Question

Write a digit in the blank space of the following number so that the number formed is divisible by 11.
92_389
[5 marks]

Answer 1

We know that a number is only divisible by ‘11’ if the difference between the sum of the digits at the odd places and the sum of the digits at the even places is zero or a multiple of ‘11’.
[0.5 mark]

Sum of digits at odd places = 9 + (blank) + 8 = 17 + blank
[0.5 mark]
Sum of digits at even places = 2 + 3 + 9 = 14
[0.5 mark]

Now the difference = 17 + blank - 14 = 3 + blank
[0.5 mark]

Now to make it divisible by 11, the difference should be 0, 11, 22, 33…

Difference equals zero is not possible because it is already some number added to 3.
[0.5 mark]

If we take the difference equal to 11,
Then, 3 + blank = 11
⇒ blank = 11 - 3 = 8
So, 8 is the possible value of blank.
[1 mark]

Now if we take the difference equal to 22,
Then, 3 + blank = 22
⇒ blank = 22 - 3 = 19, which is a two-digit number, can’t be added in blank.

Similarly we will be getting two or more digits if we take the difference equal to 33, 44, 55….
[1 mark]

So we will write 8 in blank and the number will be 928389.
[0.5 mark]