At a family summer party, each of the \(x\) members of the family chose whether or not to have a hamburger and whether or not to have a hotdog. If \(\dfrac13\) chose to have a hamburger, and of those \(\dfrac17\) chose to also have a hotdog, then how many family members chose NOT to have both?

A. \(\dfrac{x}{21}\)

B. \(\dfrac{x}{10}\)

C. \(\dfrac{9x}{10}\)

D. \(\dfrac{10x}{21}\)

E. \(\dfrac{20x}{21}\)

Answer: E

Source: EMPOWERgmat