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,

(B) appear to have been equipped to face any obstacle the environment could put in their path,

(C) appear as equipped to face any obstacle the environment could put in their paths,

(D) appeared as equipped to face any obstacle the environment could put in their paths,

(E) appeared to have been equipped for facing any obstacle the environment could put in their path,


We need to use logic and grammar to solve this question.

Appear as suggests that Neanderthals still exist. This would make the sentence illogical. Hence we need to use appear to have been - (once- in the past) to show that when they existed they were equipped to face any obstacle the environment could put in their path. Eliminate options A, C, and D.
E- equipped for facing is incorrect. Equipped to is the correct idiom.
(B) appear to have been equipped to face any obstacle the environment could put in their path,
B is correct.