In the original question the answer is supposed to come from looking at a diagram. It says-What information from the diagram supports the theory that the outer core of the earth is in the liquid state? Diagram shows crust, mantle, outer core, inner core, densities, pressure, temp and depth below surface of the earth.
Basically heat which comes from various sources, friction, radioactivity, etc…
My understanding is that the heat comes from radioactive elements in the rock.
The path of P and S waves from earthquakes provided the information to determine that the outer core of the Earth is liquid. P waves can travel through liquids; however, S waves cannot travel through liquids.
Probably a better question would be why is the inner core solid? Although the inner core has a higher temperature than the outer core, the intense pressure causes the inner core to remain sold. The outer core has less pressure and, as a result, is liquid.