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1.[A] = ?
(A) 6
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(B) 7
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(C) 8
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(D) 9
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(E) 10
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Minimizing 1 and 2 maximizes 6.
2.[B] = ?
(A) 2
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(B) 3
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(C) 4
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(D) 5
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(E) 6
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Minimizing 1 and 2 maximizes 6.
3.[C] = ?
(A) 1
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(B) 2
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(C) 3
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(D) 4
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(E) 5
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5 gives [E] = 7, and these are given in 6-8 and 13-16. 2 gives [B] = 2, and these are given in 11 and 25.10, 17, and 21 are all C. 3C would contradict itself.
4.[D] = ?
(A) 4
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(B) 5
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(C) 6
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(D) 7
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(E) 8
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3D and 7E imply 4C
5.[E] = ?
(A) 7
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(B) 8
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(C) 9
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(D) 10
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(E) 11
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Given 6, [C] + [D] + [E] must be 17. This is the minimum from 5 and 7.
6.[A] + [B] = ?
(A) 4
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(B) 5
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(C) 6
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(D) 7
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(E) 8
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Minimizing 1 and 2 maximizes 6.
7.[C] + [D] = ?
(A) 14
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(B) 13
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(C) 12
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(D) 11
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(E) 10
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Given 6, [C] + [D] + [E] must be 17. This is the minimum from 5 and 7.
8.Which set includes 3 unique answers?
(A) None of the below
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(B) {5,6,7}
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(C) {6,7,8}
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(D) {7,8,9}
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(E) {8,9,10}
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B and C are ruled out by 6 and 7. 9 contradicts D. A contradicted by 9 and 10.
9.What is the answer to question 13?
(A) B
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(B) C
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(C) D
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(D) E
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(E) A
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From 10.
10.What is the answer to question 9?
(A) B
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(B) C
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(C) D
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(D) E
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(E) A
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15 rules out E, A (from 5), and B (from 25). D implies 9E, which is contradicted by 16.
11.What is the answer to question 10?
(A) B
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(B) C
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(C) D
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(D) E
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(E) A
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From 10.
12.What is the answer to question 11?
(A) B
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(B) C
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(C) D
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(D) E
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(E) A
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From 11.
13.What is the answer to question 12?
(A) B
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(B) C
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(C) D
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(D) E
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(E) A
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From 12.
14.Questions 14, 15, and 16 all share which answer?
(A) A
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(B) B
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(C) C
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(D) D
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(E) E
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From 16.
15.How many unique answers exist in the set {5,10,15,20,25}?
(A) 1
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(B) 2
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(C) 3
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(D) 4
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(E) 5
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From 14.
16.How many unique answers exist in the set {1,4,9,16,25}?
(A) 1
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(B) 2
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(C) 3
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(D) 4
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(E) 5
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From 25.
17.How many unique answers exist in the set {18,19,20,21,22,23,24}?
(A) 1
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(B) 2
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(C) 3
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(D) 4
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(E) 5
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5 gives [E] = 7, and these are given in 6-8 and 13-16. 2 gives [B] = 2, and these are given in 11 and 25. A, C, and D are all already found in this set. Thus, 3.
18.What is the most common answer in the set {3,6,9,12,15,18,21,24}?
(A) A
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(B) B
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(C) C
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(D) D
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(E) E
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Among other multiples of 3, there are 3 Ds and 2 or fewer of every other letters.
19.What is the most common answer in the set {2,3,5,7,11,13,15,19,23}
(A) A
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(B) B
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(C) C
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(D) D
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(E) E
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Among other primes, there are two each of A, D, and E. All other answers must be solved first, then using the totals in questions 1-5, D and E must be eliminated.
20.How long is the longest sequence of consecutive questions which have the same answer?
(A) 1
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(B) 2
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(C) 3
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(D) 4
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(E) 5
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A, B, and C contradicted by 13-16. E contradicted by 25.
21.Which is the last question to have the answer A?
(A) 20
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(B) 21
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(C) 22
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(D) 23
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(E) 24
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A contradicts itself. B contradicts itself. D implies 23A which implies 24C which implies 23D, which is a contradiction. E contradicts 25.
22.Which is the last question to have the answer B?
(A) 25
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(B) 24
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(C) 23
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(D) 22
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(E) 21
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From 21.
23.Which is the last question to have the answer C?
(A) 24
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(B) 23
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(C) 22
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(D) 21
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(E) 20
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A contradicts 21. B contradicts itself. C contradicts itself. E contradicts 25.
24.Which is the last question to have the answer D?
(A) 21
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(B) 22
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(C) 23
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(D) 24
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(E) 25
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23 rules out A, B, and C. 25 rules out E.
25.Which is the last question to have the answer E?