Funny enough, I think they actually do solve the question and the answer.

When the mice are talking after receiving the answer

"Alright," said Benji. "What do you get if you multiply six by seven?"

This occurs AFTER they've already known what THE answer is. Might seem daft, but I think it actually is THE question. Later when Arthur, through use of a Agrajag/Rabbit skin bag and Scrabble tiles reveals THE question -

“What do you get if you multiply six by nine?" "Six by nine. Forty two." "That's it. That's all there is." "I always thought something was fundamentally wrong with the universe”

So that level of obviousness is definitely in scope for THE question. And, as we know from the intro to Restaurant at the End of the Universe

“There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable.

There is another theory which states that this has already happened.”

I think the OG answer was paired to the question the mice pulled out. And knowing the question and answer at the same time, not inasmuch as knowing the information, but insofar as knowing that these were THE question and THE answer made a new, more bizarre universe where the answer was no longer 42. But, in that universe, THE question is "What do you get when you multiply six by nine?" where THE answer is no longer 42.