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If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers to the last problem. Why is this so?

 If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers to the last problem. Why is this so?

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
11 months ago
Dear Student

31z5 is a multiple of 9.
Therefore, according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.
3 + 1 + z + 5 = 9 + z
Therefore, 9 + z is a multiple of 9.
This is only possible when 9 + z is any one of these numbers: 0, 9, 18, 27, and so on.
This implies, 9 + 0 = 9 and 9 + 9 = 18
Hence 0 and 9 are two possible answers.

Thanks

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