Question

How many 3 digit numbers are divisible by 6 but not by 9?

Answer 1

total 3 digit divisible by 6,
a=102
d=6
$a_n = 996$
$a_n = a + (n - 1)d$
999=102+(n-1)6
900=6n
n= 150
total 3 digit no. divisible by 9
a=108
d=9
$a_n = 999$
999=108+9n-9
900=9n
n=100

now total3digit no. divisible by 6 but not by 9
is 150-100=50
therefore 50 3-digit no. are divisible by 6 but not by9