Final answer:
Variable stars with longer periods have greater luminosities, allowing them to be observed at greater distances due to the period-luminosity relation.
Step-by-step explanation:
The correct statement that describes variable stars is that those with longer periods have greater luminosities, which means they can be observed even when they are farther away. This is due to the direct relationship between the period of variability and luminosity as discovered in the period-luminosity relation. Astronomer Henrietta Leavitt was instrumental in discovering this relation, which now serves as a critical tool for measuring distances to stars beyond our solar system.