What number am I?

I am a number between 501 and 599.

I am not an even number.

I am divisible by 5 and 9.

Since the number is divisible by 5, we can go up by 5's, starting from 500.

Since the number is NOT an even number, we can skip the numbers 510, 520, 530, so on.

I kept going up, 505, 515, 525, 535, 545, etc ... and tried to divide them by 9. 585 is the only number that is divisible by 9. It is an odd number and is also divisible by 5.

The answer is 585.

The number that you are looking for is 540