In the phrase "How many people live there?", why we don't use "do"?
I learned that in interrogative phrases without "to be", we must use "do" or "does" or "did". Why in the question above, where the verb is "to live", we don't use "do"?

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This is called a subject question. A subject question asks about the subject of the sentence. In subject questions where we want to ask about the subject, we do not use  auxiliary verbs.

Who wants to go the cinema? is another example of a subject question.

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"How many people do live there" is technically correct, but old-fashioned. You could still use it today to stress that you want to know exactly how many people live there.

For example:
If you said "I think 5 people live there" and someone said, "No, that's wrong"
You could ask "Well, how many people DO live there?" By stressing the 'do', you are implying that you want to know an exact number.

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It's a good question, Vitor, and one that confuses a lot of language learners. It even puzzles some native speakers when they are forced to think about it. Iris has given you the perfect answer below.

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