Final answer:
The difference in climate between the two sides of the Washington mountains is most likely caused by the Westerlies, which result in a wet climate on the western side and a drier climate on the eastern side, due to orographic precipitation.
Step-by-step explanation:
The factor most likely responsible for the difference in climate between the two sides of the mountains in Washington is B. Westerlies, global winds that blow from west to east. These winds carry moist air from the Pacific Ocean toward the Washington mountains. When this moist air rises over the mountains, it cools and condenses, forming precipitation. This results in a wet climate on the western side of the mountains.
After the air passes over the crest and descends on the eastern side, it becomes drier, creating a rain shadow effect and a drier climate on the eastern side of the mountains. This phenomenon is a clear demonstration of orographic precipitation, which is directly influenced by the topography of the region, in this case, mountain barriers. The Gulf Stream, while influential in European climate, does not directly affect the climate on the two sides of the mountains in Washington.