Answer:
(a) 0
(b) 1
(c) 8
(d) 6
Step-by-step explanation:
You want the digit in the * position that makes each number divisible by 11.
Divisibility rule
If the difference of the sum of digits in odd positions and the sum of digits in even positions is divisible by 11, the number is divisible by 11.
(a) 4*3271
The difference of interest is ...
(4 +3 +7) -(x +2 +1) = 11 -x
This will be a multiple of 11 for x = 0.
403271 = 11 · 36661
(b) 22*0978
The difference of interest is ...
(2 +x +9 +8) -(2 +0 +7) = 10 +x
This will be a multiple of 11 for x = 1.
2210978 = 11 · 200998
(c) 2*45678
The difference of interest is ...
(2 +4 +6 +8) -(x +5 +7) = 8 -x
This will be a multiple of 11 for x = 8.
2845678 = 11 · 258698
(d) 2472*9
The difference of interest is ...
(2 +7 +x) -(4 +2 +9) = x -6
This will be a multiple of 11 for x = 6.
247269 = 11 · 22479
The needed digits are 0, 1, 8, 6.
