3.4 Logic, Letter Sequences & Statement Relationships

3.4 Logic, Letter Sequences & Statement Relationships

Logical reasoning forms the ultimate test of analytical thinking in the 11+ Kent Test. This section covers four distinct puzzle categories: letter series, linear ordering logic, statement deductions (True / False / Cannot Tell), and multi-variable grid puzzles.

1. Alphabet Letter Series and Pair Sequences

Letter series questions present a sequence of single letters or letter pairs and ask for the next term. Success requires analyzing the pattern for both the first letters and second letters independently.

Pattern Categories

1. Simple Arithmetic Step: $+2, +2, +2$ or $+3, +4, +5$.
2. Interleaved / Dual Series: Term 1 connects to Term 3, while Term 2 connects to Term 4.
3. Mirrored / Reverse Pairs: First letter moves forward from A ($A, B, C \dots$), second letter moves backward from Z ($Z, Y, X \dots$).

Worked Example: Mirrored Pair Series

Sequence: AZ , CX , EV , GT , ____

• Analyze 1st Letters: $A (1) \xrightarrow{+2} C (3) \xrightarrow{+2} E (5) \xrightarrow{+2} G (7) \xrightarrow{+2} \mathbf{I (9)}$
• Analyze 2nd Letters: $Z (26) \xrightarrow{-2} X (24) \xrightarrow{-2} V (22) \xrightarrow{-2} T (20) \xrightarrow{-2} \mathbf{R (18)}$
• Next Pair in Series: IR.

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2. Linear Ordering & Inequality Chains

Linear ordering puzzles give a series of comparative clues about people or objects (e.g., height, age, exam scores, race finish times).

The Inequality Chain Method

Instead of holding clues in your head, convert each clue into a mathematical inequality ($>$ or $<$) and link them into a single continuous chain:

Problem: Five children (Amir, Beth, Charlie, Daisy, Ethan) ran a race.

1. Amir finished before Beth but after Charlie. $\rightarrow$ $\text{Charlie} > \text{Amir} > \text{Beth}$
2. Daisy finished before Charlie. $\rightarrow$ $\text{Daisy} > \text{Charlie}$
3. Ethan finished after Beth. $\rightarrow$ $\text{Beth} > \text{Ethan}$

Combining into a Master Chain

$\text{Daisy} > \text{Charlie} > \text{Amir} > \text{Beth} > \text{Ethan}$

• 1st Place (Winner): Daisy
• Last Place (5th): Ethan
• Middle (3rd): Amir

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3. True / False / Cannot Tell Deductions

In GL Assessment VR papers, statement verification questions present a short passage followed by a statement. You must decide whether the statement is True, False, or Cannot Tell based strictly and solely on the text provided.

Definitions of the Three Options

[!WARNING] The 'Cannot Tell' Trap: Do NOT bring in real-world knowledge! If a passage says "All Zorks have blue fur," and the statement says "Zorks live in cold climates," the answer is Cannot Tell—even if real-world arctic animals have thick fur!

Quantifier Rules Matrix

Worked Example

Passage: "All students who join the Chess Club must be in Year 5 or Year 6. Some members of the Chess Club play in the school orchestra. Oliver is in Year 5 and plays the violin in the school orchestra."

• Statement: "Oliver is a member of the Chess Club."
• Analysis: Oliver meets the age requirement (Year 5) and plays in the orchestra. However, the text only states that some orchestra players are in the Chess Club. It does not state that all orchestra players belong to the Chess Club, nor that Oliver specifically joined.
• Verdict: Cannot Tell.

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4. Grid Logic & Elimination Matrices

Multi-variable logic puzzles involve matching individuals to specific attributes (e.g., four friends, four pets, four house colors).

Solving with an Elimination Matrix

Construct a grid with names on the rows and attributes on the columns. Mark an X for eliminated pairings and a Check ($\checkmark$) for confirmed pairings. When a check is placed in a cell, place X in all other cells of that row and column.

Puzzle: Four friends (Liam, Mia, Noah, Olivia) each own a different pet (Dog, Cat, Rabbit, Hamster).

1. Liam does not own a Dog or a Cat. ($\rightarrow$ Liam owns Rabbit or Hamster)
2. Mia owns a Rabbit. ($\rightarrow$ Mia = Rabbit; eliminate Rabbit for everyone else)
3. The Cat owner is not Noah.

Step-by-Step Elimination Grid

• Since Mia owns the Rabbit, Liam's remaining option between Rabbit and Hamster is Hamster ($\checkmark$).
• For the Cat, Liam has X, Mia has X, and Noah cannot own a Cat (Rule 3). Therefore, Olivia MUST own the Cat ($\checkmark$).
• Remaining pet for Noah is Dog ($\checkmark$).