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I've created two different buffers (1 mile and 3 miles) in ArcMap, I need to see how many people live within 1 and 3 miles. In other words, I need to subtract the bigger buffer from the smaller one. I have no idea how to do it.

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To do this try using the Erase tool which:

Creates a feature class by overlaying the Input Features with the polygons of the Erase Features. Only those portions of the input features falling outside the erase features outside boundaries are copied to the output feature class.

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