Permutation Combination Question 9
Question 9 - 29 January - Shift 2
The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is
(1) 472
(2) 432
(3) 507
(4) 400
Show Answer
Answer: (2)
Solution:
Formula: Divisibility of numbers
Total 3 digit number $=900$
Divisible by $3=300 \quad$ (Using $\frac{900}{3}=300$ )
Divisible by $4=225$ (Using $\frac{900}{4}=225$ )
Divisible by $3 ; & ; 4=108, \ldots$
$ \text{ (Using } \frac{900}{12}=75) $
Number divisible by either 3 or 4
$ =300+2250-75=450 $
We have to remove divisible by 48 ,
$144,192, \ldots . ., 18$ terms
Required number of numbers $=450-18=432$
