Thinking Skills · Module 3
Non-Verbal Reasoning
From the basics to challenge level — theory, worked examples and four tiers of practice.
Page 1 · Introduction
What is non-verbal reasoning?
Non-verbal reasoning tests how well you spot patterns and relationships using numbers, shapes and sequences instead of words. Selective tests love it because you can't memorise your way through — you have to think.
Here's the reassuring part: almost every question is secretly asking one thing — what is the rule? Find the rule, and the answer follows automatically.
The big ideaDon't hunt for the answer first. Hunt for the rule that connects the items. The answer is simply whatever fits the rule.
💡We'll build from easy patterns up to genuinely tricky ones, step by step. By the end you'll spot rules that most students miss.
On the real testWhere this appearsPattern and sequence reasoning is central to the Thinking Skills section (25% of your mark, from 2025). The official test lists finding procedures, identifying similarity and spotting patterns — exactly these skills.
Page 2 · Number sequences
Finding the rule in a sequence
A sequence follows a hidden rule. Your job: find it, then continue it. The common rules are:
The rules to check
- Add / subtract the same amount: 3, 7, 11, 15… (add 4)
- Multiply / divide: 2, 6, 18, 54… (times 3)
- Growing gaps: 1, 2, 4, 7, 11… (add 1, 2, 3, 4…)
- Two rules alternating: 5, 10, 8, 16, 14… (times 2, minus 2…)
✅Best first move: write the gap between each pair of numbers. Equal gaps mean add/subtract. Growing gaps mean there's a pattern in the gaps themselves.
Page 3 · Worked examples
Sequences in action
1. 4, 9, 14, 19, ?
Gaps are +5 each time. 19 + 5 = 24.
24
2. 3, 6, 12, 24, ?
Each term doubles. 24 × 2 = 48.
48
3. 1, 4, 9, 16, ?
Square numbers: 1², 2², 3², 4²… next is 5² = 25.
25
💡If gaps and multiplying both fail, check for square numbers (1,4,9,16,25) — the test uses them often.
Page 4 · Odd one out
Spotting what breaks the rule
You're given items that share a rule — except one. Find the shared rule, then the odd one.
Odd one out: 12, 15, 18, 22, 24
All are multiples of 3 (12,15,18,24) — except 22.
22
Odd one out: 2, 3, 5, 9, 11
All are prime numbers except 9 (= 3×3).
9
✅Test one property at a time: even/odd? multiples? primes? squares? When four fit and one doesn't, you've found it.
Page 5 · Analogies
"A is to B as C is to ?"
Work out the relationship in the first pair, then apply the same relationship to the second.
2 is to 8 as 3 is to ?
2 × 4 = 8, so apply ×4: 3 × 4 = 12.
12
10 is to 5 as 18 is to ?
10 ÷ 2 = 5, so 18 ÷ 2 = 9.
9
KeyFind the rule from the pair you're given, then apply exactly the same rule to the new number. Don't change the rule halfway.
Page 6 · Letter patterns
Letters as position numbers
Letters follow patterns too — the trick is to turn each letter into its position number (A=1, B=2 … Z=26).
A, C, E, G, ?
Positions 1, 3, 5, 7 — odd numbers. Next is 9 = I.
I
Z, X, V, T, ?
Positions 26, 24, 22, 20 — down by 2. Next is 18 = R.
R
💡Lightly write A=1 to Z=26 on your scrap paper at the start. It turns every letter puzzle into a number puzzle you already know how to solve.
Page 7 · Practice
Level 1 · Easy
Warm up
Clear patterns to get your eye in. Tap to check.
1. 5, 10, 15, 20, ?
Add 5 each time. 20 + 5 = 25.
2. Odd one out: 4, 8, 12, 14, 16
All are multiples of 4 except 14.
3. 3 is to 9 as 5 is to ?
3 × 3 = 9, so 5 × 3 = 15.
🎉Eye for patterns is warming up nicely. Let's add a twist.
Page 8 · Practice
Level 2 · Medium
Trickier rules
The rule is a little more hidden here. Try the gaps first.
1. 2, 5, 11, 23, ?
Rule: double and add 1. 23 × 2 + 1 = 47.
2. B, D, G, K, ?
Positions 2, 4, 7, 11 — gaps grow +2, +3, +4. Next gap +5 → 11+5 = 16 = P.
3. Odd one out: 16, 25, 36, 40, 49
All are square numbers (4²,5²,6²,7²) except 40.
💪"Double and add 1" and "growing gaps" are exam favourites. Now you know to look for them.
Page 9 · Practice
Level 3 · Hard
Hidden rules
These hide their rule well. If one type of rule stalls, switch to another.
1. 1, 1, 2, 3, 5, 8, ?
Each number is the sum of the two before it (Fibonacci): 5 + 8 = 13. When gaps and multiples fail, try "add the two previous terms".
2. 3 is to 12 as 5 is to ?
Not ×4 (that gives 20). The multiplier is one more than the number: 3×4=12, so 5×6=30. The rule is n×(n+1).
3. 2, 6, 12, 20, 30, ?
Gaps are 4, 6, 8, 10 — growing by 2. Next gap 12, so 30 + 12 = 42. (Also each term is n×(n+1).)
💡Fibonacci and n×(n+1) are the "secret weapons" of hard pattern questions. Spotting them puts you ahead of the pack.
Page 10 · Challenge
Level 4 · Challenge
Think smart
The toughest tier. These need you to try several rule-types calmly. Don't be discouraged if they take a few goes.
1. 1, 4, 9, 16, 25, ?
Square numbers: 1²,2²,3²,4²,5²… next is 6² = 36. (The gaps also grow 3,5,7,9,11 — another way to see it.)
2. 2, 3, 5, 7, 11, 13, ?
These are the prime numbers in order. After 13 the next prime is 17. When a sequence isn't arithmetic, ask: could these be primes?
3. 1, 2, 6, 24, 120, ?
Each term is multiplied by the next counting number: ×2, ×3, ×4, ×5… So 120 × 6 = 720. Spotting a changing multiplier is the clever leap.
🌟Recognising primes and changing-multiplier patterns is advanced stuff. Every one you crack builds real thinking power.
Complete
Great thinking!
You've completed the Non-Verbal Reasoning module.
You've built a real toolkit of rules: gaps, multiples, squares, Fibonacci, n×(n+1), primes and changing multipliers. The golden habit stays the same — always find the rule first, and the answer follows.