2. 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 for the last problem. Why is this so?

Answers (1)

If a number is a multiple of 9, then the sum of its digit will be divisible by 9 .

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

hence 9 + z have to be multiple of 9 

this possible when 9 + z = 0, 9 , 18, 27 ...

since z is a single digit number this sum can only be 9 or 18 . therefore, z should be 0 or 9 .

hence two possible values of z = 0 or 9.

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