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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 for 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 for the last problem. Why is this so?

Grade:12

2 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Since, 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
Ram Kushwah
110 Points
3 years ago
Dear Pawanji,
 
Let N=31z5
Sum of digits=3+1+z+5=9+z
 
If N is divisible by 9 then sum of digits should be divisible by 9
thus 9+z must be divisble by 9
 z is a digit so it can be 0 to 9 any number
 
If z=0 then 9+z=9+0=9 is divisible by 9
or z=9 then 9+z=9+9=18 is divisible by 9
 
Thus z=0 or 9
 
Please aprove
 
Thanks

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