Final answer:
The provided UPC code 0-51201-67421-5 is not valid according to the modulo 10 algorithm, as the calculated check digit does not match the given check digit.
Step-by-step explanation:
To determine if the UPC code 0-51201-67421-5 is valid, we need to perform a check-digit calculation using the assigned numbers. The UPC (Universal Product Code) uses a specific algorithm, known as the modulo 10 algorithm, to validate the accuracy of the numbering. This involves summing alternating digits, multiplying, and comparing the result with the last digit (check digit). Let's check the given UPC code step-by-step:
- Start with odd-positioned digits (not including the check digit): 0 + 5 + 2 + 1 + 7 + 2 = 17.
- Multiply by 3: 17 * 3 = 51.
- Now, take the even-positioned digits (excluding the first digit): 1 + 0 + 1 + 4 + 1 = 7.
- Add the results of step 2 and step 3: 51 + 7 = 58.
- Find the smallest number that, when added to the result in step 4, makes a multiple of 10. In this case, 2 makes it 60, which is a multiple of 10.
- The check digit should be the number from step 5, which is 2. The actual check digit on our code is 5, therefore, the UPC code provided is not valid according to the calculation.
In doing this check, we've determined that the UPC code in question does not pass the validity test and appears to be incorrect based on the modulo 10 algorithm.