The period when the great painted caves at Lascaux and Altamira were occupied by Upper Paleolithic people has been established by carbon-14 dating, but what is much more difficult to determine are the reason for their decoration, the use to which primitive people put the caves, and the meaning of the magnificently depicted animals.
Two instances of subject-verb agreement must be observed in this sentence: The period ... has been established and what is much more difficult to determine ... is. Both clauses have singular subjects and must have singular verbs. Only B, the best choice, observes these requirements. A incorrectly uses the plural form are in the second clause. Choices C and D incorrectly use the plural form have in the first clause, and D incorrectly uses are in the second clause as well. E incorrectly uses the plural form are in the first clause. Furthermore, because the date of the period in question was established before the writing of the sentence, the verb of that clause must be in the present perfect form (has been established).