The correct answer must fit grammatically and logically with the sentence, describing the relationship between great inventions and simplicity.
"Hinge upon" means to depend entirely on something, which perfectly expresses the idea that the success or nature of great inventions is based on a simple starting idea.
Option (a) "stumbles upon" means to find by accident, which does not fit here as the sentence is about dependency, not discovery.
Option (c) "starves without" is awkward and overly informal in this context.
Option (d) "lacks" would completely change the meaning to imply that inventions do not have simplicity, which is opposite of the intended sense.
Therefore, "hinge upon" is the most precise and contextually correct choice.