Number Analogies

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Number Analogies appear in the NCEE Quantitative Reasoning section and test your ability to recognise numerical relationships. A typical question looks like this:

“12 : 144 :: 5 : ?

You must find the relationship between 12 and 144, then apply the same relationship to 5 to find the answer.

Common Relationship Types:

Relationship	Example	Pattern
Square	6 : 36	$6^2 = 36$
Cube	3 : 27	$3^3 = 27$
Multiply by itself	9 : 81	$9 \times 9 = 81$
Double	7 : 14	$7 \times 2 = 14$
Add a constant	3 : 7	$+4$ each time

⚡ NCEE Exam Tip: Always check if the first pair involves multiplication, division, addition, subtraction, squaring, or cubing before applying to the second number.

---

🟡 Standard — Regular Study (2d–2mo)

Standard content for students building quantitative reasoning skills.

Detailed Breakdown of Number Analogy Types

Number analogies require you to identify the mathematical operation connecting the first pair of numbers, then apply that same operation to find the missing number.

Type 1: Square/Cube Relationships

• $4 : 16$ → $4^2 = 16$
• $3 : 27$ → $3^3 = 27$
• $7 : 49$ → $7^2 = 49$
• $5 : 125$ → $5^3 = 125$

Type 2: Arithmetic Operations

Addition: $8 : 11$ → $+3$ → so $15 : 18$ Subtraction: $20 : 15$ → $-5$ → so $12 : 7$ Multiplication: $6 : 30$ → $\times 5$ → so $8 : 40$ Division: $45 : 9$ → $\div 5$ → so $35 : 7$

Type 3: Ratio and Proportion

$3 : 9 :: 4 : 12$ → Ratio is $1:3$ $5 : 20 :: 7 : 28$ → Multiply by 4

Type 4: Mixed Operations

Sometimes the relationship involves multiple steps:

• $6 : 35$ → $6 \times 6 - 1 = 35$
• $8 : 63$ → $8 \times 8 - 1 = 63$

⚡ NCEE Strategy:

1. Look at the first number in the first pair — what can you do to it to get the second?
2. Test your hypothesis on the second pair
3. If it works, apply to the question number
4. If it doesn’t, try another operation

Common Number Patterns to Memorise:

Number	Square	Cube
1	1	1
2	4	8
3	9	27
4	16	64
5	25	125
6	36	216
7	49	343
8	64	512
9	81	729
10	100	1000

---

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for thorough preparation.

Advanced Number Analogy Patterns and Problem-Solving

Mastering number analogies requires systematic practice and recognition of increasingly complex patterns.

Pattern Recognition Hierarchy:

When approaching a number analogy problem, test relationships in this order:

Level 1 — Direct Operations

1. Is B = A + constant?
2. Is B = A - constant?
3. Is B = A × constant?
4. Is B = A ÷ constant?

Level 2 — Power Relationships 5. Is B = $A^2$? 6. Is B = $A^3$? 7. Is B = $\sqrt{A}$?

Level 3 — Composite Operations 8. Is B = $(A \times \text{constant}) \pm \text{constant}$? 9. Is B = $(A^2) \pm A$? 10. Is B = $(A + B_{\text{second pair}}) \div 2$?

Type Examples with Solutions:

Example 1: $24 : 48 :: 36 : ?$ Solution: $24 \times 2 = 48$, so $36 \times 2 = 72$

Example 2: $81 : 9 :: 64 : ?$ Solution: $\sqrt{81} = 9$, so $\sqrt{64} = 8$

Example 3: $2 : 8 :: 5 : ?$ Solution: $2^3 = 8$, so $5^3 = 125$

Example 4: $3 : 30 :: 4 : ?$ Solution: $3 \times 10 = 30$, so $4 \times 10 = 40$

Example 5 (Complex): $6 : 35 :: 9 : ?$ Solution: $6^2 - 1 = 35$, so $9^2 - 1 = 80$

⚡ NCEE Common Mistakes:

1. Assuming multiplication when it’s actually division
2. Mixing up square and cube relationships
3. Not checking if the operation works for the second pair before answering
4. Rushing — always verify your answer

Practice Problems:

Try these NCEE-style questions:

1. $7 : 49 :: 9 : ?$ (Answer: 81 — square)
2. $5 : 11 :: 8 : ?$ (Answer: 17 — double plus 1)
3. $3 : 12 :: 7 : ?$ (Answer: 28 — multiply by 4)
4. $100 : 10 :: 144 : ?$ (Answer: 12 — square root)
5. $4 : 64 :: 3 : ?$ (Answer: 27 — cube)

⚡ Exam Day Strategy:

• Read the first pair carefully
• Ask “what happened to A to get B?”
• Test your theory on the known third number
• If it fits, apply to the unknown fourth number
• If not, try another relationship