Self-Referential Aptitude Test

The solution to this puzzle is unique, but you don’t need this information in order to find it.

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 questions 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 preceding 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 (only)
    (B) wind-velocity (only)
    (C) latitude (only)
    (D) longitude (only)
    (E) temperature, wind-velocity, latitude, and longitude

Remark: The answer to question 20. is (E).

The answers are:

1. D
2. A
3. D
4. B
5. E
6. D
7. D
8. E
9. D
10. A
11. B
12. A
13. D
14. B
15. A
16. D
17. B
18. A
19. B
20. E

Jim Propp

Website

Jim Propp is a winner of the United States of America Mathematical Olympiad, and an alumnus of the Hampshire College Summer Studies in Mathematics. He obtained his AB in mathematics at Harvard and his PhD at the University of California at Berkeley. He has held professorships at multiple universities, including Harvard and MIT.