Question

Write a digit in the blank space of the following number so that the number formed is divisible by 11:

8 ______ 9484

Answer 1

Let a be placed in the blank.

Sum of the digits at odd places = 4 + 4 + a = 8 + a

Sum of the digits at even places = 8 + 9 + 8 = 25

Difference = 25 − (8 + a)

= 17 − a

For a number to be divisible by 11, this difference should be zero or a multiple of 11.

If 17 − a = 0, then

a = 17

This is not possible.

A multiple of 11 has to be taken. Taking 11, we obtain

17 − a = 11

a = 6

Therefore, the required digit is 6.