In which context would the word 'luck' be appropriately used: Did you manage to persuade your brother to lend you his car? No such _____?

The context of the sentence is about the outcome of a persuade attempt. The phrase "No such luck" is a common idiomatic expression in English that means "there was no good fortune" or "it didn't go well." Using 'luck' here conveys that despite the effort to persuade the brother, the speaker was unsuccessful, suggesting that they didn’t have the good fortune needed for success. This aligns perfectly with the intended meaning of the sentence, providing a smooth and natural completion to the thought being expressed.

The other options do not fit the idiomatic expression or the conversational context. For instance, while 'decision,' 'rejection,' and 'response' could relate to various situations in general, they do not convey the same connotation of missed opportunity or failure that 'luck' does in this particular instance. Therefore, 'luck' is the most suitable word to complete the sentence and accurately reflect the speaker's situation.