Elizabeth P. answered 07/29/19
Patient math/stats tutor with Ph.D. in Psychology
First sentence, "Modern agricultural practices have been extremely successful in increasing the productivity of major food crops, yet despite heavy use of pesticides, __ losses to diseases and insect pests are sustained each year."
The key here is the word "despite." Even though they use pesticides, they still lose a lot of crops each year due to insects and such. I would choose the words "significant" and "considerable" (C & D).
Second sentence, "The judge's standing in the legal community, though shaken by phony allegations of wrongdoing, emerged, at long last, __"
The judge's reputation was shaken by false accusations, but we know it didn't damage him in the long run because of the word "though" In the end his reputation is undiminished (B) and undamaged (D).
Let me know if you want a more detailed explanation.