Question

In each of the following numbers, replace * by the smallest number to make it divisible by 11
1. 35*6 2. 439*71 3. 86*72

Answer 1

1. 8 2. 5 3. 3

Given:

1. 35*6 2. 439*71 3. 86*72

To Find:

Smallest number with which we can replace * to make them divisible by 11.

Solution:

Divisibility by 11:

The sum of digits at odd places - the sum of digits at even places = 0 or 11k

If the difference between the sum of digits at odd places and the sum of digits at even places is 0 or 11, then that number is divisible by 11.

1. 35*6

The sum of digits at odd places = 3 + *

The sum of digits at even places = 5 + 6 = 11

Difference = 11 - 3 - * = 8 - *

* can be replaced by 8 to make the number divisible by 11.

8 - 8 = 0

Thus making 3586 divisible by 11.

2. 439*71

The sum of digits at odd places = 4 + 9 + 7 = 20

The sum of digits at even places = 3 + * + 1 = 4 + *

Difference = 20 - 4 - * = 16 - *

* can be replaced by 5 to make the number divisible by 11.

16 - 5 = 11

Thus making 439571 divisible by 11.

3. 86*72

The sum of digits at odd places = 8 + * + 2 = 10 + *

The sum of digits at even places = 6 + 7 = 13

Difference = 13 - 10 - * = 3 - *

* can be replaced by 3 to make the number divisible by 11.

3 - 3 = 0

Thus making 86372 divisible by 11.

1. 8 2. 5 3. 3

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