Digit sum Check for Division

If x is the greatest 4-digit number that is divisible by 237, then the sum of digits of x is

How many two digit number are divisible by 13 ? Also find their sum.

The sum of all four digit numbers which are divisible by 7 is :

Find the sum of all odd numbers of four digits which are divisible by 9 :

The sum of the digits of a two-digits number is 15. If the number formed by reversing the digits is less than the original number by 27, find the original number. Check your solution.

The sum of the digits of a two-digits number is 12. If the number formed by reversing the digits is less than the original number by 54, find the original number. Check your solution.

Find the sum of all the three digit natural numbers which on division by 7 leaves remainder 3.

If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 9.

If the sum of digits of a number is divisible by three, then the number is always divisible by