both are grammatically ok, but with different meanings:
1) in general
2) a specific document in question (would usually be identified at the end of the sentence), ex: It's important to carefully read this contract
I gleefully use split infinitives myself. But in the context of that problem I feel certain they were checking for the ability to spot a split infinitive.
It's one of the grammar points that native speakers are increasingly becoming unable to recognize. It very seldom causes any trouble regarding comprehension. And since English grammar is in large descended from German grammar....which has split verbs....the rule about split infinitives has always been somewhat arbitrary and unnatural.
Yes I agree, though in response to the phrasing of the original question, both a) and b) are used, regardless of their relative grammatical correctness.
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