1.句子结构，and后面必须是一个完整的句子，D错，没有谓语
2.逻辑推理，修饰对象，BE的of which修饰的对象都是communities,因为,whcih就近修饰，BE错
3.动词时态，date不能加have，现在完成时的date?过去就不date了？未来就不date了？BC错
知识点：A的both dating不是伴随状语，而是独立主格，在此表示补充说明，与each型独立主格同一原理
Both是代词。

has date 是说现在不是了，以前是

(b) and (c) are incorrect because of the tense used; "has dated" implies that this is not the case anymore. (this particular construction really only makes sense in the present tense -- or as an -ing modifier attached to a present-tense clause, since -ing modifiers adopt the tense of the clause to which they are attached.)
(e) has subject-verb disagreement ("each one of which" must be singular).

A.Both dating back...是一个独立主格，和前面主句有一定的关联。
B.错在both of which,这里的which指代的是communities, 错误，应该直接指代A和H
C.这里就用一个逗号加and构成了两个完全独立的句子，但是其实这两个部分之间是有联系的，最好用独立主格。而且each在这里的没有指代对象的。
D.and后面应该加独立的句子。
E.错误大杂烩，把上面错误都犯了一遍。

【The Acoma and Hopi 】are probably the two oldest surviving Pueblo communities, 【both dating】 back at least a thousand years.
【阿科马人和霍皮人】可能是现存最古老的两个普韦布洛社区，【这两种人都可以追溯到】至少一千年。
Aboth dating不是伴随状语，而是独立主格，在此表示补充说明，与each型独立主格同一原理

B. both of 【which（×） 远距离跳跃修饰】 have dated
C. 【and （×）修饰改成了并列】each has dated

【The Acoma and Hopi 】are probably the two oldest surviving Pueblo communities, 【both dating】 back at least a thousand years.
【阿科马人和霍皮人】可能是现存最古老的两个普韦布洛社区，【这两种人都可以追溯到】至少一千年。
Aboth dating不是伴随状语，而是独立主格，在此表示补充说明，与each型独立主格同一原理

B. both of 【which（×） 远距离跳跃修饰】 have dated
C. 【and （×）修饰改成了并列】each has dated

1.which，就近修饰名词，所以指代communities,实际应该指代A&P，排除BE
2.D选项后面，and结构和前面不能构成平行的结构，错误
3.C选项！仍然时逻辑语义判断，但在逻辑上，显然后半句是对前半句主语的修饰，不能是并列关系。【古老的村庄，可以追溯到xx年以前】

A选项：Correct. 本选项在语法和逻辑上均是正确的。both dating back at least a thousand years是独立主格结构。

B选项：定语从句both of which have dated at least a thousand years就近修饰名词the two oldest surviving Pueblo communities，这是不正确的。可以被追溯到1000年以前的显然是Acoma and Hopi（请注意，这里the two oldest surviving Pueblo communities是泛指）。

RON：if you were to replace "both" with "each" in the correct answer, you would have another correct answer.
(c) and (d) are incorrect because of the word "and";

1. and表示并列，但这里不是并列关系
2. have dated 时态不对
3. ，。。。。

A选项：✅dating是对主语The Acoma and Hopi的描述
B选项：定语从句，which指代surviving Pueblo communities，是一种泛指❌

B选项：定语从句both of which have dated at least a thousand years就近修饰名词the two oldest surviving Pueblo communities，这是不正确的。可以被追溯到1000年以前的显然是Acoma and Hopi（请注意，这里the two oldest surviving Pueblo communities是泛指）。

"date" can have either of those meanings.

this pottery dates to the second century B.C.
(same type of usage as the sentence at hand)
––> this is a statement of the actual age of the pottery, not anyone's estimate of that age.

it's also possible to write "experts have dated this pottery...", if that's the intended meaning.

现在完成时没有时间标致

标记both dating逻辑主语A和H
B which指代the two oldest surviving Pueblo communities（泛指），应该指代A和H

you want the "which" modifier to be attached directly to the thing that it modifies; in this case, that would mean that "each of which" should be tagged directly onto "acoma and hopi".

https://www.manhattanprep.com/gmat/forums/the-acoma-and-hopi-are-probably-the-two-t9670.html

Both of two x重复

首先根据并列还是修饰的关系，可以排除CD，BE中的Which无法跳过are去修饰Acoma and Hopi，所以不如A的dating

就近修饰，没仔细看！