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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
one year ago
Dear Student

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.
0, 3, 6 or 9 are four possible answers for z.

Thanks

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