jmc

Question

The UPC code, made up of numbers and dashes, on a video tape is 9-78094-11006-x. The digit x is in the 12^th position. Let n be the value obtained by adding the digits in the odd positions, tripling that sum, and then adding the digits in the even positions. A valid UPC code is such that n is divisible by 10. For what value of x will this UPC code be valid?

Accepted Answer

Tripling the sum of the odd digits and adding the even digits, we get n = (9 + 8 + 9 +1+ 0 + 6) 3 + (7 + 0 + 4 +1 + 0) = 33 3 + 12 = 99 +12 = 111. To make this value divisible by 10, the twelfth digit must be 9.