Question

Count the number of 5-digit numbers (in the decimal system; integers from 10000 to 99999) which are not divisible by 11.

Answer 1

So total number which is not divisible by 11 = 89999-8181 = 81819

Explanation:

We have to find the total numbers which are not divisible by 11 from 10000 to 99999

Total number from 10000 to 99999 = 99999-10000+1=90000

Just after 10000 the number which is divisible by 11 is 10010

And just below 99999 the number which is divisible by 11 is 99990

Using AP formula

`T_N=a+(n-1)d`, here a is first term, d is common difference and n is number of terms

So
`99990=10010+(n-1)11`

n-1 = 8180

n= 8181

So total number which is not divisible by 11 = 90000-8181 = 81819