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Question:

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

Solution:

For 31z5 to be a multiple of 3, 3 + 1 + z + 5 should be a multiple of 3. So, the values of z can be 0, 3, 6, or 9. If z = 0, then the sum is 9. If z = 3, sum is 12. If z = 6, sum is 15. If z = 9, then the sum is 18. In the above cases, we see that the sums are all multiples of 3. Hence, z can be 0, 3, 6, or 9.