Select the most appropriate option to fill in the blank. He ____ left his…

Concept: In sentence-completion items that pair an action with a stated consequence (here, "..., and it was stolen"), the blank must be filled with the word that logically explains how that consequence came about — not merely one that is grammatically well-formed. A manner adverb naming the vulnerability behind the outcome is required; an adverb describing something orthogonal to that vulnerability (for instance, how often the action occurred) leaves the stated outcome unexplained.

Application: The second clause, "it was stolen," is a consequence that needs an explanation of what made the document vulnerable to theft. "Carelessly" names exactly that vulnerability — the document was left without due care or attention, in a way that allowed it to be taken unnoticed. This manner directly accounts for why the document ended up stolen.

Cross-check — contrasting the other options by value:

• "Frequently" tells us only how often he left the document on the table, not the manner in which he left it on this occasion; even granting frequent repetition, frequency alone does not explain why the document was left vulnerable — the sentence's stated outcome (theft) still goes unexplained by a repetition adverb.

• "Usefully" describes an action carried out to a beneficial or practical effect, which does not describe how an item comes to be left unattended and taken.

• "Loudly" describes the volume of an action, an attribute with no bearing on how a document came to be exposed to theft.

Result: Only "carelessly" supplies the manner that explains the stated consequence, so it correctly completes the sentence.