Question

If 74z5 is a multiple of 3, where z is a digit, then what are the possible values of z?

• A. 2
• B. 5
• C. 8
• D. All of these

Answer 1

The correct option is D All of these

Since 74z5 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.
$\therefore$ 7 + 4 + z + 5 = 16 + z
The first multiple of 3 which is greater than 16 is 18
$\Rightarrow$ 16 + z = 18 $\Rightarrow$ z = 2
The next multiple of 3 which is greater than 16 is 21
$\Rightarrow 16+z=21\Rightarrow z=5$
The next multiple of 3 which is greater than 16 is 24
$\Rightarrow 16+z=24\Rightarrow z=8$
The next multiple of 3 which is greater than 16 is 27
$\Rightarrow 16+z=24\Rightarrow z=11$
But z is a digit.
Therefore, z cannot be 11.
Hence 2, 5 and 8 are the possible values of z.