Number & Letter Analogy

Analogy means SIMILARITY or correspondence. In an analogy question, the relationship between the first pair must be applied to the second pair. Format: A : B :: C : ? You must find how B relates to A, then apply the SAME logic to C.

Key rule: Always check the relationship FIRST (square, cube, multiply, add, prime, etc.), then confirm direction. Memory aid: 'Same Maths Both Sides.' If 2:8 means 2-cubed=8, then 3:? must be 3-cubed=27.

Common number relations: square (4:16), cube (3:27), double (5:10), +consecutive, multiply, prime numbers, and digit-sum. Always test the simplest operation first before trying complex ones.

If you can convert any English letter into a number in under a second, every letter-analogy question in the RPF paper becomes pure arithmetic. The whole topic rests on one trick most aspirants underuse: the alphabet has a predictable scaffold, and once you build it in your head, you stop counting letters one-by-one.

Definition: A letter analogy is a reasoning question of the form "A is to B as C is to ?", where the relationship between A and B must be re-applied between C and the answer. The relationship is almost always an arithmetic gap, a positional mirror, or a skip pattern.

Definition: Forward position of a letter is its place from A=1 to Z=26. Reverse position is its place counting backward from Z=1 to A=26.

The EJOTY Scaffold

You should never count "A, B, C, D, E… that's 5" in an exam. Instead, memorise five anchor points spaced exactly five letters apart:

E = 5, J = 10, O = 15, T = 20, Y = 25.

These five letters spell EJOTY. From any anchor, you walk only a step or two left or right to fix any letter. For example, to find the position of M: closest anchor is O (15), and M is two letters before O, so M = 15 − 2 = 13. To find P: closest anchor is O (15), and P is one letter after O, so P = 16. This is faster than counting from A and never goes wrong by more than two steps.

A useful companion mnemonic for the backward direction is VQLGB: V = 5 from end, Q = 10 from end, L = 15 from end, G = 20 from end, B = 25 from end. If you can recall both EJOTY and VQLGB you can place any letter from either end without arithmetic.

The 27-Rule for Opposites

Here is the cleanest result in this topic, and the one RPF examiners love:

Forward position + Reverse position = 27.

Why 27 and not 26? Because positions are 1-indexed: A=1 from front and 26 from back, and 1 + 26 = 27. Use this rule both ways. If you know D is the 4th letter, then its mirror is 27 − 4 = 23 = W. So D ↔ W is an opposite pair. Run the same arithmetic and you uncover the famous pairs:

A↔Z, B↔Y, C↔X, D↔W, E↔V, F↔U, G↔T, H↔S, I↔R, J↔Q, K↔P, L↔O, M↔N.

Notice how the two pillars meet at M and N in the middle — those are the only two letters whose mirror is their immediate neighbour.

Why it matters: A huge proportion of RPF letter-analogy questions are not about gaps but about mirror image pairs. If the question asks "AZ : BY :: CX : ?", you must instantly see that each pair sums to 27, and the answer is DW. Without the 27-rule you would need to count from both ends, wasting precious seconds.

The Four Patterns You Will Actually See

In the RPF and other railway exams, almost every letter analogy belongs to one of four families:

Pattern 1 — Equal gaps (arithmetic progression). Example: A : C :: E : ? Each pair has a gap of +2. Answer: G. Or B : F :: D : ?. Gap +4. Answer: H. To solve, compute the gap once, apply it to the new letter.

Pattern 2 — Opposite letters (the 27 rule). Example: A : Z :: B : ?. Mirror of B is 27 − 2 = 25 = Y. Answer: Y. Or sometimes the analogy puts the two halves on opposite sides — D : W :: G : ?. Mirror of G = 27 − 7 = 20 = T. Answer: T.

Pattern 3 — Skip letters. Example: A : C :: C : E (skip one letter). Or A : D :: D : G (skip two letters). The skip is the same on both sides of the analogy.

Pattern 4 — Reverse order / interleaved order. Example: AB : BA :: CD : ?. Answer: DC. Sometimes the question gives you two pairs whose internal order has been flipped — your job is to apply the same flip to the new pair.

Real-world example: In the 2022 RPF Constable paper, a question read "DOG : WLT :: CAT : ?". Each letter of "DOG" is mirrored using the 27 rule: D→W (27−4=23), O→L (27−15=12), G→T (27−7=20). So "CAT" maps to: C→X (27−3=24), A→Z (27−1=26), T→G (27−20=7). Answer: XZG. A student who applies the 27 rule reflexively answers in 8 seconds; a student counting letters takes a minute.

Common misconception: Many students think "the opposite of D is V because they look symmetric." Wrong — that is a visual guess, not arithmetic. Always use 27 − position. Mirror of D is W, not V (V is the mirror of E).

Question: AZ : GT :: BY : ?

Solution:
Step 1: Confirm the relationship. A and Z are opposite pair (1+26=27). G and T are opposite pair (7+20=27). So the rule is "pair sums to 27 — they are mirror letters."
Step 2: Apply the same rule to BY. B = 2, Y = 25. Yes, they are also a mirror pair (2+25=27). So the analogy is consistent — but it asks what comes after BY, suggesting an additional shift.
Step 3: Look for a secondary pattern. From AZ to GT, the front letter shifted A → G (+6), and the back letter shifted Z → T (−6). So the front advances by 6 and the back retreats by 6 (which preserves the mirror property).
Step 4: Apply the same +6 / −6 shift to BY. B + 6 = H. Y − 6 = S.
Conclusion: Answer = HS.

Building Speed in Practice

Spend ten minutes a day building a reflex. Write the alphabet vertically with numbers 1–26 beside each letter, then again with 26–1 beside each letter, then practise the 27-pair drill: see a letter, instantly call out its mirror. Within a week the response becomes automatic and you save 30–40 seconds per analogy question. In an exam where every second counts and there are 35 reasoning questions to clear, this single skill can lift your score by 4–5 marks.

Number analogies look intimidating only until you find the hidden rule connecting the first pair — then the second answer drops out in one step. The trick is not memorising every possible formula; the trick is having a small mental checklist that you run through quickly on each first pair. This lesson works through the classic RPF Constable / SSC examples to build that checklist.

Definition: Number analogy — a reasoning question of the form A : B :: C : ? where you must discover the rule that turns A into B, then apply the same rule to C to get the missing value.

The basic mental checklist

When you see a pair, run through these candidates in order. Stop the moment one fits the entire first pair, not just looks close:

1. Addition / subtraction: B = A + k or A − k.
2. Multiplication / division: B = A × k.
3. Square / cube: B = A² or A³ (or A² ± small constant).
4. Square / cube ± 1, ± 2: e.g., n² + 1, n² − 1, n³ + 1.
5. n(n+1) or n(n−1) — product of two consecutive integers.
6. Reverse digits, sum of digits, prime factor count.
7. Place in a sequence (n-th prime, n-th Fibonacci).

Most exam-level number analogies fall in steps 1–5. Spotting whether the target value is close to a perfect square or factorisable as two consecutive numbers is the single most powerful habit you can build.

Worked example 1 — n² + 1

Q: 7 : 50 :: 9 : ?
Step 1: Find the relation between 7 and 50.

• 50 is just 1 more than 49 = 7².
• Therefore the rule is B = A² + 1.
  Step 2: Apply to 9.
• 9² = 81, then 81 + 1 = 82.
  Conclusion: Answer = 82.

How do you guess "square plus one" so quickly? Because 50 is suspiciously close to a famous perfect square (49). When the second number is close to A² — within ±3 or so — always test A² ± k first.

Worked example 2 — n(n+1)

Q: 6 : 42 :: 8 : ?
Step 1: Find the relation between 6 and 42.

• 42 = 6 × 7. So the rule is B = A × (A + 1) = n(n+1).
  Step 2: Apply to 8.
• 8 × 9 = 72.
  Conclusion: Answer = 72.

You recognise this pattern by factorising the second number: 42 = 6 × 7 = 2 × 3 × 7. The factors 6 and 7 — two consecutive integers — are a flashing signal. Whenever the second value factors neatly into two consecutive numbers and one of them equals A, the rule is almost certainly n(n+1) or n(n−1).

Practise spotting the pattern by sight

The most useful skill is recognising "neighbours of squares" instantly. Here is a short table you should drill until it feels automatic:

Notice how 42 appears twice — as 6 × 7 and as 7 × 6. Whenever an analogy uses such overlapping values, examiners try to confuse you between the n(n+1) and n(n−1) rules. The fix: verify on the first pair carefully and then apply.

More worked drills

Question: 5 : 26 :: 8 : ?
Solution:
Step 1: 26 = 25 + 1 = 5² + 1.
Step 2: Apply to 8: 8² + 1 = 64 + 1 = 65.
Conclusion: 65.

Question: 4 : 12 :: 7 : ?
Solution:
Step 1: 12 = 4 × 3 = n(n − 1).
Step 2: Apply to 7: 7 × 6 = 42.
Conclusion: 42.

Question: 3 : 27 :: 5 : ?
Solution:
Step 1: 27 = 3³. The rule is n³.
Step 2: Apply to 5: 5³ = 125.
Conclusion: 125.

Question: 11 : 121 :: 13 : ?
Solution:
Step 1: 121 = 11². The rule is n².
Step 2: Apply to 13: 13² = 169.
Conclusion: 169.

The "verify the rule on the FIRST pair completely" principle

Suppose you spot that 6 maps to 42 via 6 × 7. You feel confident. But you must check: could the rule also be "n² + 6"? Test: 6² + 6 = 36 + 6 = 42 — yes! Both rules fit the first pair. Which to choose?

In a real exam you almost never see two rules that both fit a textbook pair perfectly and both give clean answers on the second. Try both:

• n(n + 1) → 8 × 9 = 72.
• n² + 6 → 8² + 6 = 70.

You then ask: which option is in the answer choices? The exam-setter knows there is exactly one valid rule per problem, and the option list usually rules out the imposter. If both options happen to appear, prefer the rule that is simpler and more "natural" — typically the multiplicative one (n(n+1)) over a quirky n² + 6. Examiners reward elegance.

Beyond pure numbers — sequence-position rules

Sometimes A and B are not arithmetically related but positionally related:

• A is the n-th prime → B is the (n+1)-th prime. e.g. 7 : 11 :: 13 : 17.
• A is the n-th Fibonacci → B is the (n+1)-th. e.g. 5 : 8 :: 13 : 21.

If no arithmetic rule fits, scan the sequence-position checklist.

Why it matters: In RPF Constable, SSC GD, and similar exams, analogies form a chunk of the reasoning section. Each takes 15–20 seconds when you train the eye to scan for "close to a perfect square" and "factorises as consecutive integers." That speed is the difference between finishing the paper or not.

Real-world example: When you write a competitive exam and notice that 50 is the target — 50 lies in your mental table next to 49 — you instantly suspect n² + 1. This is exactly how strong reasoning-section students think; it is not "talent," it is the table above, drilled until it is reflexive.

Common misconception: "I'll find the rule from the second pair." Wrong. The only defined relation is between A and B; C and the answer must follow the same rule. Always extract the rule from the first pair, then apply.

Another misconception: "If two rules fit the first pair, both answers are valid." Almost never. Try both on the second pair; the correct option matches exactly one answer in the choices, and that's your rule.

Cover the answer, recall, then check. 12 must-know cards for RPF Constable analogy.

Q1. Letter positions to memorise for speed?
A1. EJOTY: E=5, J=10, O=15, T=20, Y=25. Count forward/back from these anchors instead of A=1 each time.

Q2. 6 : 36 :: 9 : ? — what relation, what answer?
A2. Square (6²=36), so 9²=81.

Q3. 3 : 27 :: 5 : ?
A3. Cube (3³=27), so 5³=125.

Q4. What does AZ : BY signal?
A4. Opposite (complement) pair — positions add to 27: A(1)+Z(26), B(2)+Y(25). Reverse-letter relation.

Q5. Reverse position of a letter, quick formula?
A5. 27 − position. G=7 → 27−7 = 20 = T.

Q6. DF : HJ — find the rule.
A6. Add a constant: D→H (+4), F→J (+4). Same gap applied to each letter.

Q7. 12 : 20 :: 30 : ?
A7. n(n+1): 12=3×4, 20=4×5, 30=5×6, next 6×7 = 42.

Q8. 16 : 4 :: 81 : ?
A8. Square-root: √16=4, so √81 = 9.

Q9. How to crack a mixed number–letter analogy?
A9. Convert letters to position numbers, find the arithmetic rule, apply, convert back. B:4 → B=2, 2×2=4; D=4, 4×2=8 = H.

Q10. AC : EG :: IK : ?
A10. +2 within a pair, +4 between pair-starts. IK → MO.

Q11. Biggest MCQ trap in analogy?
A11. A distractor that fits a weaker relation. Pick the MOST specific rule that holds for BOTH given pairs, then apply.

Q12. 7 : 56 :: 9 : ?
A12. n×(n+1): 7×8=56, so 9×10 = 90.

Why it matters

Analogy is the single most predictable scorer in RPF Constable reasoning — expect 3–5 questions across number, letter and mixed analogy in the 35-question General Intelligence section. Each is a 20–25 second mark once you spot the relation, so this topic is pure speed-and-accuracy territory.

The method

An analogy says A is to B as C is to D. Your only job is to find the exact rule linking A→B, then apply the same rule to C.

1. Convert letters to position values (A=1 … Z=26). Anchor on EJOTY (E5, J10, O15, T20, Y25) to count fast.
2. Test relations in this order: square → cube → ×/÷ → +/− constant → n(n+1) → opposite/reverse pair.
3. Apply and reverse-convert if the answer must be a letter.

Common relations

Pair	Rule	Applied
6 : 36	square (n²)	9 → 81
3 : 27	cube (n³)	5 → 125
12 : 20	n(n+1)	30 → 42
AZ : BY	opposite (sum 27)	CX, DW …
DF : HJ	+4 to each letter	LN → PR
16 : 4	square-root	81 → 9

Exam Tricks & Tips

• 🎯 Memorise squares to 30 and cubes to 15 — most number analogies are disguised recall.
• 🎯 For letter pairs, always check the opposite pair (positions add to 27) before assuming a simple gap.
• 🎯 A gap that "doesn't fit" forward often fits backward — count both directions.
• 🎯 In mixed pairs (letter→number), convert first; never guess from shape.
• 🎯 When two rules both fit the first pair, the correct rule is the one that also fits the answer options cleanly.
• ❌ Common mistake: locking onto "+ constant" and missing a multiplicative or n(n+1) pattern that also matches — verify the rule on BOTH sides before committing.

Expected exam pattern

"Select the option related to the third term in the same way as the second is to the first." Choices are single numbers or letter pairs, spaced so only one rule fits. Difficulty is easy-to-moderate; do these first in the section.

Quick recap

Convert to numbers, test square/cube/×/±/n(n+1)/opposite in order, apply to the third term, convert back. EJOTY anchors + squares/cubes to memory = near-free marks.