Read the speech from the play The Importance of Being Earnest.Algernon. You have invented a very useful younger brother called Ernest, in order that you may be able to come up to town as often as you like. I have invented an invaluable permanent invalid called Bunbury, in order that I may be able to go down into the country whenever I choose. Bunbury is perfectly invaluable. If it wasn’t for Bunbury’s extraordinary bad health, for instance, I wouldn’t be able to dine with you at Willis’s to-night, for I have been really engaged to Aunt Augusta for more than a week.Which responses clearly describe how a student who didn’t know the word invaluable could determine its meaning?

The student could use the context to determine that invaluable means "relative worth or degree of excellence" because Algernon finds his "Bunbury" strategy quite useful.

Explanation:

Oscar Wilde's comedy play "The Importance of Being Earnest" revolves round the theme of Victorian society's approach to status, wealth and upbringing as factors to determine an individual's worth. The characters' farcical attempts to escape the societal obligations by pretending to be someone else shows how the society deems importance to its useless and at times outrageous practices.

The given excerpt is from the first act in the conversation between Algernon and Jack over their "invented" identities of Ernest and Bunbury to escape the societal obligations that they are required to be a part of. In his use of the word "invaluable", Algernon suggests that his "Bunbury" identity is a necessity which is useful to him. So, a student can determine the meaning of the word "invaluable" and considering the context of the text, he/ she can determine that it meant "Bunbury" is a worthy and excellent strategy which is extremely useful for him.