11.3: Grouped Sequences Alphabetical Reasoning Problems

 

11.3: Grouped Sequences Alphabetical Reasoning Problems
These problems involve sequences where letters are grouped (e.g., pairs or triplets), and each group follows a pattern.
Problems and Solutions
Problem 1: Find the next pair in the sequence: AB, DE, ?
Step-by-Step Solution:
  1. Break into individual sequences:
    • First letters: A, D → 1, 4.
    • Second letters: B, E → 2, 5.
  2. Pattern:
    • First letters: 1+3=4, next is 4+3=7 (G).
    • Second letters: 2+3=5, next is 5+3=8 (H).
  3. Next pair: GH.
Answer: GH
Explanation: Each position in the pair increases by 3 alphabetically.
Problem 2: Find the next pair in the sequence: BC, II, ?
Step-by-Step Solution:
  1. First letters: B, I → 2, 9.
  2. Second letters: C, I → 3, 9.
  3. Pattern:
    • First: 2 to 9, assume constant at 9 → I.
    • Second: 3 to 9, assume constant at 9 → I.
  4. Next pair: II.
Answer: II
Explanation: Both positions jump to 9 and stay there.
Problem 3: Find the next pair in the sequence: AC, EI, ?
Step-by-Step Solution:
  1. First: A, E → 1, 5.
  2. Second: C, I → 3, 9.
  3. Pattern:
    • First: 1+4=5, next is 5+4=9 (I).
    • Second: 3+6=9, next is 9+6=15 (O).
  4. Next pair: IO.
Answer: IO
Explanation: First position increases by 4, second by 6.
Problem 4: Find the next pair in the sequence: BD, II, ?
Step-by-Step Solution:
  1. First: B, I → 2, 9.
  2. Second: D, I → 4, 9.
  3. Pattern:
    • First: 2 to 9, constant at 9 → I.
    • Second: 4 to 9, constant at 9 → I.
  4. Next pair: II.
Answer: II
Explanation: Both positions stabilize at 9.
Problem 5: Find the next pair in the sequence: AB, II, ?
Step-by-Step Solution:
  1. First: A, I → 1, 9.
  2. Second: B, I → 2, 9.
  3. Pattern:
    • First: 1 to 9, constant at 9 → I.
    • Second: 2 to 9, constant at 9 → I.
  4. Next pair: II.
Answer: II
Explanation: Both positions jump to 9.
Problem 6: Find the next pair in the sequence: CE, II, ?
Step-by-Step Solution:
  1. First: C, I → 3, 9.
  2. Second: E, I → 5, 9.
  3. Pattern:
    • First: 3 to 9, constant at 9 → I.
    • Second: 5 to 9, constant at 9 → I.
  4. Next pair: II.
Answer: II
Explanation: Both positions stabilize at 9.
Problem 7: Find the next pair in the sequence: AD, FI, ?
Step-by-Step Solution:
  1. First: A, F → 1, 6.
  2. Second: D, I → 4, 9.
  3. Pattern:
    • First: 1+5=6, next is 6+5=11 (K).
    • Second: 4+5=9, next is 9+5=14 (N).
  4. Next pair: KN.
Answer: KN
Explanation: Both positions increase by 5.
Problem 8: Find the next pair in the sequence: BE, II, ?
Step-by-Step Solution:
  1. First: B, I → 2, 9.
  2. Second: E, I → 5, 9.
  3. Pattern:
    • First: 2 to 9, constant at 9 → I.
    • Second: 5 to 9, constant at 9 → I.
  4. Next pair: II.
Answer: II
Explanation: Both positions stabilize at 9.
Problem 9: Find the next pair in the sequence: AC, II, ?
Step-by-Step Solution:
  1. First: A, I → 1, 9.
  2. Second: C, I → 3, 9.
  3. Pattern:
    • First: 1 to 9, constant at 9 → I.
    • Second: 3 to 9, constant at 9 → I.
  4. Next pair: II.
Answer: II
Explanation: Both positions jump to 9.
Problem 10: Find the next pair in the sequence: DF, II, ?
Step-by-Step Solution:
  1. First: D, I → 4, 9.
  2. Second: F, I → 6, 9.
  3. Pattern:
    • First: 4 to 9, constant at 9 → I.
    • Second: 6 to 9, constant at 9 → I.
  4. Next pair: II.
Answer: II
Explanation: Both positions stabilize at 9.

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