during summer / last summer

Hi there!

You have to choose the correct pair for the following sentence:

They went to Australia ______ a month __________summer.

a) during, the b) for, during c) for, last d) last, during

I'd choose c), but the answer key in my book says it's b). I think this must be a mistake, for option c) fits perfectly in the sentence: "For" conveys the meaning of "over a period of time", and "Last" is, in my opinion, better than "During" since it's a time expression for the simple past, therefore agreeing with the main verb "went". Besides, I think that if we were to choose b) as the right option, "during" should be followed by "the", specifying which summer (last, I would be inclined to say), not any. I don't think the word "summer" can be used on its own in this context. What do you think?

Thanks a lot!

Mara.