Fill in the blanks to make the statements true. The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and …………… .

Question

Philoid · Accepted Answer

Let x, y and z be the digits in a three-digit number A = xyz.

Reversing the digits, we get B = zyx.

Sum of the digits in A is (100x + 10y + z).

Sum of the digits in B is (100z + 10y + x).

Difference S = A + B = (100x + 10y + z) - (100z + 10y + x).

S = 100x-x + 10y-10y + z-100z = 99x-99z

99(x-z) = 9x11(x-z)

The number is divisible by 9 and 11.

Fill in the blanks to make the statements true.The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and …………… .

Fill in the blanks to make the statements true.
The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and …………… .