The number of 3 digit numbers, that are divisible by either 3 or 4...

We know that,

Total number of three digit number will be $999 - 99 = 900$,

Now,

Number of $3 -$ digit number which are divisible by $3$ will be \left[\dfrac{900}{3}\right] = 300$,</p><p>Number of$3 -$digit number which are divisible by$4$will be \left[\dfrac{900}{4}\right] = 225$,

Number of $3 -$ digit number which are divisible by $3 \text{\text{ and } }$ 4 both will be \left[\dfrac{900}{12}\right] = 75$,</p><p>So , number of$3 -$digit number which are divisible by$3\text{or}4$will be$300 + 225 - 75 = 450$,</p><p>Now, number of$3 -$digit number which are divisible by$48$is \left[\dfrac{900}{48}\right] = 18$

So, number of $3 -$ digit number which are divisible by $3\text{or}4\text{but not}48$ will be

$= 450 - 18 = 432$