divisible by 3
3%2B5%2B6%2B4=18 is already divisible by 3 since 18=3%2A6 .
To make 3%2B5%2B6%2B4%2BX=18%2BX divisible by 3, X itself must be divisible by 3.
So to make 35X64 divisible by 3, X itself must be divisible by 3, or zero.
The possible values for X are
0, 3, 6, and 9.