This will be answered through an argument of authority. While, I do not expect this community to accept the answer, I'm sure it will help.
According to the University of Oklahoma, it is true. Professor John.J.Chiodo regave the quiz in 1996 where it had this objective:
Students take and score the 68 items of the 1965 Alabama Literacy Test to experience in a small way the frustration and the injustice this kind of test produced (45 minutes).
As you see in the snapshot it has the same answer keys you had for the first quiz:
Also, PBS and member stations, America’s largest classroom and the nation’s largest stage for the arts and a trusted window to the world, posted this quiz online called The Rise and Fall of Jim Crow. Tools and Activities | PBS, with the same question of the original quiz as you posted.
The American Bar Association reposted the test:
The Quiz is also found in a book called Toward a Literacy of Promise: Joining the African-American Struggle:
The quiz is found on hundreds of university archives, for example, a version is found on Appstate.edu and the same question is found on uncw.edu too.
Another skeptis.se member, ChrisW, pointed out, that the exam you mentioned might be one of the many exams that you are questioning, and suggested another similar exam with same level difficulty (if not worse), the test's name is Louisiana Literacy Test, also mentioned by ferris.edu. Snapshot:
The good news about this exam is state of tennessee itself posted a version of it! Here is the link (notice blackhistory):
http://www.tn.gov/ reported also:
Another insidious method of eliminating African American votes was the use of literacy tests. Surviving copies of these tests indicate that they were designed to cause the test taker to fail. One commonly used test asked the voter to explain complex passages from the United States Constitution; another test asked confusing, ambiguous questions that could be interpreted in a number of ways, so that every answer could be judged as wrong; some tests were so long, no one could finish them in the allotted time. Some voting places offered “help” – a Tennessee law made it possible for illiterate voters to obtain help marking their ballots . . . if they had voted in 1857! Thus black voters were not permitted to receive help, while illiterate white voters were protected, at least for a while.
Also giving many test samples:
"Literacy & Voter test examples"
- Voter registration for Alabama
- [VR ALA]
- Voter tests for Alabama
- , , , .
- Voter registration for Mississippi [VRMiss].
- Louisiana Literacy Test