Using divisibility tests, determine which of the following numbersare divisible by 11:

(a) 5445 (b) 10824 (c) 7138965 (d) 70169308

(e) 10000001 (f) 901153

(a) 5445

Sum of the digits at odd places = 5 + 4 = 9

Sum of the digits at even places = 4 + 5 = 9

Difference = 9 − 9 = 0

As the difference between the sum of the digits at odd places and thesum of the digits at even places is 0, therefore, 5445 is divisibleby 11.

(b) 10824

Sum of the digits at odd places = 4 + 8 + 1 = 13

Sum of the digits at even places = 2 + 0 = 2

Difference = 13 − 2 = 11

The difference between the sum of the digits at odd places and thesum of the digits at even places is 11, which is divisible by 11.Therefore, 10824 is divisible by 11.

(c) 7138965

Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24

Sum of the digits at even places = 6 + 8 + 1 = 15

Difference = 24 − 15 = 9

The difference between the sum of the digits at odd places and thesum of digits at even places is 9, which is not divisible by 11.Therefore, 7138965 is not divisible by 11.

(d) 70169308

Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17

Sum of the digits at even places = 0 + 9 + 1 + 7 = 17

Difference = 17 − 17 = 0

As the difference between the sum of the digits at odd places and thesum of the digits at even places is 0, therefore, 70169308 isdivisible by 11.

(e) 10000001

Sum of the digits at odd places = 1

Sum of the digits at even places = 1

Difference = 1 − 1 = 0

As the difference between the sum of the digits at odd places and thesum of the digits at even places is 0, therefore, 10000001 isdivisible by 11.

(f) 901153

Sum of the digits at odd places = 3 + 1 + 0 = 4

Sum of the digits at even places = 5 + 1 + 9 = 15

Difference = 15 − 4 = 11

The difference between the sum of the digits at odd places and thesum of the digits at even places is 11, which is divisible by 11.Therefore, 901153 is divisible by 11.