Question

If 31z5 is a multiple of 3 where z is a digit, then what might be the value(s) of z?

Answer 1

possible values are 3,6,9

Answer 2

Heya !!!

Thanks for asking the question!

Here is your answer : -

Things which you must need to know before reading the solution :

What are multiples ?
- Multiples are those numbers which when divided by any other no. leaves remainder 0 .
Then we can call the particular no. is multiple of that dividend.For example : - 12 is a multiple of 4.

What are divisibility tests?
- Divisibility tests are small methods to find out the given no. is divisible by the required no. or not.

What is the divisibility test for 3?
- A given no. is only divisible by 3 only if it's sum of all digits is divisible by 3. For example : 108 is divisible by 3 as it's sum of digits is 9 which is in turn divisible by 3.

Now coming back to our question :

The given no. is 31z5 and it is a multiple of 3.
To find ,
The possible values of z.

Now according to divisibility test of 3,

3 + 1+ z + 5 must be divisible by 3.
i.e 9+z must be divisible by 3

So,
The values of z which will make the given algebraic expression true for the given condition are :
z = 3,
z = 6, and
z = 9.



Hope it helps you.