Question

Determine whether each of these 15 -digit numbers is a valid airline ticket identification number.

a) 101333341789013

b) 007862342770445

c) 113273438882531

d) 000122347322871

Short answer

1. Thus the check digit is\(3\), which is also the last digit of the given number and thus the airline ticket identification number is valid.

2. Thus the check digit is\(3\), which is also the last digit of the given number and thus the airline ticket identification number is not valid.

3. Thus the check digit is\(3\), which is also the last digit of the given number and thus the airline ticket identification number is valid.

4. Thus the check digit is \(3\) , which is also the last digit of the given number and thus the airline ticket identification number is valid.

Step-by-step solution

Step 1

For a\(Itextbf\{ identificationnumber{a_1}{a_2} \ldots {a_{15}}ofairlinetickets\) the check digit is calculated using the following expression

\({a_{15}} = {a_1}{a_2} \ldots {a_{14}}\,mod\,7\)

Step 2

1. Given :

\(101333341789013\)

Use the above expression to calculate the check digit:

\(\begin{array}{l}{a_{15}} = {a_1}{a_2} \ldots {a_{14}}\,mod\,7\\ = 10133334178901\,mod\,7\\ = 3\end{array}\)

Thus the check digit is 3 , which is also the last digit of the given number and thus the airline ticket identification number is valid.

Step 3

1. Given :

\(007862342770445\)

Use the above expression to calculate the check digit:

\(\begin{array}{l}{a_{15}} = {a_1}{a_2} \ldots {a_{14}}\,mod\,7\\ = 007862342770445\,mod\,7\\ = 6\end{array}\)

Thus the check digit is 3 , which is also the last digit of the given number and thus the airline ticket identification number is not valid.

Step 5

1. Given :

\(000122347322871\)

Use the above expression to calculate the check digit:

\(\begin{array}{l}{a_{15}} = {a_1}{a_2} \ldots {a_{14}}\,mod\,7\\ = 000122347322871mod\,7\\ = 1\end{array}\)

Thus the check digit is 3 , which is also the last digit of the given number and thus the airline ticket identification number is valid.