Question

A number is multiplied by 11 and 11 is added to the product. if the resulting number is divisible by 13, what is the smallet number?

Answer 1

Let the required number be x.
Then, (11x + 11) = 11(x+1) is divisible by 13.
So, x = 12. 

Answer 2

Given:

A number is multiplied by 11

11 is added to the product

The number is divisible by 13

To Find:

The smallest number.

Solution:

Let the number be $x$,

So, according to the question

$11x+11$ = $11(x+1)$

$11(x+1)$ is divisible by 13

We know that 11 is not divisible by 13

so, $(x+1)$  should be divisible by 13

Let us take the value of x as 1,2,3,4,..... to check its divisibility by 13,

Any  number less than 12 will not make  $(x+1)$ divisible by 13

when x = 12

$(x+1)$ = 12 +1

           = 13

And 13 is divisible by 13.

Hence, the smallest number will be 12