# Self-Referential Aptitude Test

Jim Propp (propp@math.mit.edu)

The solution to the following puzzle is unique; in some cases the knowledge that the solution is unique may actually give you a short-cut to finding the answer to a particular question, but it's possible to find the unique solution even without making use of the fact that the solution is unique. (Thanks to Andy Latto for bringing this subtlety to my attention.)

I should mention that if you don't agree with me about the answer to #20, you will get a different solution to the puzzle than the one I had in mind. But I should also mention that if you don't agree with me about the answer to #20, you are just plain wrong. :-)

You may now begin work.

1. The first question whose answer is B is question
1. 1
2. 2
3. 3
4. 4
5. 5

2. The only two consecutive questions with identical answers are questions
1. 6 and 7
2. 7 and 8
3. 8 and 9
4. 9 and 10
5. 10 and 11

3. The number of questions with the answer E is
1. 0
2. 1
3. 2
4. 3
5. 4

4. The number of questions with the answer A is
1. 4
2. 5
3. 6
4. 7
5. 8

5. The answer to this question is the same as the answer to question
1. 1
2. 2
3. 3
4. 4
5. 5

6. The answer to question 17 is
1. C
2. D
3. E
4. none of the above
5. all of the above

7. Alphabetically, the answer to this question and the answer to the following question are
1. 4 apart
2. 3 apart
3. 2 apart
4. 1 apart
5. the same

8. The number of questions whose answers are vowels is
1. 4
2. 5
3. 6
4. 7
5. 8

9. The next question with the same answer as this one is question
1. 10
2. 11
3. 12
4. 13
5. 14

10. The answer to question 16 is
1. D
2. A
3. E
4. B
5. C

11. The number of questions preceding this one with the answer B is
1. 0
2. 1
3. 2
4. 3
5. 4

12. The number of questions whose answer is a consonant is
1. an even number
2. an odd number
3. a perfect square
4. a prime
5. divisible by 5

13. The only odd-numbered problem with answer A is
1. 9
2. 11
3. 13
4. 15
5. 17

14. The number of questions with answer D is
1. 6
2. 7
3. 8
4. 9
5. 10

15. The answer to question 12 is
1. A
2. B
3. C
4. D
5. E

16. The answer to question 10 is
1. D
2. C
3. B
4. A
5. E

17. The answer to question 6 is
1. C
2. D
3. E
4. none of the above
5. all of the above

18. The number of questions with answer A equals the number of questions with answer
1. B
2. C
3. D
4. E
5. none of the above

19. The answer to this question is:
1. A
2. B
3. C
4. D
5. E

20. Standardized test : intelligence :: barometer :
1. temperature (only)
2. wind-velocity (only)
3. latitude (only)
4. longitude (only)
5. temperature, wind-velocity, latitude, and longitude

Updated at 15:47 EST on Tue Apr 11, 2006