Question

a and b plays a game with numbers. a ask b to choose a two digit number then reverse the digit of the number. a ask b to add them up and divide the number by 11. a guarantees there will no remander left . what was logic behind it? ​

Answer 1

Any two digit number can be expressed in the form of 10x+y where x is ten's digit and y is the unit digit.

let 10x+y be the number.

number obtained by reversing its digit will be 10y+x.

when we add both them up,

10x+y+10y+x=11x+11y

when we divide the number by 11,

(11x+11y)/11

=11(x+y)/11

=x+y. since 11 on both sides will be cut.

since x and y are whole numbers because the number is a natural number.

and no fraction is left.

It will exactly be divisible by 11 even if we take any two digit number