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Question

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

(a) 92 ___ 389 (b) 8 ___9484

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Solution

(a) 92_389

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.

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

3 + a = 11

a = 8

Therefore, the required digit is 8.

(b) 8_9484

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.


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