Suppose I have 2 white bags A and B, and 2 black bags C and D. All these bags only contain a bunch of cool beans and bad beans.
Bag A has a greater % of cool beans than C. Bag B has a greater % of cool beans than D. I combine the two white bags into a giant white bag and black bags into a giant black bag. Is it possible for the % of cool beans in the giant white bag is less than that of the giant black bag?
I don't think this is possible because the individual components already maintain that the white bag will have a greater % of cool beans.