Number Analogy Patterns: The 5-Category Method for Logical Reasoning

Number analogy questions give you one number pair with a hidden rule, then ask you to apply that same rule to a second pair. Almost every test variant falls into one of five pattern categories, and recognising which category you’re facing is most of the work.

The question format is straightforward: given A:B, find ? such that C:? follows the same relationship. The trap is trying random arithmetic. The five-category method replaces guesswork with a 30-second checklist.

What Number Analogy Questions Look Like

A typical question reads: “7 : 56 :: 9 : ?” with four options. Your job is to find the rule in 7:56, then apply it to 9.

The rule here is n : n(n+1). Verify: 7 × (7+1) = 7 × 8 = 56. Apply: 9 × (9+1) = 9 × 10 = 90. Answer: 90.

What separates fast solvers from slow ones is not arithmetic speed but pattern recognition. The same skill applies to blood relations in logical reasoning where you build a relationship tree before answering any single question. In both cases, naming the rule first is the shortcut.

The Five Pattern Categories

Category	Rule Form	Signal to Look For
1. Arithmetic shift	n : (n + k)	One number is obviously larger by a fixed amount
2. Two-step linear	(an + b) : n	Factoring reveals a linear relationship
3. Power family	n : n², n : n³, n : (n+1)²	One number is close to a perfect square or cube
4. Consecutive-product	n(n+1) : (n+1)(n+2)	Both numbers factor into products of adjacent integers
5. Digit-property	digit sum, digit product	Neither standard arithmetic nor powers explain the pair

Each category has a 6-second test. Run them in order. Stop at the first one that fits.

Category 1: Arithmetic Shift

Both numbers in the pair differ by a constant k. Compute B - A. Then check whether D - C = k.

Example from Q5 below: 149 and 238 differ by 89. Apply to 159: 159 + 89 = 248.

Category 2: Two-Step Linear

The rule takes the form (an + b) : n or similar. Factoring the first number of each pair against the second reveals the multiplier and offset.

Example from Q3 below: the pair 14:9 fits (2n - 4) : n. Verify: 2(9) - 4 = 14. Apply: if 2n - 4 = 26, then n = 15.

Category 3: Power Family

One number in the pair is the square, cube, or offset power of the other. Write both numbers in exponential notation before checking.

Examples: n : (n+1)² gives 5:36 (since 6² = 36). The form (n² + 1) : n gives 26:5 (since 5² + 1 = 26).

Category 4: Consecutive-Product

Both numbers factor into products of two consecutive integers: n × (n+1). The pair advances the shared factor by one each step.

Example: 42 = 6 × 7, 56 = 7 × 8, 72 = 8 × 9. Missing: 9 × 10 = 90. Verify the shared factor carries forward correctly.

A more complex variant is the cubic-offset pattern n³ + n, which is n(n² + 1). Check for this if standard consecutive products don’t fit.

Category 5: Digit-Property

Neither arithmetic nor powers fit? Count or sum the digits. Common sub-variants:

• Digit sum of first = digit sum of second + constant
• Digit product relationship
• Reversal or rotation of digits

These are the hardest to spot under time pressure. Practise recognising when the numbers look structurally similar but arithmetically unrelated.

For a large bank of practice questions across all five categories, IndiaBix’s number analogy section provides 50+ questions with answers. Freshersworld’s aptitude guide covers additional campus-placement variants.

Nine Worked Examples by Category

The nine examples below are drawn from common placement question banks. Every answer is re-derived from first principles.

Category 1: Arithmetic Shift

• Q5. 149 : 238 :: 159 : ?
• Rule check: 238 - 149 = 89. Arithmetic shift of +89.
• Apply: 159 + 89 = 248.
• Answer: 248

Category 2: Two-Step Linear

• Q3. 14 : 9 :: 26 : ?
• Rule check: Try (2n - 4) : n. Verify: 2(9) - 4 = 18 - 4 = 14. Fits.
• Apply: Set 2n - 4 = 26. So 2n = 30, n = 15.
• Answer: 15

Category 3: Power Family (Type A — inverse square plus one)

• Q1. 26 : 5 :: 65 : ?
• Rule check: The first number looks like a square plus one. Try (n² + 1) : n. Verify: 5² + 1 = 25 + 1 = 26. Fits.
• Apply: n² + 1 = 65, so n² = 64, n = 8.
• Answer: 8

Category 3: Power Family (Type B — next-integer square)

• Q8. 5 : 36 :: 6 : ?
• Rule check: 36 = 6² = (5+1)². Try n : (n+1)². Verify: (5+1)² = 36. Fits.
• Apply: (6+1)² = 7² = 49.
• Answer: 49

Category 4: Consecutive-Product (Type A — single step)

• Q2. 7 : 56 :: 9 : ?
• Rule check: 56 = 7 × 8 = 7 × (7+1). Try n : n(n+1). Fits.
• Apply: 9 × (9+1) = 9 × 10 = 90.
• Answer: 90

Category 4: Consecutive-Product (Type B — advancing pair, two-term)

• Q7. 42 : 56 :: 72 : ?
• Rule check: 42 = 6 × 7, 56 = 7 × 8, 72 = 8 × 9. Each number is a product of consecutive integers; the shared factor advances by one.
• Apply: Next pair: 9 × 10 = 90.
• Answer: 90

Category 4: Consecutive-Product (Type C — skip-step series)

• Q4. 42 : 56 :: 110 : ?
• Rule check: 42 = 6 × 7, 56 = 7 × 8. Same consecutive-product pattern. Now 110 = 10 × 11.
• Apply: Next: 11 × 12 = 132.
• Answer: 132

Category 4: Cubic offset — n³ + n

• Q6. 68 : 130 :: ? : 350
• Rule check: Try n³ + n. Verify: 4³ + 4 = 64 + 4 = 68. 5³ + 5 = 125 + 5 = 130. 7³ + 7 = 343 + 7 = 350. Series is n = 4, 5, ?, 7.
• Apply: Missing term is n = 6: 6³ + 6 = 216 + 6 = 222.
• Answer: 222

Category 5: Digit-Property

• Q9. 583 : 293 :: 488 : ?
• Rule check: No standard arithmetic or power fits. Check digit sums.
  • 583: 5 + 8 + 3 = 16. 293: 2 + 9 + 3 = 14. Difference: 2.
  • Rule: digit sum of first exceeds digit sum of second by 2.
• Apply: 488: 4 + 8 + 8 = 20. Answer must have digit sum 20 - 2 = 18.
  • Check options: 222 gives 6, 378 gives 3 + 7 + 8 = 18. Fits.
• Answer: 378

The 30-Second Elimination Sequence

This is the exam-day procedure for every number analogy question:

1. Write both numbers in the given pair — do not try to “see” the rule mentally.
2. Test Category 1 (arithmetic shift): compute B - A. Does the same difference apply to C?
3. Test Category 3 (powers) immediately after: are either of the numbers close to a perfect square or cube? Write √n or ∛n and see if it’s an integer.
4. Test Category 4 (consecutive-product): factor each number. Do they share a factor that differs by 1?
5. Test Category 2 (two-step linear): divide A by B or B by A. Does a clean ratio emerge? Is there a leftover offset?
6. Test Category 5 (digit-property): sum the digits of both numbers. Is the difference constant?

• Shortcut: Categories 1 and 3 resolve the majority of questions in campus placement tests. If neither gives a clean answer within 10 seconds, continue to step 4.

Where These Questions Appear in Placement Tests

Number analogy questions appear in the logical reasoning or quantitative sections of most campus placement tests: AMCAT, Cocubes, eLitmus, and company-specific tests. Frequency varies by company.

For tests known for heavier quantitative sections, such as those used in the Cadence campus placement process or in D.E. Shaw interview questions rounds, number analogy questions are part of a broader aptitude section that also includes data interpretation and logical sequences.

For general campus placements at service-tier companies, expect 2 to 5 number analogy questions within a 30 to 40 question logical reasoning block. The five-category method described above is directly applicable to all of them.

---

The five-category method trains one precise habit: name the rule before calculating. That same precision, stating the pattern you want to find before applying it, is what makes prompting language models effective for data extraction and reasoning tasks. If you want to test that transfer in a hands-on LLM environment, TinkerLLM is a playground for engineering students at ₹299.