Question

If 74z5 is a multiple of 3, where z is a single digit number, what might be the values of z?

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

Answer 1

The correct option is D

All of these

We have been given that 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.
Also, z is a single digit number.
$\therefore$ 7 + 4 + z + 5 = 16 + z should be a multiple of 3.
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 11 is a double digit number, therefore, z cannot be 11.

Hence 2, 5 and 8 are the possible answers.