4. 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

(b) 10824

(c) 7138965

(d) 70169308

(e) 10000001

(f) 901153

(a) Given number = 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

Hence, the given number is divisible by 11.

(b) Given number = 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

which is divisible by 11.

Hence, the given number is divisible by 11.

(c) Given number = 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

which is not divisible by 11.

Hence, the given number is not divisible by 11.

(d) Given number = 70169308

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

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

Difference = 17-17 = 0

Hence, the given number is divisible by 11.

(e) Given number = 10000001

Sum of all the digits at odd places = 1 + 0 + 0 + 0 = 1

Sum of all the digits at even places = 0 + 0 + 0 + 1 = 1

Difference = 1 – 1 = 0

Hence, the given number is divisible by 11.