Question

Determine whether each of the strings of 12 digits is a valid UPC code.

a) 036000291452

b) 012345678903

c) 782421843014

d) 726412175425

Short answer

1. Since the result is zero, the UPC code is valid.

1. Since the result is nonzero, the UPC code is not valid.

1. Since the result is zero, the UPC code is valid.

1. Since the result is zero, the UPC code is valid.

Step-by-step solution

Step 1

For a UPC code $x_1{x}_2\dots x_{11}{x}_{12}$the following congruence holds:

Step 2

1. Given :

Use the above expression to calculate the check digit:

Since the result is 0, the UPC code is valid.

Step 3

1. Given :

Use the above expression to calculate the check digit:

Since the result is nonzero, the UPC code is not valid.

Step 4

1. Given :

Use the above expression to calculate the check digit:

Since the result is 0, the UPC code is valid.

Step 5

1. Given :

Use the above expression to calculate the check digit:

Since the result is 0, the UPC code is valid.