The number of 3 digit numbers that are divisible by either 3 or 4 but not divisible by 48, is:
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Official solution
Total 3-digit numbers: 900.
Divisible by 3: 900/3=300. Divisible by 4: ⌊999/4⌋−⌊99/4⌋=249−24=225. Divisible by both 3 and 4 (i.e. by 12): 900/12=75.
By inclusion-exclusion, divisible by 3 or 4: 300+225−75=450.
Numbers divisible by 48 among 3-digit numbers: from 144 to 960, giving 18 terms.
\[\text{Required} = 450-18 = 432\]