1. The first question whose answer is B is question
A) 1   B) 2   C) 3   D) 4   E) 5

2. The only two consecutive questions with identical answers are questions
A) 6 and 7   B) 7 and 8   C) 8 and 9   D) 9 and 10   E) 10 and 11

3. The number of questions with the answer E is
A) 0   B) 1   C) 2   D) 3   E) 4

4. The number of quesions with the answer A is
A) 4   B) 5   C) 6   D) 7   E) 8

5. The answer to this question is the same as the answer to question
A) 1   B) 2   C) 3   D) 4   E) 5

6. The answer to question 17 is
A) C   B) D   C) E   D) none of the above   E) all of the above

7. Alphabetically, the answer to this question and the answer to the following question are
A) 4 apart   B) 3 apart   C) 2 apart   D) 1 apart   E) the same

8. The number of questions whose answers are vowels is
A) 4   B) 5   C) 6   D) 7   E) 8

9. The next question with the same answer as this one is question
A) 10   B) 11   C) 12   D) 13   E) 14

10. The answer to question 16 is
A) D   B) A   C) E   D) B   E) C

11. The number of questions preceeding this one with the answer B is
A) 0   B) 1   C) 2   D) 3   E) 4

12. The number of questions whose answer is a consonant is
A) an even number   B) an odd number   C) a perfect square   D) a prime   E) divisible by 5

13. The only odd-numbered problem with answer A is
A) 9   B) 11   C) 13   D) 15   E) 17

14. The number of questions with answer D is
A) 6   B) 7   C) 8   D) 9   E) 10

15. The answer to question 12 is
A) A   B) B   C) C   D) D   E) E

16. The answer to question 10 is
A) D   B) C   C) B   D) A   E) E

17. The answer to question 6 is
A) C   B) D   C) E   D) none of the above   E) all of the above

18. The number of questions with answer A equals the number of questions with answer
A) B   B) C   C) D   D) E   E) none of the above

19. The answer to this question is
A) A   B) B   C) C   D) D   E) E

20. Standardized test is to intelligence as barometer is to
A) temperature   B) wind-velocity   C) latitude   D) longitude   E) all of the above

I can't go through all my logic, but here's what I've come up with, and what each answer means:

1. D (4 = first B)

2. A (6 = 7)

3. D (3 E's)

4. B (5 A's)

5. E (5 = E, how self-referential!)

6. D (17 = A or B)

7. D (8 = C or E)

8. E (8 vowels)

9. D (13 = next D)

10. A (16 = D)

11. B (1 preceding B)

12. A (even number of consonants)

13. D (15 = only odd A)

14. B (7 D's)

15. A (12 = A)

16. D (10 = A)

17. B (6 = D)

18. E (number of A's = none of the above)

19. C (19 = C)

20. A (Standardized test is to intelligence as barometer is to temperature, i.e. one does not measure the other. Take that, SATs!)

Or, for a less cynical answer, 20) B and 18) A also works.