Question

A number of the form abab, where a & bare natural numbers, in the
range 1 to 9 is necessarily divisible by
​

Answer 1

Step-by-step explanation:

Let’s have some examples.

Take a=1, b=9.

ab = 19 and ba = 91

Now ab + ba = 91 + 19 = 110.

Take a = 2, b = 4.

Now ab + ba = 24 + 42 = 66.

Take a = 3, b = 2.

Now, ab + ba = 55.

You can observe that all the results are multiples of 11.

Theoretically,

If ab is a number (where a and b are digits), then the number is given by:

a+10b.

The number ba is given by:

b+10a.

Now

ab+ba=(a+10b)+(b+10a)

=11a+11b=11×(a+b)

Thus ab+ba is always a multiple of 11.