Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001 (f) 901153
(a) 5445
Sum of odd digits = 5 + 4 = 9
Sum of even digits = 4 + 5 = 9
Difference = 0
Difference is divisible by 11. Therefore, 5445 is divisible by 11.
(b) 10824
Sum of odd digits = 1 + 8 + 4 = 13
Sum of even digits = 0 + 2 = 2
Difference = 13-2 = 11
Difference is divisible by 11. Therefore, 10824 is divisible by 11.
(c) 7138965
Sum of odd digits = 7 + 3 + 9 + 5 = 24
Sum of even digits = 1 + 8 + 6 = 15
Difference = 24-15 = 9
Difference is not divisible by 11. Therefore, 7138965 is not divisible by 11.
(d) 70169308
Sum of odd digits counting from right = 8 + 3 + 6 + 0 = 17
Sum of even digits counting from right = 0 + 9 + 1 + 7 = 17
Difference = 17-17 = 0
Difference is divisible by 11. Therefore, 70169308 is divisible by 11.
(e) 10000001
Sum of odd digits = 1 + 0 + 0 + 0 = 1
Sum of even digits = 0 + 0 + 0 + 1 = 1
Difference = 1-1 = 0
Difference is divisible by 11. Therefore, 10000001 is divisible by 11.
(f) 901153
Sum of odd digits = 9 + 1 + 5 = 15
Sum of even digits = 0 + 1 + 3 = 4
Difference = 15-4 = 11
Difference is divisible by 11. Therefore, 901153 is divisible by 11.
From the discussion above, we can say that numbers (a), (b), (d), (e) and (f) are divisible by 11.
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