It depends. Most states, when they determine your nonresident tax, first calculate how much tax you would have on all of your income, and then assess the tax proportionate to the amount of income you earned in the state. MN does list all of your income, but you are only taxed on what you actually earned in MN. In your case, if you earned 17.5 K overall, you will pay almost exactly 10% of the tax MN charges on 17.5K, because that is the percentage of income you had in MN.
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