Question

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

• A. 472
• B. 432
• C. 507
• D. 400

Answer 1

Answer: (B)

Total 3 digit number $=900$
Divisible by $3=300$
(Using $\frac{900}{3}=300$ )
Divisible by $4=225$
(Using $\frac{900}{4}=225$ )
Divisible by $3$ & $4=108,\dots$.
(Using $\frac{900}{12}=75$ )
Number divisible by either 3 or 4
$=300+2250-75=450$
We have to remove divisible by $48$ ,
$144,192,\dots .,18$ terms
Required number of numbers $=450-18=432$