The problem lies in the words "there's only one answer". Professor Pullum, co-author of The Cambridge Grammar of the English Language, has written of the problematic nature of exam questions which require a binary choice. [See below.]
In the present case, both answers are grammatical, although one is more probable than the other.
The construction "are to" has various possible uses. Swan in Practical English Usage (p80) lists 6 of these. Among them:
Usage 1: We use this structure in a formal style to talk about
official and other plans and arrangements.
- The President is to visit Nigeria next month.
- We are to get a 10 per cent wage rise in June. ...
Usage 5: The structure is used to give orders, often by parents speaking to children.
- You are to do your homework before watching TV. ...
Both of the above uses are conceivable in the present context. Much more likely, however, is the use of have to to express a necessity, equivalent to:
Students will need to make tough decisions after the final exams are
Pullum in Correct/Incorrect Grammar-Test Items
I wish people would avoid using this sort of differential preference
in grammar-test items, testing for knowledge of a fictive
grammaticality distinction. If “Correct/Incorrect” test items are to
be used, the “Incorrect” choice better be genuinely incorrect.
See also Pullum in Grammar-Test Dispute Resolution.