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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
Since 31z5 is a multiple of 3, the sum of its digits will be a multiple of 3.
That is, 3 + 1 + z + 5 = 9 + z is a multiple of 3.
This is possible when 9 + z is any one of 0, 3, 6, 9, 12, 15, 18, and so on …
Since z is a single digit number, the value of 9 + z can only be 9 or 12 or 15 or 18 and thus, the value of x comes to 0 or 3 or 6 or 9 respectively.
Thus, z can have its value as any one of the four different values 0, 3, 6, or 9.
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