Select the correct option:
The company expanded so quickly that its systems could _______ keep up.

The correct option is barely.

Explanation:

To choose the correct word for the blank, let's analyze the context and meaning of the options:

1. Barely means "only just", "almost not", or "hardly". In the context of the sentence, "The company expanded so quickly that its systems could barely keep up," it indicates that the company's systems were struggling and could only just manage to handle the rapid expansion.

2. Merely means "only" or "simply" and is used to emphasize how small or unimportant something is (e.g., "He is merely a child"). It does not fit the context of struggling to keep up.

3. Scarcely can mean "hardly", but "barely" is the standard collocated adverb used to describe managing a difficult physical or operational effort under pressure (such as keeping up with fast growth).

4. All but means "almost completely" or "very nearly" (e.g., "The project is all but finished"). Placing "all but" here would mean the systems "almost completely" kept up, which contradicts the emphasis on how fast the company expanded.

Therefore, barely is the correct word to complete the sentence logically.