Pretty sure I've got it right. Think of it this way:
If I have a good exposure at iso 100, f/8, 1/60 second, and I flip the iso to 1600, but leave the aperture and shutter speed where they are, I'll have overexposed the picture by four stops. Higher iso => higher sensitivity => grabbing more light.
Higher/faster the shutter speed, the less light you get.
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