This Is Only A Test

Posted on May 19, 2005

First, the instructions are massively useful in completing this test. Keep this in mind as we progress.

Second, this is just one possible walkthrough, and it’s the second time I have gone through the test. It was much harder the first time.

Easy Ones:

It’s my sincerest wish that identity will hold in this exam; the answer to #5 is E.

#20 gets special attention in the instructions, and by consulting reference material, we establish that answer is E

Warming Up:

Questions #10 and #16 refer to each other. The only correct set of answers possible means #10 is A and #16 is D.

Questions #6 and #17 refer to each other. When one considers that the answer to #17 cannot be D because of question #2, the only correct set of answers; #6 is D, and #17 is B.

The instructions state that the solution to the quiz is unique. I am not afraid to use shortcuts, so let’s do some analysis on #12. Uniqueness would imply that neither C,D, nor E could be the answer, as that would necessitate A or B also being a possible answer. Thus, not only can we eliminate C,D, and E as choices, we also establish that the number of consonants cannot be in the following:

1, 4, 9, 16 (perfect squares)
2, 3, 5, 7, 11, 13, 17, 19 (primes)
10, 15, 20 (divisible by 5)

This means that the number of consonant answers can be either 6, 8, 12, 14, or 18. These are all even numbers, so the answer to #12 is A.

#15 directly references this answer, so #15 is also A. #15 is now established as the only odd-numbered question with the answer of A, which means the answer to #13 is D.

Catchup:

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

Let Me See

#1 cannot possibly be A or B and remain internally consistent. There are already two questions answered E so #1 cannot be C. The answer to #5 is E, eliminating E as a possibility. The answer to #1, therefore, is D. This means the answer to #4 is B.

#4 states that there are 5 A’s, and we already have two E’s. This means that the only possible answer to #8 is E. There are eight vowels and twelve consonants. The answer to #3 is D, as 8 vowels — 5 A’s = 3 E’s. We have eight vowels and twelve consonants.

My Head Is Starting To Hurt A Little:

#9 is not A because of the answer to #13 indicates that #15 is the only odd-numbered question with the answer A. It cannot be C because the answer to #12 is not C. It cannot be E because we already have 3 E’s per #3. Suppose the answer to #9 was B. The answer to #11 would then necessarily be B but that would be a contridiction, since the answers to #4 and #9 would be B. Hence the answer to #9 is D.

The answer to #11 cannot be A since #4 is B. Hence the answer to #2 must be A as the other answers have been established. This means the answer to #7 is D. We can now count to see that the answer to #11 is B.

Catchup:

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

Almost There:

Let’s do a little letter counting.

A: 4 B: 3 C: 0 D: 7 E: 3

#18 cannot possibly be B, C, or D because of the letter counts and number of questions left. It cannot be E because of #3. #18 must be A, satisfying the A requirement of 5.

#14 and #19 must therefore both be B to make 5 answers B. We see that the count for letter D in question #14 is correct.

Give yourself a pat on the back for asking the indomitable #19! Note also that the answer spells DAD BEDDED A BAD BAD BABE, which the author recognizes as a Fatal Attraction reference. What a great test!