Question

Find the value of the digit indicated with a question mark . ISBN value 0-321-50230-?

Answer 1

An ISBN (International Standard Book Number) is a 10 digit number that is used to identify a book.

Nowadays 13 digit ISBN are being used but earlier it was 10 digit ISBN.

The first nine digits of the ISBN number are used to represent the Title, Publisher and Group of the book and the last digit is used for checking whether ISBN is correct or not.

We will consider an example using alphabets instead of numbers for easier understanding.

Let abcdefghij is an ISBN with 10 digits.

Now a*10+b*9+c*8+d*7+e*6+f*5+g*4+h*3+i*2+j*1 should be a number that is exactly divisible by 11 without leaving any remainder. Then it is a valid ISBN. otherwise invalid.

So we follow this technique to find the last digit of our question ISBN. Let m be the last digit.

0*10+3*9+2*8+1*7+5*6+0*5+2*4+3*3+0*2+m*1

= 0+27+16+7+30+0+8+9+0+m

= 97+m for this to be exactly divided by 11 we have to give m value as 2. Then 97+2 = 99 will be divided by 11 without leaving any remainder.

So the last digit of the given ISBN is 2.

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Thanks for understanding.