capegemini - find the probability that a number selected at random from the set of 3 digit numbers will be a multiple of 9 and a divisor of 900 - skillgun

The three digit numbers are 100,101,102,...,999
There are a total of 900 three digit numbers.
We know that the number 99 preceded by 100 is divisible by 9 and then every nine-th number from 101 will be divisible by '9'.
Therefore, there are (900/9) 100 of those numbers that are divisible by '9'.
Now, the 3 digit divisors of 900 are 900/1, 900/2, 900/3, 900/4, 900/5, 900/6 and 900/9.
i.e., the 3 digit divisors of 900 are 900, 450, 300, 225, 180, 150 and 100.
Here, except 150 and 100 other numbers are multiple of 9.