If 31z5 is a multiple of 3, where z is a digit, what might be the values of z is ____

Question

If 31z5 is a multiple of 3, where z is a digit, what might be the values of z is ____

Accepted Answer

Concept: We'll start by taking into account the provided expression,

31 z 5

. We must ascertain the values of z. Given that

31 z 5

is an integer multiple of 3, it follows that 31z5 is divisible by 3. Therefore, we will use the three-digit divisibility test, which determines if the sum of all the digits is divisible by three. Now that we are aware, z will have a value between 0 and 9. Therefore, as the number is divisible by three, we will enter z as

0, 3, 6, or 9 .

This will provide us with all of the z's potential values.
We will initially take into account the provided phrase,

31 z 5 .

We must ascertain all z's potential values.
Given that

31 z 5 i

s a multiple of 3, which indicates that

31 z 5

is divisible by 3, the answer to the question is that it is.
Thus, we will examine the three-digit divisibility test, which requires adding all the digits to determine whether the number is divisible by three.
The sum in this case is

3 + 1 + z + 5 = 9 + z .

9+z is therefore a multiple of 3 and is divisible by 3.
Z has a single digit value, hence it can range from 0 to 9.
Consequently, values that z in 9
Given that the number may be divided by three, z will accept the values 0, 3, 6, and 9.
Therefore, the range of z's potential values is

9 + 0 = 9

So, the possible values of z will be
0+9=9
9+1=10
9+2=11
9+3=12
9+4=13
9+5=14
9+6=15
9+7=16
9+8=17
9+9=18
Now, from the obtained sum of digits only 9,12,15,18 are divisible by 3 .
So, the possible values of z are 0,3,6,9.
ExamType: CBSE

If $31 z 5$ is a multiple of 3, where z is a digit, what might be the values of $z$ is ____

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App