7.2: Backward Skipping Sequence - Alphabetical Reasoning Problems

7.2: Backward Skipping Sequence - Alphabetical Reasoning Problems

These problems involve a sequence where letters move backward in the alphabet, skipping a fixed or increasing number of letters.

Problems and Solutions

Problem 1: Z, X, I, ?

• Step-by-Step Solution:
  1. Positions: Z = 26, X = 24, I = 9.
  2. Differences: 26 - 24 = 2, 24 - 9 = 15.
  3. The pattern is irregular. Check skips:
     • Z to X: skip 1 letter (Y).
     • X to I: skip 14 letters (W, V, ..., J).
  4. Assume an increasing skip pattern. Try a geometric progression (e.g., skip doubles): 1, 14, next could be large.
  5. Alternatively, test a simpler backward skip from I. Assume a reset or new skip (e.g., 2): 9 - 2 = 7 (G).
  6. The next term is G.
• Answer: G
• Explanation: The sequence has an irregular jump. Assuming a simpler backward skip of 1 letter from I gives G.

Problem 2: Y, U, I, ?

• Step-by-Step Solution:
  1. Positions: Y = 25, U = 21, I = 9.
  2. Differences: 25 - 21 = 4, 21 - 9 = 12.
  3. Differences: 4, 12. Assume a pattern (e.g., multiply by 3).
  4. Next difference: 12 × 3 = 36.
  5. Subtract 36 from I’s position (9): 9 - 36 = -27. Add 26: -27 + 26 = -1. Add 26 again: -1 + 26 = 25 (Y).
  6. The next term is Y.
• Answer: Y
• Explanation: The backward skip increases (3, 11 letters). From I, a large skip cycles back to Y.

Problem 3: X, S, I, ?

• Step-by-Step Solution:
  1. Positions: X = 24, S = 19, I = 9.
  2. Differences: 24 - 19 = 5, 19 - 9 = 10.
  3. Differences: 5, 10. The next difference is likely 15 (increasing by 5).
  4. Subtract 15 from I’s position (9): 9 - 15 = -6. Add 26: -6 + 26 = 20 (T).
  5. The next term is T.
• Answer: T
• Explanation: The backward skip increases by 5 (4, 9, 14 letters). From I, skip 14 letters to T.

Problem 4: Z, W, I, ?

• Step-by-Step Solution:
  1. Positions: Z = 26, W = 23, I = 9.
  2. Differences: 26 - 23 = 3, 23 - 9 = 14.
  3. Differences: 3, 14. Assume an increasing pattern (e.g., next is 25).
  4. Subtract 25 from I’s position (9): 9 - 25 = -16. Add 26: -16 + 26 = 10 (J).
  5. The next term is J.
• Answer: J
• Explanation: The backward skip increases (2, 13 letters). From I, a large skip gives J.

Problem 5: Y, I, S, ?

• Step-by-Step Solution:
  1. Positions: Y = 25, I = 9, S = 19.
  2. Differences: 25 - 9 = 16, 9 - 19 = -10 (but backward: 19 - 9 = 10).
  3. The sequence is backward. Check skips: Y to I (16 positions), I to S (10 positions backward).
  4. Assume a constant skip of 10 positions backward from S: 19 - 10 = 9 (I).
  5. The next term is I.
• Answer: I
• Explanation: The sequence skips backward (15, 9 letters). From S, skip 9 letters to I.

Problem 6: Z, U, I, ?

• Step-by-Step Solution:
  1. Positions: Z = 26, U = 21, I = 9.
  2. Differences: 26 - 21 = 5, 21 - 9 = 12.
  3. Differences: 5, 12. Assume the next difference is 19 (increasing by 7).
  4. Subtract 19 from I’s position (9): 9 - 19 = -10. Add 26: -10 + 26 = 16 (P).
  5. The next term is P.
• Answer: P
• Explanation: The backward skip increases by 7 (4, 11, 18 letters). From I, skip 18 letters to P.

Problem 7: W, I, Q, ?

• Step-by-Step Solution:
  1. Positions: W = 23, I = 9, Q = 17.
  2. Differences: 23 - 9 = 14, 9 - 17 = -8 (backward: 17 - 9 = 8).
  3. Backward skips: 13, 7 letters. Assume the next skip is 7 (constant from Q).
  4. Subtract 8 from Q’s position (17): 17 - 8 = 9 (I).
  5. The next term is I.
• Answer: I
• Explanation: The sequence alternates skips. From Q, skip 7 letters backward to I.

Problem 8: X, I, I, ?

• Step-by-Step Solution:
  1. Positions: X = 24, I = 9, I = 9.
  2. Differences: 24 - 9 = 15, 9 - 9 = 0.
  3. The repetition at I suggests a pause. Assume a backward skip of 15 from I.
  4. Subtract 15 from I’s position (9): 9 - 15 = -6. Add 26: -6 + 26 = 20 (T).
  5. The next term is T.
• Answer: T
• Explanation: The sequence pauses at I. Assuming the same skip (14 letters) from I gives T.

Problem 9: Z, O, I, ?

• Step-by-Step Solution:
  1. Positions: Z = 26, O = 15, I = 9.
  2. Differences: 26 - 15 = 11, 15 - 9 = 6.
  3. Backward skips: 10, 5 letters. Assume the next skip is 5.
  4. Subtract 6 from I’s position (9): 9 - 6 = 3 (C).
  5. The next term is C.
• Answer: C
• Explanation: The backward skip decreases (10, 5 letters). From I, skip 5 letters to C.

Problem 10: Y, S, I, ?

• Step-by-Step Solution:
  1. Positions: Y = 25, S = 19, I = 9.
  2. Differences: 25 - 19 = 6, 19 - 9 = 10.
  3. Backward skips: 5, 9 letters. Assume the next skip is 13 (increasing by 4).
  4. Subtract 14 from I’s position (9): 9 - 14 = -5. Add 26: -5 + 26 = 21 (U).
  5. The next term is U.
• Answer: U
• Explanation: The backward skip increases by 4 (5, 9, 13 letters). From I, skip 13 letters to U.