Quantity of money demanded varies:

While nominal GDP reflects the overall economic activity and can influence money demand, it does not establish a direct relationship. The quantity of money demanded may increase with higher nominal GDP due to greater transaction needs, but this relationship is not purely direct as it also depends on other factors like interest rates and inflation.

The quantity of money demanded does increase with the price level, as higher prices require more money to facilitate transactions. However, this relationship is not absolute and can be affected by changes in interest rates and economic expectations, making it less straightforward than the inverse relationship with interest rates.

This option is incorrect as real GDP typically indicates the overall economic output. Generally, an increase in real GDP leads to an increase in the quantity of money demanded because more economic activity necessitates more liquidity for transactions. Thus, the relationship is not inverse.