• # question_answer 4)                 If $24x$ is a multiple of 3, where $x$ is a digit, what is the value of $x$? (Since $24x$ is a multiple of 3, its sum of digits $6+x$ is a multiple of 3; so $6+x$ is one of these numbers: 0, 3, 6, 9, 12, 15, 18, ... .But since $x$ is a digit, it can only be that $6+x=6$ or 9 or 12 or 15. Therefore, $x=0$ or 3 or 6 or 9. Thus, $x$ can have any of four different values.)

Solution given with question.                 If $31z5$ is a multiple of 3, where z is a digit, what might be the values of z?                 Since $31z5$ is a multiple of 3, its sum of digits $3+1+z+5=9+z$ is a multiple of 3; so $9+z$ is one of these numbers: 0, 3, 6, 9, 12, 15, 18, ... . But since z is a digit, it can only be that $9+z=9$ or 12 or 15 or 18. Therefore, z = 0 or 3 or 6 or 9.