Excavators at the Indus Valley site of Harappa in eastern Pakistan say

I recognized this question immediately from the Diagnostic Test in the OG. My thoughts:

Key points: Follow the subject, not the prepositional phrase, for agreement.
Breakdown: This is another long sentence, but the underlined portion is short enough to allow a quick check of all the differences between the answers, starting with the first word. Should it be “indicate” or “indicates”? The hasty test-taker would probably read the sentence, pair “shards” with “indicate,” and proceed to examine the differences between choices (A) or (B). However, the subject that dictates verb agreement is actually a little further back, before the preposition “of”--the apt discovery. Watch out for “of” prepositional phrases--they are an agreement trap that question-writers love to toss at unwitting test-takers. These tend to run in one of two ways:

1) Plural subject + of + singular noun + singular verb
Example: Theories of how the universe began and eventually created our planet Earth is…

2) Singular subject + of + plural noun + plural verb
Example: Dr. Hahn of the Max Planck research institutes have written…

In general, it is a good idea (in your mind) to cross off anything following “of” to ensure that you agree the correct noun and verb. Sure, the above sentences are short enough to pose less of a challenge, but that is often not the case on actual GMAT™ questions, which place a bunch of distracting filler or fluff between the subject and the verb. That brings us to the next part of the discussion.

Answers: Backtracking from the head of the underlined portion, we can skip over the “of” prepositional phrase to see that the verb needs to agree with the subject of the dependent clause, the one that starts after “say” (and answers the question of what was said). We can ignore the excavators altogether. See what you can trim away on your own, and whether you can do it quickly, a good sign after a few similar questions, or whether you need additional practice, which is still fine if you are aiming to improve.

(A) the discovery… indicate
(B) the discovery… indicate
(C) the discovery… indicates that
(D) the discovery… indicates the
(E) the discovery… indicates that

You should have eliminated (A), (B), and (D). The first two choices fail to agree the singular subject of the clause with a fitting verb, while (D) falls by the wayside for leaving out the essential “that” that will launch into the next part of the sentence. With three options out of the way, we can scrutinize the differences between (C) or (E) to pick the winner.

(C) the discovery… indicates that their development
(E) the discovery… indicates that the development

Hold up--what does “their” refer to in (C)? Look for antecedents in the form of plural nouns to qualify the pronoun. All I see are “excavators” and “shards.” Certainly, the sentence is neither driving at the shards nor the excavators as having developed the Harappan writing system, but the ancient peoples of the Indus Valley instead. If we are left to our own devices to supply the correct antecedent, though, then (C) must be unclear and therefore incorrect. That leaves (E) as the final answer. A quick readthrough can help set any doubts to rest. Look at and admire those perfectly parallel nouns and prepositions of (E): the development of a Harappan writing system… the use of inscribed seals… the standardization of weights.

Guessing: As we have seen a few times now, a look at just the tip of the tail can sometimes reduce the number of viable answer choices to as few as two. See what we can come up with on this one.

(A) the use of inscribed seals
(B) using inscribed seals
(C) using inscribed seals
(D) their use of inscribed seals
(E) the use of inscribed seals

Already, we can see that there are only three answer types, since (A) and (E) match, and (B) and (C) match each other as well. The easy targets are (B) and (C), since there is no other -ing form of a verb anywhere in the sentence, except for right after the “for” in a self-contained, three-word prepositional phrase. For “using” to work, we would expect the sentence to continue, “using inscribed seals… and standardizing weights,” rather than the non-negotiable (i.e. non-underlined) “the standardization of weights.” Thus, the answer must include “use of.” Between “the use” or “their use,” we would have to do the same detective work as we had before to make sure that “their” pointed back to a clear-cut and sensible noun. Although people often say “they” or “their” in reference to a single entity--e.g., The store is closing their doors at 8.00pm--it is too casual, once again, for standard written American English. The only answers that could work, then, would be (A) or (E), a 50/50 proposition.