Unit 3: Logical reasoning

Logical reasoning tests the ability to analyze information, identify patterns, and apply rules to solve problems. This unit focuses on sequence-based logic and encryption/decryption patterns fundamental to analytical thinking.

1. Number Series

Number series questions involve a sequence of numbers that follow a specific mathematical logic or rule. The objective is to identify the pattern and find the missing or wrong term.

Key Concepts and Patterns

1. Arithmetic Progressions (AP): The difference between consecutive terms is constant (e.g., ).
2. Geometric Progressions (GP): The ratio between consecutive terms is constant (e.g., ).
3. Prime Number Series: Numbers are consecutive primes (2, 3, 5, 7, 11...).
4. Square and Cube Series:
   • Perfect squares: (1, 4, 9, 16...)
   • Perfect cubes: (1, 8, 27, 64...)
   • Variations: , , .
5. Two-Tier (Difference of Differences): The logic is not in the numbers themselves but in the difference between them.

Solved Examples

Example 1: Mixed Arithmetic

• Series: 5, 11, 24, 51, 106, ?
• Logic:
• Solution: .

Example 2: Alternating Series

• Series: 15, 14, 19, 11, 23, 8
• Logic: Two series intermixed.
  • Series A (Odd positions): 15, 19, 23 (+4 pattern)
  • Series B (Even positions): 14, 11, 8 (-3 pattern)

2. Alphabet Series

Alphabet series require finding the missing letter(s) based on position in the English alphabet. Mastery of positional values is essential.

The Positional Value System

• Forward Order (A to Z): A=1, B=2 ... Z=26.
• Reverse Order (Z to A): Z=1, Y=2 ... A=26.

Mnemonic Techniques:

• EJOTY: E=5, J=10, O=15, T=20, Y=25 (Multiples of 5).
• CFILORUX: Multiples of 3 (3, 6, 9, 12, 15, 18, 21, 24).

Reverse Pairs

Letters that sum to 27 in positional value (1+26, 2+25, etc.).

• A - Z (Amazon)
• B - Y (Boy)
• C - X (Crux)
• D - W (Dew)
• M - N (Man)

Example:

• Series: B, E, H, K, ?
• Logic: B(2) +3 = E(5); E(5) +3 = H(8); H(8) +3 = K(11).
• Next: K(11) +3 = N(14). Answer: N.

3. Alphanumeric Series

These series combine numbers, alphabets, and symbols. The logic for the number component and the letter component usually runs independently but concurrently.

Strategy

1. Separate the series into elements (First letter, Number, Second letter).
2. Solve the pattern for the first letter.
3. Solve the pattern for the numbers.
4. Solve the pattern for the final letter.

Example:

• Series: 2Z5, 7Y7, 14X9, 23W11, 34V13, ?
• Number Logic: 2 (+5) → 7 (+7) → 14 (+9) → 23 (+11) → 34 (+13) → 47
• Letter Logic: Z (-1) → Y (-1) → X (-1) → W (-1) → V (-1) → U
• Last Number Logic: 5 (+2) → 7 (+2) → 9 (+2) → 11 (+2) → 13 (+2) → 15
• Answer: 47U15

4. Alphabet Test

This topic tests the ability to manipulate letters based on specific instructions rather than finding a missing term.

Types of Problems

1. Word Formation: Can a specific word be formed using the letters of a given keyword?

   • Keyword: ESTABLISHMENT
   • Target: TABLE (Yes), TENT (No - only one 'T' available? Check count. 'ESTABLISHMENT' has two T's, so Yes. 'TENT' requires two T's. If target was 'TITAN', no, because no 'I').

2. Dictionary Order: Arranging words alphabetically.

   • Compare first letters; if same, move to the second, etc.

3. Position Test: Locating a letter based on left/right directions.

   • Formula: If directions are Same (Left-Left or Right-Right), Subtract values.
   • Formula: If directions are Different (Left-Right or Right-Left), Add values.
   • Example: Which letter is 5th to the right of the 10th letter from the left?
     • Different directions (R + L) → .
     • 15th from Left = O.

5. Coding and Decoding

Coding involves encoding a message into a pattern; decoding involves deciphering it.

Major Patterns

1. Letter Coding: Shifting letters forward or backward.

   • Forward Shift: A → B (+1)
   • Backward Shift: B → A (-1)
   • Cross Coding: Letters exchange positions in a specific pattern.

2. Number Coding: Words are assigned numerical values.

   • Sum of Place Values: CAT = 3 + 1 + 20 = 24.
   • Reverse Sum: Using Z=1 values.

3. Substitution Coding: Specific names are substituted.

   • Question: If "White" is called "Blue", "Blue" is called "Red", "Red" is called "Yellow". What is the color of blood?
   • Logic: Blood is Red. In code, Red is called Yellow.
   • Answer: Yellow.

6. Language Coding (Chinese Coding)

In these problems, artificial sentences are translated into code. The goal is to identify which code word represents a specific natural word by comparing sentences and eliminating common terms.

Steps to Solve:

1. Identify two sentences that share a common word.
2. Look for the common code term between those two sentences.
3. Map the common word to the common code.
4. Eliminate mapped words to find the remaining ones.

Example:

• Statement 1: pit dar na means "you are good"
• Statement 2: dar tok pa means "good and bad"
• Statement 3: tim na tok means "they are bad"

Analysis:

• Compare (1) and (2): Common word is "good". Common code is dar. Therefore, good = dar.
• Compare (2) and (3): Common word is "bad". Common code is tok. Therefore, bad = tok.
• Compare (1) and (3): Common word is "are". Common code is na. Therefore, are = na.

Result:

• In statement 1, remaining word is "you" and remaining code is pit. So, you = pit.