Using Venn Diagrams to Solve a Combinatorics Problem

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

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