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

For (10) & (16), the only thing that works is 10=A and 16=D

Likewise for (6)&(17), one is B and the other is D, but since 16 & 17 isn't one of the consecutive pairs listed in (2), 17 must be the B.

Consider (12): if this is C,D, or E, then either A or B would also apply to an number with that property. So (12) must be only A or only B. For the choices of vowels in (8), only 6 vowels or 8 vowels would satisfy that condition (14 consonants is only an even number, as is 12). So 12=A and 8= either C or E. Therefore, 15=A, and 13=D.

(1) cannot be A or B because they would lead to paradoxes, and it also cannot be E since if 5=B, then 2=B also, which is the same paradox as before. So 1= either C or D and 5= either C, D, or E. If 5=D, then 4&5 would be the same, even though this is not one of the pairs listed in (2). So 5= either C or E. So 4 cannot be E, and because the number of As plus the number of Es must be either 6 or 8, (3) cannot be A (which we already could have known since 3 is an odd number). (2) cannot be B for the same reason as (1), and also cannot be D or E since 10=A.

So far we've got: (problem on the left, along with possible answers on the right, excluding problems we haven't yet considered):

1:CD
2:AC
3:BCDE
4:ABCD
5:CE
6:D
8:CE
10:A
12:A
13:D
15:A
16:D
17:B

Supposing 1=C, then 3=B => 5=E, so we've discovered the one and only E. So 8 must be C, and then 4=B. But then (3) and (4) are the same, which contradicts (2).

So 1=D, which means (3) is not B, but (4) is. Since the vowels have to total either 6 or 8, the only possibility left for (3) is D, so 8=E. So now we know there are 5 As, 3 Es, and 12 consonants.

(5) must be E, since none of the previous questions work to be the same as (5).  Since there are 3 E's, there must be exactly one more out there. This means (9) cannot be it, since that would imply (14) was E also. Since (8) and (9) are shown to be different, the two consecutives must be (6)&(7): so 2=A and 7=D. Also (9) cannot be A since 9 is odd, and cannot be C since (12) is not C. If 9 is B, then (11) would be B, which would be incorrect since both 4 and 9 are then Bs. Therefore 9=D. Now that we have everything from 1-10, it's easy to see that 11=B.

We now have 3 Bs, and we are promised 8 vowels, leaving 9 remaining between the remaining C's,B's, and D's. So (14) cannot be E, and since 13&15 are D&A respectively, 14 cannot be either of those. So there must be either 7 or 8 Ds. (18) cannot be B because of (17), cannot be C because this is incompatible with the remaining choices for (14), and cannot be D because we already know there are 5 As and 3 Es. If 18=A, then there are 2 more Bs left to be discovered, with only (then) 3 remaining questions which also ought to contain two more vowels. So 18=E. There is also one more A to be discovered, and we know it is not in (14). It also cannot be in (19) since 19 is odd, so it must be 20 (I would have thought the answer was Pressure, which is why I didn't answer this non-recursive question first, and when that wasn't a choice, I figured that the analogy was depicting the fact that a Standardized test doesn't actually measure intelligence, but intelligence helps, and likewise all the answer choices aren't what a barometer measures but can still affect the reading you get - making me think then it was E).

Here's what we've got now, in the same format as before:

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:BC
15:A
16:D
17:B
18:E
19:BCD
20:A

We've satisfied all our vowels, so 14 and 19 are not restricted by that. The only restriction left is the number of Ds. If 14=C, then 19=D, but if 14=B, 19 could be either B or C. Am I missing something here, or did I reason incorrectly above? I note that my solution overlaps greatly with Eric's but doesn't seem to be contradictory, whereas Eric's clearly is.

Edited on January 17, 2006, 3:29 pm

Posted by Avin on 2006-01-17 15:25:25