Combining enormous physical strength with higher intelligence, the Neanderthals
appear as equipped for facing any obstacle the environment could put in their path, but their relatively sudden disappearance during the paleolithic era indicates that an inability to adapt to some environmental change led to their extinction.
(A) appear as equipped for facing any obstacle the environment could put in their path,
The use of appear here is correct here as we are making a general statement about how the Neanderthals appear when looking at them in the past. But, Appear as is the wrong idiom. When you say appear as, it is used as a comparison but there is no comparison. Also, the use of for facing is better phrased as to face in the other options since it was an intent of the of the Neanderthals to be equipped to face any obstacle.
(B) appear to have been equipped to face any obstacle the environment could put in their path,
B corrects all the errors in A and looks good. Hang on to this one. While the use of passive past perfect here in “to have been equipped” looks questionable, it is indeed correct because they were equipped to face obstacles before their sudden appearance. Since we are comparing two events in the past, the earlier event is correctly phrased using past perfect here. Additionally, appear to is the right idiom.
(C) appear as equipped to face any obstacle the environment could put in their paths,
Appear as is again the wrong idiom and appear to have been is more clear in B.
(D) appeared as equipped to face any obstacle the environment could put in their paths,
Appeared and indicates are not parallel here. Appeared is wrong here because this would mean that they appeared to us in the past but don’t any more - this is illogical since we are making a general statement in the present about how Neanderthals appear just as the sentence later says that their disappearance “indicates”. Both are general statments in the present. Additionally, the use of appeared as is incorrect, we are not comparing anything.
(E) appeared to have been equipped for facing any obstacle the environment could put in their path,
While this fixes the idioms error appeared as to appeared to have been and uses the correct past perfect tense, the use of appeared still remains an issue as it does in D.