Question

Which of the following numbers are divisible by 11?
(a) 12221 (b) 4867216
[3 marks]

Answer 1

Numbers, in which the difference between the sum of the digits at odd places and the sum of the digits at even places is 0 or a multiple of 11, are divisible by 11.
[1 mark]

(a) In the number 12221, the sum of the digits at odd places is 1 + 2 + 1 = 4, and the sum of the digits at even places is 2 + 2 = 4.
Now, the difference between these sums = 4 $-$ 4 = 0

Hence, 12221 is divisible by 11.
[1 mark]

(b) In the number 4867216, the sum of the digits at odd places is 4 + 6 + 2 + 6 = 18, and the sum of the digits at even places is 8 + 7 + 1= 16.
Now, the difference between these sums = 18 $-$ 16 = 2

Hence, 4867216 is not divisible by 11.
[1 mark]