Final answer:
In 'The Importance of Being Earnest' by Oscar Wilde, Jack is called a Bunburyist by Algernon for inventing an imaginary brother, which is true.
Step-by-step explanation:
In Oscar Wilde's play The Importance of Being Earnest, the character Algernon does indeed refer to Jack as a Bunburyist because he has created a fictitious younger brother named Earnest to justify his trips to town.
Thus, the statement that Jack invented an imaginary young brother called Earnest so that he may come into town whenever he likes is (A) True.