Final answer:
The Donner party likely ran out of food supplies about 3 weeks after being stranded in the Sierra Nevada Mountains, though they faced a gradual depletion of resources rather than a sudden end of supplies. The correct option is C.
Step-by-step explanation:
The length of time it took for the Donner party to run out of food after being stranded high in the Sierra Nevada Mountains is not precisely mentioned in historical records. However, the Donner party became trapped in late October 1846, and according to historical sources, the group had consumed the bulk of their provisions by December.
It suggests that the party managed their food resources for several weeks before their situation became dire. Considering typical food consumption and preservation methods of the time, the most likely duration corresponds to a period of about 3 weeks to a month. Therefore, option C (3 weeks) is the closest approximate answer to the question asked, albeit it is essential to note the gradual depletion of their food supplies rather than an abrupt end.