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If $$31z5$$ is a multiple of $$3$$, where $$z$$ is a digit, what might be the values of $$z$$?
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## QuestionMathsClass 8

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

$$0,3,6$$ or $$9$$
4.6
4.6

## Solution

Since $$31z5$$ is a multiple of $$3$$.
Therefore according to the divisibility rule of $$3$$, the sum of all the digits should be a multiple of $$3$$.
That is, $$3 + 1 + z + 5 = 9 + z$$
Therefore, $$9 + z$$is a multiple of $$3$$.
This is possible when the value of $$9 + z$$ is any of the values: $$0, 3, 6, 9, 12, 15,..$$ and so on.
At $$z = 0, 9 + z = 9 + 0 = 9$$
At $$z = 3, 9 + z = 9 + 3 = 12$$
At $$z = 6, 9 + z = 9 + 6 = 15$$
At $$z = 9, 9 + z = 9 + 9 = 18$$
The value of $$9 + z$$ can be $$9$$ or $$12$$ or $$15$$ or $$18$$.
Hence $$0, 3, 6$$ or $$9$$ are four possible answers for $$z$$.