Select the correct option:

Her reasoning sounded persuasive; ________, it relied on old figures.

The correct option is nevertheless.

Let's analyze the sentence structure and meaning to understand why this is the most suitable transition word:

The first clause, "Her reasoning sounded persuasive," presents a positive statement or a strong initial impression.
The second clause, "it relied on old figures," introduces a contrast or counter-argument that qualifies or limits the first statement.

We need a conjunctive adverb that shows contrast or concession between two independent clauses (functioning similarly to "however" or "in spite of that"):

1. nevertheless: Means "in spite of that" or "however." It perfectly bridges the contrast between her reasoning sounding persuasive and the reality that it relied on outdated figures.
2. otherwise: Means "or else" or "under other circumstances," which does not fit the context.
3. conversely: Used to introduce an opposite statement or reverse perspective, typically between two opposing ideas, which is not applicable here.
4. subsequently: Means "afterward" or "later," indicating chronological sequence rather than contrast.

Therefore, the complete and correct sentence is:
"Her reasoning sounded persuasive; nevertheless, it relied on old figures."