Final answer:
The correct application of the equivalence partitioning test technique to the requirement would be option C, which involves verifying that the video application can play videos on each of the listed display sizes, effectively testing four partitions corresponding to the four resolutions.
Step-by-step explanation:
The equivalence partitioning test technique is a black box testing method that divides input data of software into partitions of equivalent data from which test cases can be derived. The basic idea behind this technique is that if a software works correctly for a representative value in one partition, it should work for all values in that partition.
Therefore, to apply the equivalence partitioning test technique to the requirement stated, test cases should be designed to cover each of the specified resolutions, ensuring that they are representative of the partition they belong to. Option C: Verify that the application can play a video on each of the display sizes in the requirement (4 test cases) effectively covers this requirement, as it tests each of the mentioned display resolutions (640x480, 1280x720, 1600x1200, 1920x1080), which can be considered as separate equivalence partitions.