The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

We need to find 3-digit numbers divisible by either 3 or 4 but not divisible by 48.

Range: 100 to 999. First multiple: 102, last: 999.

$$\text{Count} = \frac{999 - 102}{3} + 1 = \frac{897}{3} + 1 = 299 + 1 = 300$$

First multiple: 100, last: 996.

$$\text{Count} = \frac{996 - 100}{4} + 1 = \frac{896}{4} + 1 = 224 + 1 = 225$$

First multiple: 108, last: 996.

$$\text{Count} = \frac{996 - 108}{12} + 1 = \frac{888}{12} + 1 = 74 + 1 = 75$$

$$|A \cup B| = 300 + 225 - 75 = 450$$

First multiple: 144, last: 960.

$$\text{Count} = \frac{960 - 144}{48} + 1 = \frac{816}{48} + 1 = 17 + 1 = 18$$

$$450 - 18 = 432$$

The answer is Option B: $$\mathbf{432}$$.