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

Q4. If $31z5$ is a multiple of 3, where $z$ is a digit, what might be the values of $z$?

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If a number is multiple of 3, the the sum of its digits will be multiple of 3.

Sum of digits of 31z5 = 3 + 1 + z + 5 = 9 + z

9 + z is a multiple of 3 and since z is a single digit

9 + z  is any one of 9, 12, 15 or 18

thus value of z is 0, 3, 6 or 9 respectively.

Hence possible value of z is 0,3,6 or 9.

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