A. After the Great Depression’s exceptionally high unemployment rates, job prospects did improve in the late 1930’s, ----
Great Depression’s exceptionally high unemployment rates is an awkward expression, missing the point that the job prospects improved after the depression days, rather than the high unemployment rates
B. Although job prospects did improve in the late 1930’s after the Great Depression, a period in which unemployment rates were exceptionally high,---
the best choice bringing out the contrast well with the conjunction although. The possessive expression has been dropped. C. Following the Great Depression’s exceptionally high unemployment rates, job prospects did improve in the late 1930’s, and ---
following is wrong, does not expose contrast. D. While job prospects did improve in the late 1930’s after the Great Depression’s exceptionally high unemployment rates, --
While may or may not instil contrast, it may also imply simultaneousnessE. Despite the fact that job prospects did improve in the 1930’s after the Great Depression and its exceptionally high unemployment rates, ---
Despite the fact is not acceptable. Again the improvement is said to be coming after the high unemployment rates. The text means to contrast job prospects in the depression days with the post- depression days; High mortality rates are just symptoms of the problem in the 1930’s.