Question

Each of the following four digit numbers is divisible by 9. Find the value of the digit x. [4 MARKS]

i) 15x2

ii) 4x23

Answer 1

Concept: 1 Mark each
Application: 1 Mark each

i) 15x2 is divisible by 9

$\Rightarrow 1+5+x+2$ is divisible by 9

$\Rightarrow$ 8 + x is divisible by 9

8 + x = 9 or 18 or 27, .........

x = 9 - 8 or 18 - 8 or 27 - 8, ...........

x = 1 or 10 or 21, ............

Since, x is a digit.

$\Rightarrow x=1$

ii) 4x23 is divisible by 9

$\Rightarrow 4+x+2+3$ is divisible by 9

$\Rightarrow$ 9 + x is divisible by 9

9 + x = 9 or 18 or 27 .........

x = 9 - 9 or 18 - 9 or 27 - 9 ...........

x = 0 or 9 or 18

Since x is a digit,

x = 0 or 9.