This problem provides two very clear decision points for you to get started:

1) "they" vs. "it" as the first word of the sentence

2) "that of" vs. "those of" vs. (no possessive) in relation to "the Medieval period"

The key to both of these is recognizing the subject of the sentence which is "global temperatures." Since temperatures is plural, the pronoun that corresponds to them must be "they" and you can eliminate choices "it has only recently eclipsed the Medieval period, during which, scientists theorize, a" and "it has only recently eclipsed that of the Medieval period, during which scientists theorize a".

Then notice that the comparison is between current global temperatures and the temperatures during the Medieval period; you cannot logically compare "temperatures" with the timeframe, so you need to have "those of" (which "they have only recently eclipsed those of the Medieval period, during which scientists theorize that a" and "it has only recently eclipsed that of the Medieval period, during which scientists theorize a" have but "they have only recently eclipsed the Medieval period, during which scientists theorize that a" does not) to properly draw the comparison.

Between "they have only recently eclipsed those of the Medieval period, during which scientists theorize that a" and "they have only recently eclipsed those of the Medieval period, during which, scientists theorize, a", notice that the only difference is commas around "during which." Why is that important? Here you're dealing with a tense/timeline decision. Since "theorize" is present-tense but the Medieval period is clearly in the past (even if you're not a historian, the fixed past tense "sent" outside the underline tells you that those volcanoes were in the past), you cannot have "scientists theorize" as part of the phrase "during which." The scientists currently theorize that volcanoes caused the global warming, so you need to separate that subject-verb from the modifier "during (the Medieval period)." This means that answer choice "they have only recently eclipsed those of the Medieval period, during which, scientists theorize, a" is correct.

In this sentence correction problem, it is very easy to access the decision points because there is only one word underlined! So the difference between those five choices to start the sentence obviously matters and you need to figure out why.

To do this you must look at the entire sentence - a classic example of the “Whole Sentence Matters” device used by testmakers. The primary issue is which of these modifiers creates logical meaning with the rest of the sentence. Clearly, the phrase must modify “rainforests”- and do rainforests “have” or “possess” a portion of the earth’s surface? Or do they just represent it? They simply are that portion of the earth’s surface, so only “as” "being" and “although accounting for” could be correct choices. Answer choices "With" and "Despite having" illogically suggest that rainforests have or are with 7% of the world's surface areas.

For the choice between "As", "Being" and "Although accounting for", the decision comes down to the meaning of the sentence. The rest of the sentence goes on to talk about what a large impact the rainforest have on the planet, but the introductory phrase talks about how rainforests are (only) 7% of the earth’s surface. Answer choices "As" and "Being" illogically suggest that the reason they have such a large impact is because they are such a small percentage of the earth's surface area! With that in mind, you see that the sentence requires a transition to set up a logical meaning – although rainforests represent a small area, they have a huge impact. Therefore, the phrase “although accounting for” is necessary, and the correct answer is "Although accounting for".

The only decision points in this problem are the choice between "and" and "or" at the end of the series and the choice in how the series are constructed. Each one of these separate things - genetic engineering, ionizing radiation, and sewage sludge - is something that if true would prevent anything from being labeled organic. You do not need all three to be disqualified from being labeled organic so the word "and" is incorrect - it must be "or". Similarly the words "as well as" in "genetic engineering or ionizing radiation, as well as the use of sewage sludge," create the same problem so you can eliminate "genetic engineering or ionizing radiation, and with sewage sludge,", "genetic engineering or ionizing radiation, as well as the use of sewage sludge,", and "genetic engineering, ionizing radiation, and sewage sludge" for this reason. "genetic engineering or ionizing radiation, or the use of sewage sludge," is a fairly easy-to-recognize error of parallelism in the series so correct answer is "genetic engineering, ionizing radiation, or sewage sludge".

"supermoon, which is the full or new moon that occurs when the moon is at or near its closest approach to the Earth, and which can make the moon appear" contains a sentence construction error: the subject "supermoon" never gets a verb, so we are left with a fragment. "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth and can make the moon appear" suggests either that "a supermoon" can make the moon appear larger or that "the moon" can make the moon appear larger, but neither of these construals is acceptable, since a supermoon is the moon and one would never say that "the moon makes the moon appear larger." "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth and appears" correctly suggests either that "a supermoon" appears much larger than the moon typically does or that "the moon" appears much larger than the moon typically does. In "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth, a position which causes itself to appear", the phrase "causes itself" does not work logically, since the position does not make itself appear larger. "supermoon, which is the full or new moon that occurs when the moon is at or near its closest approach to the Earth, causes the moon to appear" suggests that the "supermoon" causes the moon to appear larger, but that claim is illogical, since the "supermoon" is the moon. Note: "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth and can make the moon appear" and "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth and appears are both characterized by the same flexible/fuzzy subject-verb relationships. In "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth and can make the moon appear", either "a supermoon" or "the moon" (first instance) could be legitimately posited as the subject of "can make"; in "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth and appears", either "a supermoon" or "the moon" (first instance) could be legitimately posited as the subject of "appears." What's important is that whichever construct one favors, the reasoning above holds: "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth and can make the moon appear" doesn't work and "supermoon is the full or new moon that occurs when the moon is at or near its closest approach to the Earth and appears" does.