Chapter 8.2, Problem 65ES

Banking. When banks process an electronic funds transfer (EFT), they assign a nine-digit routing number, where the ninth digit is a check digit. The check digit is chosen such that when the nine digits are multiplied in turn by the numbers 3. 7, 1, 3, 7, 1, 3, 7, and I, the sum of the resulting products is congruent to O mod 10. For instance, 123456780 is a valid routing number because

1(3) + 2(7) + 3(l) + 4(3) + 5(7) + 6(1) + 7(3) + 8(7) + 0(1) = 150 and 150 $\equiv$ 0 mod 10.

a. Compute the check digit for the routing number 72859372-?

b. Verify that 584926105 is a valid routing number.

c. If a bank clerk inadvertantly types the routing number in part b as 584962105, will the computer be able to detect the error?

d. A bank employee accidentally transposed the 6 and the 1 in the routing number from part b and entered the number 584921605 into the computer system, but the computer did not detect an error. Explain why.