During the past week, a local medical clinic tested \(N\) individuals for two infections. If \(\dfrac13\) of those tested had infection \(A\) and, of those with infection \(A,\) \(\dfrac15\) also had infection \(B,\) how many individuals did not have both infection \(A\) and \(B?\)

A. \(\dfrac{N}{15}\)

B. \(\dfrac{4N}{15}\)

C. \(\dfrac{14N}{15}\)

D. \(\dfrac{N}5\)

E. \(\dfrac{4N}5\)

Answer: C

Source: EMPOWERgmat