Question

Check each of the following numbers whether they are divisible by 11 or not. Mention the reasons for why the number is divisible or not divisible.
(a) 1221
(b) 6535
(c) 1331
(d) 19091908
(5 marks)

Answer 1

A given number is divisible by 11, if the difference between the sum of the digits at odd places and the sum of the digits at even places (from the right) is either 0 or divisible by 11. (1 mark)

(a) For 1221,

Sum of its digits at even places = 1 + 2 = 3
Sum of its digits at odd places = 2 + 1 = 3

Their difference = 3 - 3 = 0

So, 1221 is divisible by 11 (1 mark)

(b) For 6535,
Sum of its digits at even places = 6 + 3 = 9
Sum of its digits at odd places = 5 + 5 = 10

Their difference = 10 - 9 = 1
1 is not divisible by 11.

So, 6535 is not divisible by 11 (1 mark)

(c) For the the number 1331,
Sum of its digits at even places = 1 + 3 = 4
Sum of its digits at odd places = 3 + 1 = 4

Their difference = 4 - 4 = 0
So, 1331 is divisible by 11 (1 mark)

(d) For the number 19091908,
Sum of the digits at odd places = 8 +9+9+9 = 35
Sum of the digits at even places = 0 +1 + 0 + 1 = 2
Their difference = 35 -2 = 33, which is divisible by 11.

So, 19091908 is divisible by 11. (1 mark)