Suppose the seventh digit of the ISBN 0-7137-1x11-0 is obscured. What is the missing digit?
A) 2
B) 5
C) 8
D) X

Question

Quizplus · Accepted Answer

To find the missing digit, we need to use the fact that the sum of the products of the digits in the odd positions (not including the check digit) plus three times the sum of the products of the digits in the even positions (not including the check digit) must be congruent to zero modulo 10. This is known as the ISBN check digit calculation formula. By plugging in the given digits and the unknown digit (represented by x) into the formula, we get:
0 + 7 + 1 + 7x + 1 + 1 + 0 + 0 + 11 + 0 + 0 + 3(1 + 3 + x + 1 + 7) ≡ 0 (mod 10)
Simplifying this equation, we get:
28 + 10x ≡ 0 (mod 10)
Dividing both sides by 2, we get:
14 + 5x ≡ 0 (mod 5)
Subtracting 14 from both sides, we get:
5x ≡ 1 (mod 5)
Since 5 is a prime number, we can cancel it from both sides to get:
x ≡ 1/5 ≡ 6 (mod 10)
Therefore, the missing digit is 6, which corresponds to choice C.

Suppose the Seventh Digit of the ISBN 0-7137-1x11-0 Is Obscured