Question

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

92 ______ 389

Answer 1

Let a be placed in the blank.

Sum of the digits at odd places = 9 + 3 + 2 = 14

Sum of the digits at even places = 8 + a + 9 = 17 + a

Difference = 17 + a − 14 = 3 + a

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

If 3 + a = 0, then

a = − 3

However, it cannot be negative.

The closest multiple of 11, which is near to 3, has to be taken. It is 11 itself.

3 + a = 11

a = 8

Therefore, the required digit is 8.