Alright, you can see the splits of is and are. If we ignore the modifier, we can clearly see that "integrated solution shops" are being talked about. Hence, we scratch option B.

We also see that there is a parallelism issue:
Visionaries believe X but Y.
Hence the structure of X and Y should be similar. We can see that X starts with the pronoun "that" and hence A is also out.

The last issue is of if/whether. We cannot eliminate this choice and so C is out because essentially it says the following: "more research is needed to determine that this structure is more efficient". This changes the meaning. We are changing the meaning by not considering the choice that the structure can be "not more efficient".
. Now, as mentioned earlier, this is a choice between two alternatives and not a condition. Therefore, we are now left with E, which is the correct answer.

Interesting. Took me just under a minute to solve, so that might make it a solid 1:20 to do on an actual exam day. The question is by no means difficult, but I guess it does test some concepts that you have to be familiar with: parallelism and subject/verb agreement. You should also get a feel for what you don’t need to pay as much close attention to in the non-underlined portions where different specialties converge in a coordinated way to diagnose a patient as accurately as possible to save time.

To the answer choices!

Visionaries believe that integrated solution shops, where different specialties converge in a coordinated way to diagnose a patient as accurately as possible, are the future of hospitals but more research is needed to determine that this structure is or is not more efficient than the form in which the hospitals are divided by specialties.

A) are the future of hospitals but more research is needed to determine that this structure is or is not

Parallelism is at play here. Visionaries believe THAT..... but THAT... (I missed this error but is or is not is probably redundant as well).

B) is the future of hospitals but more research is needed to determine if this structure is

Freebie elimination. The subject is integrated solution shops. The plural form ARE is needed.

C) are the future of hospitals but that more research is needed to determine that this structure is

I know this may be a bad way to eliminate, but I was looking for a DETERMINE WHETHER by this point, I think. Probably best to yellow flag this answer choice till you find something better.

D) are the future of hospitals but that more research is needed for determining if this structure will be

DETERMINING is not parallel, tense wise, to the first part of this sentence. Also the IF is enough of a red flag to eliminate this. We need a weather! This usage of IF is not allowed on the GMAT, people.

E) are the future of hospitals but that more research is needed to determine whether this structure is

And we're done! We have the BUT THAT. We have the WHETHER. And it starts with ARE.
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Visionaries believe that integrated solution shops, where different specialties converge in a coordinated way to diagnose a patient as accurately as possible, are the future of hospitals but more research is needed to determine that this structure is or is not more efficient than the form in which the hospitals are divided by specialties.

A) are the future of hospitals but more research is needed to determine that this structure is or is not- awkardly wordy
B) is the future of hospitals but more research is needed to determine if this structure is- SV error
C) are the future of hospitals but that more research is needed to determine that this structure is- awkardly wordy
D) are the future of hospitals but that more research is needed for determining if this structure will be- if incorrect
E) are the future of hospitals but that more research is needed to determine whether this structure is- Correct
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