Ok let me give it a shot,
The Anasazi, ancient societies that flourished between 200 BC and 1500 AD in southwestern US, did not incorporate a writing system such as the one that allows the archaeologists to precisely date Maya inscriptions to the exact day, but
constructing several tall stone buildings that can be dated within a year,
the archaeologists have adequate information to understand the societies' history.
There is a "BUT" in between so, there must be two diffferent, related, stand alone sentences.
The first clause is the part highlighted in orange, and is perfect.
The problem is in the second clause . So let me rewrite the second part after "But".
"
constructing several tall stone buildings that can be dated within a year,
the archaeologists have adequate information to understand the societies' history."
A full sentence consists of an independent clause and an dependent clause .
Since the second part is an independent clause,
we need a dependent clause in the underlined part.
B and D are out because the options have independent clauses.
A is wrong because archaeologists didn't construct the buildings .
Now on to C and E.
C renders an obscure meaning . The "for dating" wrongfully conveys that the buildings we created in order to be dated.
So we are left with E, which is the best choice. "That can be dated" correctly modifies "buildings" .
Thus E .
Correct me if I am wrong .