3.4 Determining the Shift Pattern or Original Sequence

 3.4  Determining the Shift Pattern or Original Sequence - Practice

Description: The resulting sequence or word after alternating shifts is given, and the task is to determine the original sequence, the shift amounts, or the alternating pattern used. This is a reverse-engineering problem, often requiring deduction.

Example Question: The sequence D, E, I, I is obtained by applying alternating shifts to an original sequence of 4 letters. Odd-positioned letters were shifted forward by 2, and even-positioned letters were shifted forward by 3. What was the original sequence?

• Solution:
  • For odd positions (1st, 3rd), reverse the +2 shift: -2.
  • For even positions (2nd, 4th), reverse the +3 shift: -3.
  • D (1st, odd): D (4) - 2 = 2 → B.
  • E (2nd, even): E (5) - 3 = 2 → B.
  • I (3rd, odd): I (9) - 2 = 7 → G.
  • I (4th, even): I (9) - 3 = 6 → F.
  • Original sequence: B, B, G, F.

Key Focus: Working backward to deduce the original sequence or shift pattern based on the given result and rules.

Variants:

• Find the original sequence given the shifted sequence and shift rules.
• Determine the shift amounts or directions (e.g., what shifts produce the given result?).
• Identify the alternating pattern (e.g., is it odd/even-based or a repeating cycle?).
• Verify if a given sequence could result from specific alternating shifts.

 

3.3 Analyzing Properties of the Resulting Sequence or Word

 3.3  Analyzing Properties of the Resulting Sequence or Word - Practice

3.3  Analyzing Properties of the Resulting Sequence or Word

• Description: After applying alternating shifts to a sequence or word, the task is to analyze properties of the resulting sequence, such as the number of vowels, consonants, or specific letter types, or to compare properties before and after the shifts.
• Example Question: In the sequence A, B, C, D, E, shift odd-positioned letters forward by 3 and even-positioned letters backward by 2. How many vowels are in the new sequence? (Vowels: A, E, I, O, U)
  • Solution:
    • A (1st, odd): A (1) + 3 = 4 → D (consonant).
    • B (2nd, even): B (2) - 2 = 26 (mod 26) → Z (consonant).
    • C (3rd, odd): C (3) + 3 = 6 → F (consonant).
    • D (4th, even): D (4) - 2 = 2 → B (consonant).
    • E (5th, odd): E (5) + 3 = 8 → I (vowel).
    • New sequence: D, Z, F, B, I. Vowels: I (1 vowel).
• Key Focus: Applying shifts and evaluating properties like vowel/consonant counts or letter patterns.
• Variants:
  • Count vowels or consonants in the new sequence.
  • Compare vowel/consonant counts before and after shifts.
  • Identify specific letter types (e.g., how many letters are in the first half of the alphabet, A-M).
  • Check for repeated letters or specific patterns (e.g., are any letters unchanged?).

3.2 Finding a Specific Letter After Alternating Shifts

 3.2 Finding a Specific Letter After Alternating Shifts  - Practice

• Description: A sequence or word is given with alternating shift rules, and the task is to identify the letter at a specific position in the resulting sequence or word after applying the shifts.
• Example Question: In the word "TEST", shift odd-positioned letters forward by 1 and even-positioned letters backward by 2. What is the 3rd letter in the new word?
  • Solution:
    • T (1st, odd): T (20) + 1 = 21 → U.
    • E (2nd, even): E (5) - 2 = 3 → C.
    • S (3rd, odd): S (19) + 1 = 20 → T.
    • T (4th, even): T (20) - 2 = 18 → R.
    • New word: U, C, T, R. 3rd letter: T.
• Key Focus: Computing the new letter at a specific position while tracking alternating rules.
• Variants:
  • Find the letter at a given position (e.g., 2nd or 5th).
  • Identify the first or last letter after shifts.
  • Find letters meeting a condition (e.g., the first vowel in the new sequence).

 

3.1 Applying Alternating Shifts to a Sequence or Word

3.1 Applying Alternating Shifts to a Sequence or Word - Practice

Description: A sequence or word is given, and different shifts (e.g., in magnitude or direction) are applied to letters based on their positions (e.g., odd vs. even) or a repeating pattern (e.g., +1, +2, repeat). The task is to find the resulting sequence or word.

1. • 
     
   • Example Question: For the sequence A, B, C, D, shift odd-positioned letters forward by 2 and even-positioned letters forward by 3. What is the new sequence?
     • Solution: A (+2→C), B (+3→E), C (+2→E), D (+3→G) → C, E, E, G.
   • Key Focus: Applying multiple shift rules correctly and computing the new letters.
   • Variants:
     • Shift by different magnitudes (e.g., +2 for odd, +3 for even).
     • Shift in different directions (e.g., +2 for odd, -1 for even).
     • Apply shifts based on a repeating pattern (e.g., +1, +2, +3, repeat every 3 letters).
     • Shift specific subsets (e.g., vowels shift +2, consonants shift +1).

2 Reversing Letters - Alphabetical Reasoning

2 Reversing Letters - Alphabetical Reasoning

 In Alphabetical Reasoning, specifically within Reversing Letters problems, there are typically three distinct types of questions that can be asked. These problems involve manipulating the letters of the alphabet, often by reversing their order or positions, and the types of questions are based on how the reversal is applied and what is being asked.

1. Reversing the Entire Alphabet

• Description: The entire alphabet (A to Z) is reversed, so A becomes Z, B becomes Y, C becomes X, and so on (i.e., the nth letter from the start becomes the nth letter from the end). Questions ask for the new letter that corresponds to a given letter in the reversed alphabet or vice versa.
• Example Question: If the alphabet is reversed, what is the letter that replaces 'D'?
  • Solution: In the reversed alphabet (Z, Y, X, ..., A), D (4th letter forward) becomes W (4th letter backward), since Z-A, Y-B, X-C, W-D.
• Key Focus: Mapping letters based on their positions in the reversed alphabet (position 1 → 26, 2 → 25, ..., 26 → 1).
• Common Variants:
  • Find the letter in the reversed alphabet for a given letter.
  • Find the original letter given a letter in the reversed alphabet.
  • Identify patterns or sequences in the reversed alphabet.

2. Reversing a Specific Word or String

• Description: A given word or sequence of letters (e.g., "CAT") is reversed, and questions ask about the resulting word, specific letter positions, or properties of the reversed string.
• Example Question: If the word "APPLE" is reversed, what is the 3rd letter in the new word?
  • Solution: Reversing "APPLE" gives "ELPPA". The 3rd letter is P.
• Key Focus: Manipulating the order of letters within a specific word or substring, focusing on positional changes.
• Common Variants:
  • Find the entire reversed word.
  • Identify a specific letter at a given position in the reversed word.
  • Compare properties (e.g., vowels, consonants) before and after reversal.
  • Reverse only a portion of the word (e.g., first 3 letters).

3. Reversing Letter Positions in a Sequence or Pattern

• Description: A sequence of letters (often following a pattern, like A, C, E or positions in the alphabet) is given, and the positions of the letters are reversed. Questions ask about the new sequence, specific letters, or properties of the resulting sequence.
• Example Question: A sequence A, D, G (1st, 4th, 7th letters of the alphabet) has its positions reversed. What is the new sequence?
  • Solution: Reversing the positions (1st, 2nd, 3rd → 3rd, 2nd, 1st) gives G, D, A.
• Key Focus: Reordering a sequence of letters based on their positional indices rather than reversing the alphabet or word itself.
• Common Variants:
  • Find the new sequence after reversing the order of positions.
  • Identify the letter at a specific position in the reversed sequence.
  • Combine with other operations (e.g., shift each letter forward after reversing positions). 

1. Reversing the Entire Alphabet - Practice Problems

2. Reversing a Specific Word or String - Practice Problems

3. Reversing Letter Positions in a Sequence or Pattern - Practice Problems