Question

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

Answer 1

$\text{Since}31z5\text{is a multiple of}3.\text{Therefore according to the divisibility rule of}3,\text{the sum of all the digits should be a multiple of}3.\text{Since,}z\text{is a digit}.$
$\therefore$ $3+1+z+5=9+z$
[1 mark]
$\text{As this sum is greater than}9,\text{the multiples of}3\text{which we can take are}9,12,15,18\text{and so on}$
$\text{If}9+z=9$
$\Rightarrow z=0$
[0.5 mark]

$\text{If}9+z=12$
$\Rightarrow z=3$
[0.5 mark]

$\text{If}9+z=15$
$\Rightarrow z=6$
[0.5 mark]

$\text{If}9+z=18$
$\Rightarrow z=9$
[0.5 mark]

$\text{Hence,}0,3,6\text{and}9\text{are four possible answers.}$