Question

Question 4

If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?

Answer 1

Since 31z5 is a multiple of 3.
Therefore according to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.
Since, z is a digit.
$\therefore$ 3 + 1 + z + 5 = 9 + z
$\Rightarrow$ 9 + z = 9 $\Rightarrow$ z = 0
$If3+1+z+5=12$
$\Rightarrow 9+z=12\Rightarrow z=3$
$If3+1+z+5=15$
$\Rightarrow 9+z=15\Rightarrow z=6$
$If3+1+z+5=18$
$\Rightarrow 9+z=18\Rightarrow z=9$
Hence 0, 3, 6 and 9 are four possible answers.