Anurag@Gurome's method is the best one.
here is one more method, though not very elegant (I even dare to say, that the method below is a real nightmare
)
so, total of odd numbers from 101 to 999 inclusive is (999-101)/2+1
=450
(another method to find total-since we need only odd numbers, our last digit can be 1,3,5,7 or 9(total 5), tens digit can be anything from 0 to 9(total 10), hundreds digit is anything from 1 to 9 (total =9) . so total of odd numbers =5*10*9=450)
now we need to find out all numbers that contain digit 5 and exclude them-
first exclude all odd numbers from 501 to 599 (599-501)/2+1=
50
now let's find numbers from 105 to 195 (we have 105; 115; 125; ...195. so, the difference is 10)
195=105+10(n-1) n=10
since we also have total of 8 ranges 105-195;205-295;305-395;405-495;605-695;705-795;805-895;905-995, 10*8=
80
do not forget, that we also have numbers 151 153 157 159 (same with other ranges 2***-9***) total 4*8=
32
so, the result is 450-50-80-32=288
p.s. it is an awful method
but if u want to refresh ur knowledge of arithmetic progression, or u r simply a "pervert" , u can use this method ))).
