Number Analogy for SSC MTS — Crack Every Numeric Pair Question

beginner 18 min read

Concept

Number analogy is the Reasoning section's version of a pattern-recognition game. You are given one or two pairs of numbers that share a hidden relationship, and your job is to find the missing number in an incomplete pair by applying the same rule.

Look at it this way: if someone says "6 is related to 18", your brain immediately thinks "multiply by 3". That's exactly what number analogy demands — identify the rule, verify it, apply it. The entire challenge lives in that first step: cracking the rule.

What makes SSC MTS questions interesting is that the rule can operate in three completely different ways:

On the whole number. The number is treated as a single integer. You add, subtract, multiply, divide, raise to a power, or chain two operations. For example, n × 13 − 1 is a whole-number operation.

On individual digits. Each digit of the number shifts independently. 287 → 398 is not a 111-addition — it is every digit going up by 1. The note "operations should be performed on whole numbers" in many questions is actually a clue that the intended rule does NOT split digits. When you don't see that note, digit-level operations become fair game.

On a set. Instead of a pair, you are given a triplet or a set of three numbers inside brackets. The rule connects all three — often a² + b² = c, or a × b − c = constant, and so on.

Here is a useful real-world analogy. Think of number analogy like a machine in a factory. You feed 6 into the machine and it spits out 77. You feed 9 and it spits out 116. Your task is to reverse-engineer what the machine is doing so you can predict what comes out when you feed 11. The machine does not change — the rule is fixed.

One more thing worth flagging before you dive into technique: SSC MTS questions are not designed to require heavy arithmetic. If you are spending more than 30 seconds multiplying and getting nowhere, you are probably chasing the wrong rule. Step back, try a simpler operation, and eliminate options — the correct answer is always in the list, which is your biggest weapon.


Deep Dive

The Three Families of Rules

Every number analogy question in SSC MTS falls into one of three families. Recognising the family in the first 10 seconds saves you the remaining 50.

Family 1 — Single Arithmetic Operation

The relationship is one clean operation: add a constant, subtract a constant, multiply by a constant, or divide by a constant.

35 : 6666 − 35 = 31. So the rule is "add 31". Apply it: 29 + 31 = 60.

These are the easiest. If the difference between the two numbers in a pair is an integer with no obvious pattern beyond being a constant, you are in Family 1. Cross-check with the second pair if one is given.

Family 2 — Chained or Composite Operations

The rule involves two steps, often in the form (n + k) × m or n × m + k or n² + k.

18 : 80 → Try (18 + 2) × 4 = 80. Verify: (23 + 2) × 4 = 100. The rule holds. Apply: (36 + 2) × 4 = 152.

How do you find the two-step rule quickly? Look at the ratio first. 80 / 18 ≈ 4.4 — not a clean ratio, so pure multiplication is out. 80 − 18 = 62 — not a clean constant. That flags a composite rule. Now try: does n × 4 get you close? 18 × 4 = 72, and 80 − 72 = 8. So it is n × 4 + 8. Check: 23 × 4 + 8 = 100. Works. You can arrive at the same rule via (n + 2) × 4 — algebraically equivalent. Either form is fine in the exam hall.

Family 3 — Digit-Level Operations

Here the number is broken into its constituent digits, and each digit undergoes the same transformation.

38 : 493 → 4, 8 → 9 (each digit +1). 64 : 75 confirms it. Apply to 83: 8 → 9, 3 → 4 = 94.

A subtype: the digit sum test. Given a set like (425, 902, 713), check 4+2+5=11, 9+0+2=11, 7+1+3=11. The binding property is digit sum = 11. Scan the options for the one whose digits sum to 11.

Family 4 — Set Rules (Triplets)

When three numbers are given together as a set, the rule usually connects all three via squares, products, or a combination.

(12, 4, 160)12² + 4² = 144 + 16 = 160. Check with (6, 11, 157): 36 + 121 = 157. Rule confirmed: a² + b² = c. Apply to (14, 7, ?): 196 + 49 = 245.

Step-by-Step Rule Detection

Here is the exact sequence to run in your head:

  1. Compute difference and ratio. second − first and second ÷ first. If either is clean (whole number or simple fraction), you are likely in Family 1 or a simple multiply.

  2. Check if ratio is approximate. If second ÷ first ≈ 2, 3, 4 with a small offset, try n × k ± c for small values of c.

  3. Check squares. Is second close to first²? Try first² + c or first² − c.

  4. Check digit structure. If Family 1–3 fail and the numbers are 2–3 digits, shift gears: inspect each digit individually.

  5. Use options to reverse-verify. Once you have a candidate answer, verify that the same rule produces the given pairs cleanly.

The "NOTE" Instruction

Several recent PYQs include the instruction: "Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits." This is not decoration — it is the question setter explicitly ruling out Family 3 (digit-level) operations. When you see this note, skip the digit approach entirely and focus on Families 1, 2, and 4.

When the note is absent, digit-based rules are in play. That absence is itself a signal.


Memory Tricks & Shortcuts

patternD-R-S: Difference, Ratio, Square

Always check these three in order before doing anything else. Difference = second − first (Family 1). Ratio = second ÷ first (simple multiply). Square = is second close to first²? For Family 1 questions this takes 5 seconds. Standard trial-and-error: 40–60 seconds. D-R-S: under 10 seconds. Example: 35:66 → difference = 31, ratio ≈ 1.88 (not clean), square ≈ 1225 (too big). Difference wins. Done.

patternDigit Sum Scan

For set-based questions (425, 902, 713 style), add the digits of each member of the given set before reading the options. If all digit sums match, your only job is to scan options for the same digit sum — 3 additions of 3 digits each. This collapses a 45-second elimination exercise into a 10-second scan. Example: all three sum to 11. Options: 319 → 13, 555 → 15, 218 → 11, 624 → 12. Answer is 218. Four additions, done.

estimationBracket the Multiplier

When the rule feels like n × k + c, estimate k from the ratio (second ÷ first) and round to the nearest integer. Then solve for c: c = second − (first × k). Check with the second pair. This is a 2-step algebraic shortcut versus 4–5 steps of trial-and-error. Example: 18:80 → ratio ≈ 4.4, so k = 4. c = 80 − 72 = 8. Verify: 23 × 4 + 8 = 100. Total: 3 arithmetic steps vs. testing 5–6 candidate rules blindly.

patternEach Digit +1 Visual Check

For 2-digit or 3-digit pairs where the second number is slightly larger, align the digits vertically and subtract column by column. If every column gives the same delta, you have a digit-shift rule. 287 → 398: 3−2=1, 9−8=1, 8−7=1. Uniform delta = 1. This visual subtraction takes 8 seconds. Writing out individual digit operations: 20–25 seconds.

patternSum-of-Squares Trigger

When a triplet is given and the third number is roughly equal to first² + second², go straight to that formula without testing addition or multiplication first. Trigger: third number is noticeably larger than first + second or first × second for small first/second values. Example: (12, 4, 160)12 + 4 = 16 (too small), 12 × 4 = 48 (too small), but 144 + 16 = 160 (exact). Once you spot the trigger, the verification is one multiplication each. Standard method of testing all operations: 5–6 trials at ~10 seconds each = 50–60 seconds. Trigger method: 15 seconds.


Fast-Solving Framework

In the exam hall, run this decision tree in order. Do not skip steps.

Step 1 — Read the note. Does the question say "operations on whole numbers only"? If yes, digit-level rules are off the table. If no note, all rules are available.

Step 2 — Count the numbers. Two numbers in a pair? Go to Step 3. Three numbers in a set (triplet)? Jump to Step 5.

Step 3 — D-R-S check. Compute difference, ratio, and compare to square. If any is clean, you likely have your rule.

Step 4 — Composite check. If D-R-S gives nothing clean, estimate the multiplier and solve for the offset. Verify with the second pair before applying.

Step 5 (triplets) — Test sum-of-squares first. If that fails, try product ± constant. Digit sum is the fallback for set questions without the "whole number" note.

Always verify. Apply your rule to every given pair before committing to an answer. One failed verification means you have the wrong rule — do not guess, go back to Step 3.

If you are 60 seconds in and have no clean rule, use the options. Plug each option into the expected position and reverse-engineer what rule it implies. Eliminate the ones that don't replicate the given pairs.


Solved PYQs

Why this question: This is a classic composite-operation question from 2024, explicitly guarded by the "whole numbers only" note. It tests whether you chase digit-based shortcuts or correctly identify a two-step rule.

Previous Year Questionपिछले वर्ष का प्रश्न2024
6 is related to 77 following a certain logic. Following the same logic, 9 is related to 116. To which of the following is 11 related, following the same logic? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)
  1. 143
  2. 141
  3. 142
  4. 132
Solutionसमाधान
The pattern is: n×13 − 1: 6×13−1=77, 9×13−1=116, so 11×13−1=143−1=142.

Solving path: Difference: 77 − 6 = 71. Not a round number. Ratio: 77 ÷ 6 ≈ 12.8. Close to 13. Try n × 13: 6 × 13 = 78. Offset: 77 − 78 = −1, so rule is n × 13 − 1. Verify: 9 × 13 − 1 = 117 − 1 = 116. Confirmed. Apply: 11 × 13 − 1 = 143 − 1 = 142. Answer: 142.


Why this question: A digit-shift question without the "whole number" note — the absence of that note is itself a signal that digit-level operations are intended.

Previous Year Questionपिछले वर्ष का प्रश्न2023
287 is related to 398 following a certain logic. Following the same logic, 378 is related to 489. To which of the following is 852 related to, following the same logic?
  1. 543
  2. 643
  3. 346
  4. 963
Solutionसमाधान
Each digit of the number increases by 1: 2→3, 8→9, 7→8 gives 398; similarly 8→9, 5→6, 2→3 gives 963.

Solving path: Align digits: 287 → 398. Column deltas: 3−2=1, 9−8=1, 8−7=1. Uniform +1 per digit. Apply to 852: 8+1=9, 5+1=6, 2+1=3963. Answer: 963.


Why this question: Tests whether you correctly handle digit-based operations on a 2-digit number, and whether you apply the transformation in the right order.

Previous Year Questionपिछले वर्ष का प्रश्न2023
38 is related to 49 following a certain logic. Following the same logic, 64 is related to 75. To which of the following is 83 related to, following the same logic?
  1. 93
  2. 92
  3. 94
  4. 95
Solutionसमाधान
Each digit of the number increases by 1: 3→4, 8→9 gives 49; similarly 8→9, 3→4 gives 94.

Solving path: 38 → 49. Digits: 3→4, 8→9. Each digit +1. Verify: 64 → 75. 6→7, 4→5. Confirmed. Apply to 83: 8→9, 3→494. Answer: 94.


Why this question: Digit-sum test on a set. This is a standalone question type — no pairs, just identify the common property of the given numbers.

Previous Year Questionपिछले वर्ष का प्रश्न2020
Select the number from the options that is similar to the numbers in the given set. (425, 902, 713)
  1. 319
  2. 555
  3. 218
  4. 624
Solutionसमाधान
Each number in the set has digits that sum to 11: 4+2+5=11, 9+0+2=11, 7+1+3=11. Similarly, 2+1+8=11, so 218 matches the pattern.

Solving path: 4+2+5=11, 9+0+2=11, 7+1+3=11. Property: digit sum = 11. Scan options: 3+1+9=13, 5+5+5=15, 2+1+8=11, 6+2+4=12. Only 218 gives 11. Answer: 218.


Why this question: The 2024 triplet-set question with sum-of-squares rule. A harder variant that many candidates miss because they do not test squares early enough.

Previous Year Questionपिछले वर्ष का प्रश्न2024
Select the set in which the numbers are related in the same way as are the numbers of the following sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits.) (12, 4, 160) (6, 11, 157)
  1. (21, 4, 168)
  2. (9, 15, 90)
  3. (14, 7, 245)
  4. (6, 15, 90)
Solutionसमाधान
The pattern is: first² + second² = third. For (12,4,160): 144+16=160 ✓. For (6,11,157): 36+121=157 ✓. For (14,7,245): 196+49=245 ✓.

Solving path: Given sets (12, 4, 160) and (6, 11, 157). Test a + b = c: 16 ≠ 160. Test a × b = c: 48 ≠ 160. Test a² + b²: 144 + 16 = 160. Verify: 36 + 121 = 157. Rule confirmed. Check options: (14, 7, 245)196 + 49 = 245. Answer: (14, 7, 245).


Why this question: A clean composite-operation question from 2024 that rewards the "bracket the multiplier" trick.

Previous Year Questionपिछले वर्ष का प्रश्न2024
18 is related to 80 following a certain logic. Following the same logic, 23 is related to 100. To which of the following is 36 related, following the same logic? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits.)
  1. 152
  2. 138
  3. 144
  4. 142
Solutionसमाधान
The pattern is: (n + 2) × 4. For 18: (18+2)×4 = 80 ✓. For 23: (23+2)×4 = 100 ✓. For 36: (36+2)×4 = 152.

Solving path: Ratio: 80 ÷ 18 ≈ 4.4. Round to k=4. Offset: 80 − 72 = 8. Rule: n × 4 + 8. Equivalently, (n + 2) × 4. Verify: 23 × 4 + 8 = 100. Confirmed. Apply: 36 × 4 + 8 = 144 + 8 = 152. Answer: 152.


Why this question: Extended analogy with three pairs, testing whether you maintain the same rule across all three applications.

Previous Year Questionपिछले वर्ष का प्रश्न2021
Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 16 : 38 :: 26 : 58 :: 37 : ?
  1. 80
  2. 76
  3. 78
  4. 74
Solutionसमाधान
The pattern is: multiply by 2 and add 6. 16×2+6=38, 26×2+6=58, so 37×2+6=80. Option (d) is correct.

Solving path: 16 : 38. Ratio: 38 ÷ 16 = 2.375. Not clean. Try n × 2 + c: 32 + c = 38, so c = 6. Rule: n × 2 + 6. Verify with 26 : 58: 52 + 6 = 58. Confirmed. Apply: 37 × 2 + 6 = 74 + 6 = 80. Answer: 80.


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