Q. How many numbers from 1 to 1000 are divisible by 60 but not by 24?
Sequences and Series
Solution:
Let $n(A)=$ number divisible by $60=60+120+$......$+960=16$
$n ( B )=$ number divisible by $24=24+48+$ $+984=41$
$n ( A \cap B )=$ number divisible by both $=120+240+$ $+960=8$
Hence $n(A \cap \bar{B})=n(A)-n(A \cap B)=16-8=8$
