Question

If $ABCxCBA=65125$ where $A,B$ and $C$ are single digits the $A+B+C=$ ?

Answer 1

As the unit digit of the product is $5$ therefore the unit digit of one of
the numbers is $5$ and the unit digit of the other number is odd
Therefore $AB5\times 5BA=65125$ where $A=1,3,5,7$ or $9$
As the product
of two three-digit number is a five-digit number and not a six-digit
number A can only be equal to $1.IB5\times 5B1=65125$
The digit sums of
both numbers $1B5$ and $5B1$ will be same Therefore the product would give
digit sum of a perfect square The digit sum on the $R.H.S$. is $1$
Therefore the digit sum of each number can be $1$ or $8$ Correspondingly $B$
will be $4$ or $2$ (as digit sum cannot be equal to $1$)
Keeping $B=2$ we can see that $125\times 521=65125$