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.
Reasoning
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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.
Evaluate the two proposed answers. Which are supported? I. 64,32,16,8,... with repeated halving — the next term under the stated rule: 4. II. AB,DE,GH,JK,... moving both letters forward by three — the next term under the stated rule: MN.
Correct answer: B
I is correct: 64,32,16,8,... with repeated halving → 4. 8/2=4. II is correct: AB,DE,GH,JK,... moving both letters forward by three → MN. J and K shift to M and N.
For 1,3,6,10,15,... adding consecutive positive integers, identify the next term under the stated rule.
Correct answer: D
The next increment is 6.
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: EV. II. 1,2,6,24,120,... as successive factorials — the next term under the stated rule: 720.
Correct answer: A
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 correct: 1,2,6,24,120,... as successive factorials → 720. The next term is 6!=720.
For 1,4,9,16,25,... as consecutive squares, identify the next term under the stated rule.
Correct answer: B
The next term is 6².
Evaluate the two proposed answers. Which are supported? I. 100,96,88,76,... subtracting 4,8,12,... — the next term under the stated rule: 60. II. 2,5,10,17,26,... with successive positive odd increments — the next term under the stated rule: 37.
Correct answer: D
I is correct: 100,96,88,76,... subtracting 4,8,12,... → 60. The next subtraction is 16. II is correct: 2,5,10,17,26,... with successive positive odd increments → 37. The increments are 3,5,7,9, then 11.
For 64,32,16,8,... with repeated halving, identify the next term under the stated rule.
Correct answer: A
8/2=4.
Evaluate the two proposed answers. Which are supported? I. 5,7,11,13,17,... as consecutive primes starting at five — the next term under the stated rule: 19. II. 3,6,5,10,9,18,... alternating ×2 and −1 — the next term under the stated rule: 95.
Correct answer: C
I is correct: 5,7,11,13,17,... as consecutive primes starting at five → 19. Nineteen is the next prime after seventeen. II is incorrect: 3,6,5,10,9,18,... alternating ×2 and −1 → 17. The next operation after doubling is subtraction of one.
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: 37. II. 1,3,6,10,15,... adding consecutive positive integers — the next term under the stated rule: 21.
Correct answer: A
I is correct: 2,5,10,17,26,... with successive positive odd increments → 37. The increments are 3,5,7,9, then 11. II is correct: 1,3,6,10,15,... adding consecutive positive integers → 21. The next increment is 6.
For A,C,F,J,O,... using alphabet positions with increments 2,3,4,5,..., identify the next term under the stated rule.
Correct answer: B
Positions 1,3,6,10,15 are followed by 21.
Evaluate the two proposed answers. Which are supported? I. 81,27,9,3,... with repeated division by three — the next term under the stated rule: 1. II. 1,8,27,64,... as consecutive cubes — the next term under the stated rule: 42.
Correct answer: B
I is correct: 81,27,9,3,... with repeated division by three → 1. 3/3=1. II is incorrect: 1,8,27,64,... as consecutive cubes → 125. The next term is 5³.
For 2,6,12,20,30,... with nth term n(n+1), identify the next term under the stated rule.
Correct answer: D
The sixth term is 6×7.