The number of 3-digit numbers that are divisible by 2 and 3, but not divisible by 4 and 9, is_______

Divisible by 2 and 3 means the number should also be divisible by 6 and it should not be divisible by 4 and 9.

Smallest 3-digit multiple of 6 = 102

Largest = 996

Number of multiples: $$\dfrac{\left(996-102\right)}{6}+1=150$$

Now, we need to subtract the numbers divisible by both 4 and 9 (i.e., multiples of 36)

Smallest = 108, Largest = 972

$$\dfrac{\left(972-108\right)}{36}+1=25$$

Final answer: 150 - 25 = 125