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4.31z5 is a multiple of 3, where z is a digit, what might be the values of z?

We are given that 31z5 is a multiple of 3. So, the sum of its digits 3 + 1 + z + 5 = (9 + z) should be multiple of 3.
Therefore, (9 + z) is one of the numbers 0, 3, 6, 9, 12, 15, 18, …so on but given that z is a digit. Therefore (9 + z) must be equal to 9 or 12 or 15 or 18.

So we have, 9 + z = 9 or 12 or 15 or 18

$$\Rightarrow$$ z = 0 or 3 or 6 or 9

Hence, z can have any of the four different values, which are 0, 3, 6 or 9.