Question

Suppose that a check digit is assigned to a four-digit number by appending the remainder after division by 7. If the number 36806 has a single-digit error in the first position, determine the possibilities for the correct number.

Answer 1

solution:

Given that

Check digit is assigned to a four digit number by appending the remainder after division by 7

Given number =

3

6

8

0

6

Which indicates when the first four digits is divided by 7 we get 6 remainder.

But given that there is single digit error in the first position.

So, we have No.of possible digits at first position { 1,2,4,5,6,7,8,9} = 8

Here, Observe that

i) 1680 % 7 = 0

Possible number:   

1

6

8

0

0

ii) 2680 % 7 = 6

Possible number:

2

6

8

0

6

iii) 4680 % 7 = 4

Possible number:

4

6

8

0

4

iv) 5680 % 7 = 3

Possible number:

5

6

8

0

3

v) 6680 % 7 = 2

Possible number:

6

6

8

0

2

vi) 7680 % 7 = 1

Possible number:

7

6

8

0

1

vii) 8680 % 7 = 0

Possible number:

8

6

8

0

0

viii) 9680 % 7 = 6

Possible number:

9

6

8

0

6

we can observe that there are 2 possible numbers which satisfies the given conditions (i.e., 26806 , 96806 )

The No.of possiblities for correct number = 2