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Which of these is correct, please?

What year did you move to the US?

or

In what year did you move to the USA?

I think they are both correct and that the difference in style/formality is the same as with "What time...?" and "At what time...?". Am I right?

Thank you.
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These both seem fine to me.

You can also ask "When did you move to the U.S.?" but that could get you answers you didn't expect:

It was in the spring

After my dad got a new job

In 2003 (the one you are looking for)
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As GG said, both seem fine. In the New York Times:

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  • Bubbles In Paradise

    ... So, in what year did you open your house? P.C. ...

    August 18, 2002 - By Lisa Eisner and Román Alonso (NYT) - Style - News
  • IMMIGRANTS SHARE THE PAST WITH PEOPLE

    ... immigrants were: What year did you come? Who did you ...

    June 1, 1986 - By ELIZABETH FIELD (NYT) - Education - News
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