Question

In each of the following replace by a digit so that the number formed is divisible
by 11:
(1) 64 2456
(ii) 86 * 6194

Answer 1

(i) 64 × 2456

It is divisible by 11

The difference between the sum of digits of odd places and sum of digits of even place is divisible by 11or it is zero.

Now, 6 + 4 + * + 6 – 5 + 2 + 4 [which is divisible by 11]

16 + * – 11 is divisible by 11

5 + x is divisible by 11

∴ * is 6.

(ii) 86 × 6194

It is divisible by 11

The difference between the sum of digits of odd places and sum of digits of even places is divisible by 11 or it is zero.

Now, 4 + 1 + * + 8 = 13 + *

9 + 6 + 6 = 21

21 – (13 + *) is divisible by 11

21 – 13 – * is divisible by 11

8 – * is divisible by 11

∴ * is 8.

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Answer 2

Answer:

(i) 64 × 2456

It is divisible by 11

The difference between the sum of digits of odd places and sum of digits of even place is divisible by 11or it is zero.

Now, 6 + 4 + * + 6 – 5 + 2 + 4 [which is divisible by 11]

16 + * – 11 is divisible by 11

5 + x is divisible by 11

∴ * is 6.

(ii) 86 × 6194

It is divisible by 11

The difference between the sum of digits of odd places and sum of digits of even places is divisible by 11 or it is zero.

Now, 4 + 1 + * + 8 = 13 + *

9 + 6 + 6 = 21

21 – (13 + *) is divisible by 11

21 – 13 – * is divisible by 11

8 – * is divisible by 11

∴ * is 8.