In the following question, a phrasal verb is given in bold, it is then…

Concept

A phrasal verb is a verb combined with a particle (here check out) whose meaning is idiomatic. The same phrasal verb can carry several distinct but equally standard senses depending on context, and a usage is acceptable as long as the sentence's intended meaning is preserved. Check out has three well-established senses, and the task is to keep only the sentences in which each sense fits naturally.

Application

Test each sentence against an accepted sense of check out:

• (A) hotel sense — to formally settle the bill and leave a hotel: “don’t forget to check out at the reception desk” uses this departure sense correctly.

• (B) library sense — to borrow an item by having it officially recorded: “check out some books for my research paper” uses this borrowing sense correctly.

• (C) examine sense — to go and look at or investigate something: “check out that new restaurant downtown” uses this inspect/try-out sense correctly.

Cross-check

Each of the three sentences applies a genuine, dictionary-listed meaning of the phrasal verb and reads naturally, with no shift in the intended meaning. Since none of the three can be rejected, every sentence is a valid use.

Result

All three sentences — A, B and C — use check out correctly, so the complete set is the right choice.