Question

If 21z4 is a multiple of 9, where z is a digit, what might be the values of z?

• A. 2
• B. 0
• C. 5
• D. All of these

Answer 1

The correct option is A

2

Since 21z4 is a multiple of 9.
Therefore according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.
Since, z is a digit.
$\therefore$ 2 + 1 + z + 4 = 7 + z
The first multiple of 9 which is greater than 7 is 9
$\Rightarrow$ 7 + z = 9 $\Rightarrow$ z = 2
The next multiple of 9 which is greater than 7 is 18
$\Rightarrow 7+z=18\Rightarrow z=11$
But z is a digit.
Therefore, z cannot be equal to 11.
Hence 2 is the only possible answer.