New hardy varieties of rice show promise of producing high yields with

In this context, it's plain that both of the agricultural processes are expensive/"costly".

I see what you're saying here—you're seeing "costly X and Y" and claiming that it's not possible to tell whether the intention is "costly (X and Y)" or just "(costly X) and Y".
From the context alone, though, you should be able to deduce that it's the former of these (which is not straightforward to write in a way that totally gets rid of this supposed ambiguity—try it!). Also note that if the latter interpretation were intended, then a good writer would simply invert the order of the elements ("Y and costly X") to produce a completely unambiguous phrasing that's still compact.

This isn't the issue to get stuck on, since there are more black-and-white ways to make eliminations here.

For instance, in choice D the singular verb "was" disagrees with its subject (which has the form "x and y" and therefore must be plural)—and all three of choices A, B, and C mistakenly state that the requirements, rather than the expensive/resource-demanding processes themselves, are "costly".

The meaning issue that stands out the most in the first three choices is "costly requirements" (as opposed to the intended meaning, which is that the agricultural processes themselves are costly/expensive/resource-intensive), as pointed out above.
This issue should be especially conspicuous because it's the subject of a split at the very beginning of the answer choices.

The other problem with the phrasing in that choice (option A) is "by earlier high-yielding varieties".
This "by" is used to introduce the noun that performs the action of a passive-voice verb—as in the last two choices ("was/were required BY earlier high-yielding varieties". It almost never works in other grammatical contexts; one cannot, for instance, write "requirements of X by Y" as in choice A.

RonTargetTestPrep

I understood your point of S-V error in D], but we have ' ''application of X and Y that was required''. Now, can ''application'' be a singular subject because X and Y are just sub-parts to it.

No.
Using parentheses as in algebra: This set of specifics is not "the application of (X&Y)". It's (the application of X) & Y".

The application of fertilizer is one process. Irrigation is a second process.
It would make no sense to say "the application of irrigation", because irrigation already means "the application of mechanically transported water".

Given consideration to the fact that "that" refers to the immediate preceding noun. In E, using "were" next to "that" is ambiguous to me. Please correct my methodology.

Hi Aditi, there is no requirement that "that" must refer to the immediate preceding noun. There are numerous official examples, where "that" refers to a rather faraway noun!

For example in this sentence, "that" is referring to the faraway noun "unique system".

p.s. Our book EducationAisle Sentence Correction Nirvana discusses the modifier properties of "that", their application and examples in significant detail. If you or someone is interested, PM me your email-id; I can mail the corresponding section.
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Hello Aditi31,

We hope this finds you well.

To answer your query, "of commercial fertilizer" is a prepositional modifier, so the modifier "that were required" does not act upon "fertilizer", rather it acts upon the main noun that the prepositional phrase acts upon.

For example, "The painting of the alps that I bought yesterday looks lovely." - here, "that I bought yesterday" refers to "The painting", not "the alps".

We hope this helps.
All the best!
Experts' Global Team
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New hardy varieties of rice show promise of producing high yields without the costly requirements of irrigation and application of commercial fertilizer by earlier high yielding varieties.

Option Elimination -

(A) requirements of irrigation and application of commercial fertilizer by earlier high yielding varieties - "requirements" are not costly. The factors "application of commercial fertilizer" and "irrigation" are themselves costly. Moreover, In the passive voice verb construction, the correct structure is Subject (receiver of the action) + passive voice verb + doer. E.g., The house was painted by John. Here, "John" is the doer. To use "by" in this option, we need the right passive voice structure structure as in option E.

(B) requirements by earlier high yielding varieties of application of commercial fertilizer and irrigation - same passive voice structure issue. Moreover, "application of commercial fertilizer" and "irrigation" or application of "commercial fertilizer" and "irrigation." Ambiguous. The 2nd format doesn't make sense.

(C) requirements for application of commercial fertilizer and irrigation of earlier high yielding varieties - the usage of requirement for is mainly used to indicate a condition that needs to be fulfilled to achieve the outcome. E.g., A good GMAT score is often a requirement for admission to prestigious business schools. In our case, "without a costly" is not a requirement for "application of commercial fertilizer and irrigation." Doesn't make sense. Moreover, the same ambiguous meaning as in B.

(D) application of commercial fertilizer and irrigation that was required by earlier high yielding varieties - The same ambiguous meaning as in B. Also, SV issue.

(E) irrigation and application of commercial fertilizer that were required by earlier high yielding varieties - ok.