Question

If 24x is a multiple of 3, where x is a digit, what is the value of x? [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

24x 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.

$\therefore$ 2 + 4 + x = 6 + x

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.

$\Rightarrow 6+x=6\Rightarrow x=0$

$\Rightarrow 6+x=9\Rightarrow x=3$

$\Rightarrow 6+x=12\Rightarrow x=6$

$\Rightarrow 6+x=15\Rightarrow x=9$

Thus, x = 0, 3, 6, 9