Question

Is the following a valid UPC number? If not, what is the value that should be the "check digit"?

442578105204

a) Yes, the number is valid
b) No, the "check digit" should be 2
c) No, the "check digit" should be 5
d) No, the "check digit" should be 1

Answer 1

The UPC number 442578105204 is not valid. Upon applying the check digit verification formula, we find that the check digit should be 0, which does not match the given number and is not an option listed in the provided answers.

Step-by-step explanation:

To determine if 442578105204 is a valid UPC number, we must use the UPC check digit formula, which verifies the last digit, known as the check digit. According to this formula, we:

• Add the digits in the odd-numbered positions (first, third, fifth, etc.) and multiply the sum by 3.
• Add the digits in the even-numbered positions (second, fourth, sixth, etc.) to the result from step 1.
• Determine the difference between the result from step 2 and the nearest equal or higher multiple of 10. This difference should be the last digit of the UPC number, the check digit.

For the provided number 442578105204:

1. (4 + 2 + 7 + 1 + 5 + 0) * 3 = (19) * 3 = 57
2. 57 + (4 + 5 + 8 + 0 + 2 + 4) = 57 + 23 = 80
3. The next multiple of 10 after 80 is 80, which means the check digit should be 0 (80 - 80 = 0)

Since the current check digit is 4, the UPC is not valid. The correct check digit should be 0, but this is not an option provided in the answers. Thus, none of the proposed answer choices are correct.