Sequences and Series Part 2

Total 4-digit number =9×10×10×10=9000
4 -digit number divisible by 7
1001, 1008, …, 9996
Number of 4-digit number divisible by 7
=

9996−1001

7

+1=1286
4 -digit number divisible by 3
1002, 1005, …, 9999
Number of 4-digit number divisible by 3
=

9999−1002

3

+1=3000
4 digit number divisible by 21
1008, 1031, …, 9996
Number of 4- digit number divisible by 21
=

9996−1008

21

+1=429
∴ Number of 4- digit numbers neither divisible by 7 nor 3
=9000−1286−3000+429
= 5143