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When I learned English I was taught that the form using a auxiliar verb is the most correct such as:
- Can he speak German?
- Did they live in Manchester?
- When did you travel?
- etc.
However, after some time I realized that people ask question using another way. Using the examples above it would be:
- He can speak English?
- They lived in Manchester?
- When you traveled?

Is this second way of asking questions acceptable in a more informal situation or isn't it acceptable at all? Does it affect the meaning of the setence?

Thanks you.
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With the exception of 'when you traveled', they all would be common as a secondary thought. a)My friend Pablo is bilingual in Spanish and English" b)He can speak English? I didn't know that. a)I'm from London, but my parents lived in Manchester. b)They lived in Manchester? I didn't know that. I hope this helps.
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Your first three are examples of the natural way of asking questions in English, using inversion of subject and auxiliary verb (DO, with the past and present simple)

He can speak English?
They lived in Manchester?

These non-inverted forms are used normally only if the speaker wishes to confirm something. rather than obtain information.

When you traveled?

Question words in non-inverted questions go after the verb: You traveled when?

Note that in BrE travelled needs a second l.

Edit: Cross-posted with Philip.
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