Problem: The number of positive integers less than 1000 divisible by neither 5 nor 7, is:
Answer Choices:
A. 688
B. 686
C. 684
D. 658
E. 630
Solution:
The required number a is 999−N1(5)−N2(7)+N3(35) where N1(5) is the number of multiples of 5 , namely 199, N1(7) is the number of multiples of 7 , namely 142 , and N1(35) is the number of multiples of 35 , namely 28. ∴n=999−199−142+28=686