Taking the right approach is the key to most GMAT and GRE quant problems, and combinatorics problems are no different. Almost all combinatorics problems can be solved with a single tool that can be used in two different ways – one way when order matters, and another way when order doesn’t matter. However sometime it pays to take a different approach.

How many integers less than 1000 are divisible by neither 3, 5, nor 7?

(A) 457 (B) 507 (C) 534 (D) 543 (E) 684