Ella puede contestar a la difícil pregunta.

English Translation

She can answer the difficult question.

I thought “a” was only used after the verb when involving a person. For example “Ella puede contestar a Miguel”. But if it’s an idea or object, that the “a” wasn’t necessary. Am I mistaken?

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The rule about using ‘a’ with persons applies only to direct objects. It is not optional: you must say ‘veo a Tom’ and you must not say *‘veo al camión’. The rule may become fuzzy if one speaker conceives of something as a person and another doesn’t. But again — it only applies to direct objects.

The catch in this sentence is that ‘la difícil pregunta’ is not the direct object of ‘contestar’. The direct object of ‘contestar’ is the reply itself, not what you’re replying to. For example, in ‘contestó que vendría’, the direct object is ‘que vendría’. So ‘… a la difícil pregunta’ here is just an adverbial phrase, like ‘… con un gruñido’ or ‘… por teléfono’.

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Thanks for the detailed explanation! That said, there are a lot of examples to be find online of “contestar la pregunta”.

Yes, but that is a separate usage. That’s why the DRAE says ‘ú.t.c.intr.’; when you say ‘contesté a la pregunta’, there is no direct object.

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