9.3: Grouped or Complex Skipping Sequence

 

9.3: Grouped or Complex Skipping Sequence
These problems involve letters grouped in pairs, triplets, or sequences with alternating or complex skipping patterns.
Problems and Solutions
Problem 1: AB, DE, II, ?
  • Step-by-Step Solution:
    1. Break into groups: (A, B), (D, E), (I, I).
    2. First letters: A = 1, D = 4, I = 9. Differences: 4 - 1 = 3, 9 - 4 = 5. Next difference: 7. Next position: 9 + 7 = 16 (P).
    3. Second letters: B = 2, E = 5, I = 9. Differences: 5 - 2 = 3, 9 - 5 = 4. Next difference: 5. Next position: 9 + 5 = 14 (N).
    4. The next group is (P, N).
  • Answer: PN
  • Explanation: Each group’s letters follow forward skips (first: 2, 4, 6; second: 2, 3, 4). The next group is PN.
Problem 2: BC, FG, KL, ?
  • Step-by-Step Solution:
    1. Groups: (B, C), (F, G), (K, L).
    2. First letters: B = 2, F = 6, K = 11. Differences: 6 - 2 = 4, 11 - 6 = 5. Next difference: 6. Next position: 11 + 6 = 17 (Q).
    3. Second letters: C = 3, G = 7, L = 12. Differences: 7 - 3 = 4, 12 - 7 = 5. Next difference: 6. Next position: 12 + 6 = 18 (R).
    4. The next group is (Q, R).
  • Answer: QR
  • Explanation: Each group’s letters follow forward skips (first: 3, 4, 5; second: 3, 4, 5). The next group is QR.
Problem 3: AZ, BY, DW, ?
  • Step-by-Step Solution:
    1. Groups: (A, Z), (B, Y), (D, W).
    2. First letters: A = 1, B = 2, D = 4. Differences: 2 - 1 = 1, 4 - 2 = 2. Next difference: 4. Next position: 4 + 4 = 8 (I).
    3. Second letters: Z = 26, Y = 25, W = 23. Differences: 26 - 25 = 1, 25 - 23 = 2. Next difference: 3. Next position: 23 - 3 = 20 (T).
    4. The next group is (I, T).
  • Answer: IT
  • Explanation: First letters skip forward (0, 1, 3), second letters skip backward (0, 1, 2). The next group is IT.
Problem 4: CD, IJ, PQ, ?
  • Step-by-Step Solution:
    1. Groups: (C, D), (I, J), (P, Q).
    2. First letters: C = 3, I = 9, P = 16. Differences: 9 - 3 = 6, 16 - 9 = 7. Next difference: 8. Next position: 16 + 8 = 24 (X).
    3. Second letters: D = 4, J = 10, Q = 17. Differences: 10 - 4 = 6, 17 - 10 = 7. Next difference: 8. Next position: 17 + 8 = 25 (Y).
    4. The next group is (X, Y).
  • Answer: XY
  • Explanation: Each group’s letters skip forward (5, 6, 7). The next group is XY.
Problem 5: AC, GI, MO, ?
  • Step-by-Step Solution:
    1. Groups: (A, C), (G, I), (M, O).
    2. First letters: A = 1, G = 7, M = 13. Differences: 7 - 1 = 6, 13 - 7 = 6. Next difference: 6. Next position: 13 + 6 = 19 (S).
    3. Second letters: C = 3, I = 9, O = 15. Differences: 9 - 3 = 6, 15 - 9 = 6. Next difference: 6. Next position: 15 + 6 = 21 (U).
    4. The next group is (S, U).
  • Answer: SU
  • Explanation: Each group’s letters skip 5 letters forward. The next group is SU.
Problem 6: ZA, YI, IO, ?
  • Step-by-Step Solution:
    1. Groups: (Z, A), (Y, I), (I, O).
    2. First letters: Z = 26, Y = 25, I = 9. Differences: 26 - 25 = 1, 25 - 9 = 16. Next difference (backward): 9 - 17 = -8. Add 26: -8 + 26 = 18 (R).
    3. Second letters: A = 1, I = 9, O = 15. Differences: 9 - 1 = 8, 15 - 9 = 6. Next difference: 4. Next position: 15 + 4 = 19 (S).
    4. The next group is (R, S).
  • Answer: RS
  • Explanation: First letters skip backward, second letters skip forward (7, 5, 3). The next group is RS.
Problem 7: DE, JK, QR, ?
  • Step-by-Step Solution:
    1. Groups: (D, E), (J, K), (Q, R).
    2. First letters: D = 4, J = 10, Q = 17. Differences: 10 - 4 = 6, 17 - 10 = 7. Next difference: 8. Next position: 17 + 8 = 25 (Y).
    3. Second letters: E = 5, K = 11, R = 18. Differences: 11 - 5 = 6, 18 - 11 = 7. Next difference: 8. Next position: 18 + 8 = 26 (Z).
    4. The next group is (Y, Z).
  • Answer: YZ
  • Explanation: Each group’s letters skip forward (5, 6, 7). The next group is YZ.
Problem 8: BA, IH, PL, ?
  • Step-by-Step Solution:
    1. Groups: (B, A), (I, H), (P, L).
    2. First letters: B = 2, I = 9, P = 16. Differences: 9 - 2 = 7, 16 - 9 = 7. Next difference: 7. Next position: 16 + 7 = 23 (W).
    3. Second letters: A = 1, H = 8, L = 12. Differences: 8 - 1 = 7, 12 - 8 = 4. Next difference: 1 (decreasing by 3). Next position: 12 + 1 = 13 (M).
    4. The next group is (W, M).
  • Answer: WM
  • Explanation: First letters skip 6 letters forward, second letters have decreasing skips (6, 3, 0). The next group is WM.
Problem 9: FG, LM, SU, ?
  • Step-by-Step Solution:
    1. Groups: (F, G), (L, M), (S, U).
    2. First letters: F = 6, L = 12, S = 19. Differences: 12 - 6 = 6, 19 - 12 = 7. Next difference: 8. Next position: 19 + 8 = 27. Subtract 26: 27 - 26 = 1 (A).
    3. Second letters: G = 7, M = 13, U = 21. Differences: 13 - 7 = 6, 21 - 13 = 8. Next difference: 10. Next position: 21 + 10 = 31. Subtract 26: 31 - 26 = 5 (E).
    4. The next group is (A, E).
  • Answer: AE
  • Explanation: First letters skip 5, 6, 7; second letters skip 5, 7, 9. The next group is AE.
Problem 10: IJ, OP, GI, ?
  • Step-by-Step Solution:
    1. Groups: (I, J), (O, P), (G, I).
    2. First letters: I = 9, O = 15, G = 7. Differences: 15 - 9 = 6, 7 - 15 = -8. Assume alternating forward/backward. Next: +6. Next position: 7 + 6 = 13 (M).
    3. Second letters: J = 10, P = 16, I = 9. Differences: 16 - 10 = 6, 9 - 16 = -7. Next: +6. Next position: 9 + 6 = 15 (O).
    4. The next group is (M, O).
  • Answer: MO
  • Explanation: The sequence alternates forward and backward skips. The next group is MO.

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