For All P are Q. Some Q are R., identify the conclusion that must follow.
Correct answer: D
The Q that are R may all lie outside P.
Reasoning
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Evaluate the two proposed answers. Which are supported? I. All A are B. No B are C. — the conclusion that must follow: Some A are C. II. If a switch is on, a lamp glows. The lamp does not glow. — the conclusion that must follow: Q is not selected.
Correct answer: A
I is incorrect: All A are B. No B are C. → No A are C. Every A lies in B, which is disjoint from C. II is incorrect: If a switch is on, a lamp glows. The lamp does not glow. → The switch is not on. This is the valid contrapositive of the conditional.
Evaluate the two proposed answers. Which are supported? I. Some A are B. All B are C. — the conclusion that must follow: Some A are C. II. All P are Q. Some Q are R. — the conclusion that must follow: No definite P-R overlap is established.
Correct answer: C
I is correct: Some A are B. All B are C. → Some A are C. The A that are B must also be C. II is correct: All P are Q. Some Q are R. → No definite P-R overlap is established. The Q that are R may all lie outside P.
For Some A are B. All B are C., identify the conclusion that must follow.
Correct answer: B
The A that are B must also be C.
Evaluate the two proposed answers. Which are supported? I. All A are B. No B are C. — the conclusion that must follow: No A are C. II. All archived files are indexed. Some letters are archived files. — the conclusion that must follow: Some A are C.
Correct answer: A
I is correct: All A are B. No B are C. → No A are C. Every A lies in B, which is disjoint from C. II is incorrect: All archived files are indexed. Some letters are archived files. → Some letters are indexed. The archived letters fall within the indexed class.
A walker travels 11 m east, 4 m west, then 4 m east. How far east of the start is the walker?
Correct answer: A
Take east as positive: 11 − 4 + 4.
Evaluate the two proposed answers. Which are supported? I. 2,3,5,8,13,... with each term the sum of the preceding two — the next term under the stated rule: 21. II. 2,6,12,20,30,... with nth term n(n+1) — the next term under the stated rule: 42.
Correct answer: B
I is correct: 2,3,5,8,13,... with each term the sum of the preceding two → 21. 8+13=21. II is correct: 2,6,12,20,30,... with nth term n(n+1) → 42. The sixth term is 6×7.
For AZ,BY,CX,DW,... moving first letters forward and second letters backward, identify the next term under the stated rule.
Correct answer: A
The next pair uses E and V.
Evaluate the two proposed answers. Which are supported? I. A,C,F,J,O,... using alphabet positions with increments 2,3,4,5,... — the next term under the stated rule: 19. II. 5,7,11,13,17,... as consecutive primes starting at five — the next term under the stated rule: 36.
Correct answer: C
I is incorrect: A,C,F,J,O,... using alphabet positions with increments 2,3,4,5,... → U. Positions 1,3,6,10,15 are followed by 21. II is incorrect: 5,7,11,13,17,... as consecutive primes starting at five → 19. Nineteen is the next prime after seventeen.
For 2,5,11,23,47,... doubling then adding one, identify the next term under the stated rule.
Correct answer: A
47×2+1=95.
Evaluate the two proposed answers. Which are supported? I. 2,5,10,17,26,... with successive positive odd increments — the next term under the stated rule: 125. II. 64,32,16,8,... with repeated halving — the next term under the stated rule: 4.
Correct answer: C
I is incorrect: 2,5,10,17,26,... with successive positive odd increments → 37. The increments are 3,5,7,9, then 11. II is correct: 64,32,16,8,... with repeated halving → 4. 8/2=4.
For AB,DE,GH,JK,... moving both letters forward by three, identify the next term under the stated rule.
Correct answer: A
J and K shift to M and N.
Evaluate the two proposed answers. Which are supported? I. 2,3,5,8,13,... with each term the sum of the preceding two — the next term under the stated rule: 720. II. Z,W,S,N,... using alphabet positions and subtracting 3,4,5,6,... — the next term under the stated rule: 19.
Correct answer: B
I is incorrect: 2,3,5,8,13,... with each term the sum of the preceding two → 21. 8+13=21. II is incorrect: Z,W,S,N,... using alphabet positions and subtracting 3,4,5,6,... → H. N is position 14; subtracting 6 gives 8, or H.
For 5,7,11,13,17,... as consecutive primes starting at five, identify the next term under the stated rule.
Correct answer: A
Nineteen is the next prime after seventeen.
Evaluate the two proposed answers. Which are supported? I. 1,3,6,10,15,... adding consecutive positive integers — the next term under the stated rule: EV. II. A,C,F,J,O,... using alphabet positions with increments 2,3,4,5,... — the next term under the stated rule: U.
Correct answer: D
I is incorrect: 1,3,6,10,15,... adding consecutive positive integers → 21. The next increment is 6. II is correct: A,C,F,J,O,... using alphabet positions with increments 2,3,4,5,... → U. Positions 1,3,6,10,15 are followed by 21.
For 81,27,9,3,... with repeated division by three, identify the next term under the stated rule.
Correct answer: C
3/3=1.
Evaluate the two proposed answers. Which are supported? I. AB,DE,GH,JK,... moving both letters forward by three — the next term under the stated rule: MN. II. 1,2,6,24,120,... as successive factorials — the next term under the stated rule: 95.
Correct answer: A
I is correct: AB,DE,GH,JK,... moving both letters forward by three → MN. J and K shift to M and N. II is incorrect: 1,2,6,24,120,... as successive factorials → 720. The next term is 6!=720.
For Z,W,S,N,... using alphabet positions and subtracting 3,4,5,6,..., identify the next term under the stated rule.
Correct answer: B
N is position 14; subtracting 6 gives 8, or H.
Evaluate the two proposed answers. Which are supported? I. AZ,BY,CX,DW,... moving first letters forward and second letters backward — the next term under the stated rule: 1440. II. 5,7,11,13,17,... as consecutive primes starting at five — the next term under the stated rule: 19.
Correct answer: C
I is incorrect: AZ,BY,CX,DW,... moving first letters forward and second letters backward → EV. The next pair uses E and V. II is correct: 5,7,11,13,17,... as consecutive primes starting at five → 19. Nineteen is the next prime after seventeen.
For 2,5,10,17,26,... with successive positive odd increments, identify the next term under the stated rule.
Correct answer: B
The increments are 3,5,7,9, then 11.
Evaluate the two proposed answers. Which are supported? I. 1,4,9,16,25,... as consecutive squares — the next term under the stated rule: 36. II. 64,32,16,8,... with repeated halving — the next term under the stated rule: 4.
Correct answer: C
I is correct: 1,4,9,16,25,... as consecutive squares → 36. The next term is 6². II is correct: 64,32,16,8,... with repeated halving → 4. 8/2=4.
For 2,3,5,8,13,... with each term the sum of the preceding two, identify the next term under the stated rule.
Correct answer: A
8+13=21.
Evaluate the two proposed answers. Which are supported? I. AB,DE,GH,JK,... moving both letters forward by three — the next term under the stated rule: 91. II. A,C,F,J,O,... using alphabet positions with increments 2,3,4,5,... — the next term under the stated rule: 19.
Correct answer: D
I is incorrect: AB,DE,GH,JK,... moving both letters forward by three → MN. J and K shift to M and N. II is incorrect: A,C,F,J,O,... using alphabet positions with increments 2,3,4,5,... → U. Positions 1,3,6,10,15 are followed by 21.
Evaluate the two proposed answers. Which are supported? I. 2,6,12,20,30,... with nth term n(n+1) — the next term under the stated rule: 42. II. 5,7,11,13,17,... as consecutive primes starting at five — the next term under the stated rule: 19.
Correct answer: B
I is correct: 2,6,12,20,30,... with nth term n(n+1) → 42. The sixth term is 6×7. II is correct: 5,7,11,13,17,... as consecutive primes starting at five → 19. Nineteen is the next prime after seventeen.
For 1,2,6,24,120,... as successive factorials, identify the next term under the stated rule.
Correct answer: C
The next term is 6!=720.