On Earth, among the surest indications of sunspot cycles are believed to be the rate that trees grow, as seen in the rings visible in the cross sections of their trunks.
Option Elimination -
(A) On Earth, among the surest indications of sunspot cycles are believed to be the rate that trees grow - The intended meaning is that "amongst the surest indications (say there are 100 indications or proofs) of what? The sunspot cycles? What are sunspot cycles? It is not important to answer the question, but if you are curious, they are: Sunspot cycles are recurring patterns of sunspots on the Sun's surface, roughly every 11 years, caused by magnetic activity. They influence space weather, affecting Earth's climate and technology. Back to our sentence now. Out of these, say 100 indications or proofs, THE SUREST will be one? If there are two, then one can be surer than the other; only one can be THE SUREST. What is that? The rate at which the trees grow. So that one, THE SUREST thing, is not plural; it is singular, which is also evident from the singular "rate." However, sharing more understanding of the meaning will help eliminate other options. One more critical aspect. Remember that GMAT never wastes even a single word in a sentence. Do we understand the intent of this prepositional phrase in the beginning, "on earth"? Prepositional phrases can modify nouns or verbs. If it modifies the verb "is believed," it means it's only applicable on earth. But as we know, the "sunspot cycle" happens practically on every planet or celestial body impacted by the sun. Limiting it just to earth is not correct. So, there are a lot of problems with this one option - "on earth," limiting sunspots to earth, SV, and "the rate at which trees grow" is superior to "the rate that trees grow."
(B) On Earth, among the surest indications of sunspot cycles are, it is believed, the rate of tree growth - The same issue of SV "on Earth." Moreover, "it is believed" is redundant. The belief is already implied by "amongst the surest blah blah...."
(C) On Earth, the rate at which trees grow is believed to be among the surest indications of sunspot cycles - In addition to the "on earth" issue. Let me show you another blunder here. This says "the rate" is amongst the surest. It nonsensically opens doors to convey (not necessarily, but it can) that "the rate" is now amongst "the surest." If these "the surest" are now 100, the rate is one among them. But the intended meaning is Amongst many, the rate is THE SUREST. I know you are thinking of "their." Maybe some even thought they got the correct answer, E, because "their" is closest to trees. Let's understand the fundamentals. Does it even make sense to say trunks of sunspot cycles? No. There is practically one antecedent, which is trees. Now, if we look at the prepositional phrase introduced by "as seen in the rings....blah blah) is adverbial, modifying the complete clause. What clause "The surest indication of sunspot cycles is the rate...." as seen in the rings....So "as seen...." prepositional phrase provides additional information about the "The surest indication of sunspot cycles is the rate...." Yes, it's the other problems in this option that make it wrong - more importantly the "on earth" prepositional phrase. Getting the question for the right reason is important, as the GMAT is full of traps. We may get one question right somehow, but with 99% surety, that same question is not coming in the exam. So, it's better to get the basics right to tackle a question with a similar trap.
(D) Among the surest indications on Earth of sunspot cycles, believed to be the tree growth rate - easy peasy. No verb.
(E) Among the surest indications on Earth of sunspot cycles is believed to be the rate at which trees grow - "on earth" prepositional phrase correctly modifies "indications." No SV issue as in A and B.