A study has found that many patients
undergoing coronary bypass surgery and developing long-term medical problems that require extended and often expensive medical care, stressing families’ financial security and taxing an already strained health system.
If we take a look at this prompt, we can logically infer that "long term medical problems" are developed after undergoing the "bypass surgery".
With the use of "and", (A) and (C) literally imply that both the bypass surgery and developing long-term medical problems occur at the same time. This is certainly not the intended meaning of the passage. Hence, we can eliminate (A) and (C).
B)
undergoing coronary bypass surgery who develop long-term medical problems that require extended and often expensive medical care, stresses - (B) literally implies that it is the surgery itself that develops the long-term medical problems and not the patients themselves. This does not make sense, so we can eliminate (B).
D)
who undergo coronary bypass surgery develop long-term medical problems that require extended and often expensive medical care, stressing - here, we have a clean sentence with the correct use of an -ing clause at the end of the underlined portion. Additionally, the use of "and" correctly compares two like terms: extended and expensive (both adjectives). Hence,
(D) is your right answer.
E)
who undergo coronary bypass surgery develop long-term medical problems that require extended and often expensive medical care and stresses - With the use of the second "and" at the end of the underlined portion, (E) literally implies that the patients themselves are directly stressing "families’ financial security..." whereas its the "long-term medical problems" that's creating the "stress". Hence, we can eliminate (E).