Analogy & Classification

In RPF Sub-Inspector reasoning, number analogy questions look harmless — two pairs of numbers, find the rule. But the same examiner who built the question is also counting on you to waste a minute trying the wrong operation. A trained candidate solves these in 12 seconds; an untrained one stares for a full minute. The difference is a system.

Definition: A number analogy is a reasoning question where two numbers in the first pair are linked by some mathematical operation (square, cube, addition, multiplication, sum of digits, etc.), and you must identify the same hidden link to complete the second pair. The standard form is "A : B :: C : ?".

Definition: A relation is any rule that maps the first number of a pair to the second. The skill is matching the relation found in the given pair to the missing number in the asked pair.

The five operations that cover 90% of questions

Almost every number analogy in RPF SI / SSC / RRB falls into one of five categories. Learn this list and you will recognise patterns instantly.

1. Square — second number is the square of the first. Example: 4 : 16, 9 : 81.
2. Cube — second number is the cube of the first. Example: 5 : 125, 6 : 216.
3. Add a constant — second is first plus a fixed number. Example: 7 : 11 (+4), 12 : 16 (+4).
4. Difference / Subtract — second is first minus a constant or vice versa. Example: 20 : 13 (−7).
5. Multiply / Divide — second is first times (or divided by) a constant. Example: 6 : 36 (×6), 8 : 48 (×6).

A sixth family is the mixed operation, where you do something like n × (n+1) — for instance 5 : 30 means 5 × 6, and 7 : 56 means 7 × 8.

The SCADM order — your testing checklist

When you see a number analogy, run through the operations in this exact order: Square, Cube, Add, Difference, Multiply. Why this order? Because squares and cubes are the most common in objective tests, and they fail visibly in under two seconds — if 4 : 17 isn't 4², stop and move on. Addition and subtraction are next-easiest, multiplication tests last because it requires actual computation.

The cardinal rule is this: whatever rule fits the first pair must be tested on the second pair using the same operation. If 6 : 42 works as 6 × 7, then check whether 8 : ? could be 8 × 9 = 72. If the second pair refuses the rule, the rule is wrong — switch operations, not numbers.

The trickier patterns you must recognise

Beyond SCADM, three patterns trip up candidates regularly:

Sum / product of digits. The second number may equal the sum or product of the digits of the first. Example: 23 : 5 (because 2 + 3 = 5), or 14 : 4 (because 1 × 4 = 4).

Reverse digits. The second number is the digit reversal of the first. Example: 12 : 21, 34 : 43, 56 : 65.

Grouped numbers. When the question gives a triple like (3, 9, 27), look for geometric progression (each term × 3) or arithmetic progression. Triples are common in IBPS but appear in RPF / RRB level too.

Worked example

Question: 8 : 64 :: 12 : ?
Options: (a) 96 (b) 144 (c) 132 (d) 156

Solution:
Step 1: Apply SCADM. Try square: 8² = 64. Match! The rule is square.
Step 2: Apply the same rule to the second pair: 12² = 144.
Step 3: Match against options.
Conclusion: Answer is (b) 144.

Notice how fast that was — under five seconds once you trusted the rule.

A trickier one:

Question: 15 : 6 :: 24 : ?
Options: (a) 6 (b) 8 (c) 10 (d) 12

Solution:
Step 1: Try square (225 ≠ 6), cube (no), add a constant (15 + ? = 6 — no, but 15 − 9 = 6 — try the same subtraction). 24 − 9 = 15, not in options. Switch hypothesis.
Step 2: Try sum-of-digits: 1 + 5 = 6. Match!
Step 3: Apply same rule to 24: 2 + 4 = 6.
Conclusion: Answer is (a) 6.

Here SCADM failed on the first sweep — the secondary patterns (sum of digits) saved you. Always have those two backup checks ready.

Why it matters

In an RPF SI prelims paper of about 35 reasoning questions, 4–6 are pure analogy types (number + alphabet + meaning-based). At 12 seconds each, you bank a minute and a half of bonus time that you can spend on a harder data interpretation question. Examiners reward speed accumulation: the candidate who clears RPF SI is rarely the smartest in the room — they are the one who never gets stuck on a 30-second problem.

Real-world example

When a railway booking clerk verifies a PNR or a coach number against a manifest, she is doing exactly this — matching one pattern (the PNR digit sequence) to another (the seat allocation block). The mental skill of "spot the relation, apply it twice, verify" transfers directly. The RPF reasoning paper is testing on-the-job pattern recognition that an officer needs every day.

Common misconception

Many candidates assume that if the first relation they spot works for the given pair, it must be correct. Wrong. A pair like 4 : 16 could mean square (4²) OR multiply by 4 (4 × 4) OR add 12 — three different relations, all producing 16. You only know which one is intended by checking the same rule against the second pair (C : ?). If C = 5 and an option is 25, the rule is square. If C = 5 and an option is 20, the rule is "multiply by 4". Always test on both pairs.

A second mistake is to look at the options first, work backwards, and "engineer" a rule. This wastes time and fails when distractors are well-designed. Stick to: spot the rule on the given pair, then apply it forward.

:::compare

Pattern type	Example pair	How to test (≤ 2 sec)
Square	7 : 49	Is second = first × first?
Cube	4 : 64	Is second = first × first × first?
Add constant	9 : 16	Compute difference, check both pairs
Subtract / diff	30 : 23	Is first − second the same in both pairs?
Multiply / divide	6 : 30	Is second / first the same integer in both pairs?
n × (n+1)	5 : 30	Does second equal first × (first + 1)?
Sum of digits	23 : 5	Add the digits of the first
Reverse digits	12 : 21	Reverse the digit order
:::

:::keypoints

• Number analogies test relations, not arithmetic — speed comes from recognising the family.
• Run the SCADM checklist: Square, Cube, Add, Difference, Multiply.
• If SCADM fails, switch to sum-of-digits, product-of-digits, or reverse-digit checks.
• Apply the SAME operation to both pairs to confirm — never assume.
• Eliminate options by quick mental arithmetic; do not guess.
• Watch for grouped triples — they often hide a GP or AP.
• An "odd one out" framing is asking the same question in disguise; same techniques apply.
• A 12-second target per analogy is realistic with practice.
  :::

:::memory
SCADM — Square, Cube, Add, Difference, Multiply. Say "SCADM" out loud as you scan the pair and you cover the high-frequency patterns in under three seconds.
:::

:::recap

• Number analogies follow a small set of hidden mathematical rules.
• SCADM is your first-pass test; backup with digit-based patterns.
• Always verify the same rule on both pairs before locking an answer.
• Speed on analogies frees up time for the harder reasoning questions.
  :::

Convert letters to position numbers (A=1...Z=26). MEMORY AID 'EJOTY': E=5, J=10, O=15, T=20, Y=25 — count forward/back from these milestones to fix any letter fast. Reverse positions: A=26, Z=1 (use 27-position). Common patterns: +1 skip (AB:CD), opposite letters (A-Z, B-Y sum=27 rule), gap series (A_C, skip one). For pairs like AZ:BY, note A+Z and B+Y both pair to position-sum 27. For DH:EI type, each letter +1. Always write the position numbers below letters to expose the gap. Backward alphabet (Z,Y,X...) is favourite in SI papers — practise reciting reverse alphabet.

Q: 7 : 56 :: 9 : ? Solve: 7x8=56, so relation is nx(n+1). Apply: 9x10=90. Answer 90. Q: BD : FH :: JL : ? Positions B=2,D=4,F=6,H=8 — each pair is consecutive even letters increasing by 4 (B->F is +4, D->H is +4). Next: J=10,L=12, add 4 -> N=14, P=16, so NP. Q: 25:36 :: 49:? These are squares 5^2,6^2 then 7^2, so next 8^2=64. SHORTCUT: when both numbers are perfect squares of consecutive integers, the answer is the next perfect square. Verify by checking the difference pattern (11,13,... odd-number gaps confirm squares).

Word analogy tests logical bonds between words. Master these standard types: (1) Worker:Tool — Carpenter:Saw; (2) Worker:Product — Author:Book; (3) Cause:Effect — Spark:Fire; (4) Synonym — Big:Large; (5) Antonym — Hot:Cold; (6) Part:Whole — Petal:Flower; (7) Animal:Young — Cow:Calf; (8) Animal:Home — Bee:Hive; (9) Instrument:Measurement — Thermometer:Temperature; (10) Country:Currency — Japan:Yen. TECHNIQUE: form a clear SENTENCE linking the first pair ('A carpenter uses a saw'), then plug the options into the same sentence — only one fits exactly. Keep word order identical; if A:B is tool:worker, the answer must also be tool:worker, not reversed.

Analogy questions are one of the highest-scoring sections in the RPF Sub-Inspector paper — but they punish hesitation. The fastest reliable method is also the simplest: build a one-line sentence between the two given words, then drop the options into the same sentence and see which one fits.

Definition: An analogy is a question that presents a pair of related words (or numbers/figures) and asks you to find another pair with the same relationship. The relationship — not the topic — is what matters.

Definition: The sentence-bridge method is the technique of writing one short sentence in plain language that connects the first pair, and then substituting the options into the same sentence to test the relationship.

How the bridge sentence works

The whole trick is to translate the relationship into one ordinary sentence. For Doctor : Hospital, the natural sentence is:

"A doctor works in a hospital."

Now look at the question pair, say Teacher : ? . Plug the options into the same template:

"A teacher works in a school." ✓
"A teacher works in a book." ✗
"A teacher works in a chalk." ✗

The answer is School, because it is the only word that fits the exact relationship "X works in Y." Notice how you did not need to think about what "teacher" means in general — you only needed to fit the bridge sentence.

Make the bridge specific to break ties

What if two options seem to fit?

Suppose the question is Cow : Milk, and you build the sentence "A cow gives X." That is too vague — many animals give many things. So both Buffalo : Milk and Hen : Egg might look acceptable. Sharpen the bridge:

"A cow gives milk as its primary product."

Now Hen : Milk is clearly wrong, and Goat : Milk or Buffalo : Milk become viable parallel cases.

When the trap is even tighter, add a qualifier like "primarily," "is made of," "cures," "is the place where," "is the young of," "is the sound of." Each qualifier cuts down the field. The more precise your bridge, the fewer candidate answers survive.

Keep the direction fixed

This is the rule examiners exploit most often. Read carefully whether the relation goes from object → place or place → object, from cause → effect or effect → cause, from whole → part or part → whole. Your answer must preserve that direction.

For instance, Pen : Ink means "Pen contains/uses ink" — object first, then what is inside. So the parallel must be Lamp : Oil, not Oil : Lamp. If the question were Ink : Pen, the direction flips, and the parallel becomes Oil : Lamp.

A handy phrasing: "the order of words in the answer must match the order of words in the question." If you find yourself swapping them mentally, stop — your bridge is reversed.

Watch out for the "topically related" trap

For Pen : Write, the bridge is "used to." A pen is used to write. So the parallel for Knife : ? must be the verb that knife is used to do:

"A knife is used to cut." ✓

But the trap option is Knife : Sharp — because pens and knives are both associated with sharpness, and "sharp" is the kind of word your brain pattern-matches first. Sharp is an attribute of a knife, not what a knife is used to do, so the relationship is broken. Eliminate options that reverse or change the relationship, even if they look topically related.

This trap appears in every shift of the RPF SI exam. Train yourself to ask: "Does this option preserve the exact relation in my bridge sentence — or has the relation silently changed from function to attribute / from part to kind / from cause to consequence?"

Why it matters

Analogy is a high-frequency, low-time-cost topic in the RPF Sub-Inspector General Intelligence and Reasoning section. The paper typically asks 4–6 analogy questions, and the cut-off is decided on speed. A candidate using the sentence-bridge method usually finishes each analogy in 8–10 seconds; one who eliminates by gut takes 20–30 seconds and gets a few wrong. Across the section, that is the difference between making the cut and missing it.

Real-world example: When you say in everyday Hindi-English that "doctor hospital me kaam karta hai" or "guru gurukul me padhata hai," you are already using a bridge sentence. The technique just formalises what fluent speakers do unconsciously.

Common misconception

A common belief is that analogies need a strong general knowledge base — "I don't know enough vocabulary, so I'll lose these marks." Vocabulary helps, but the method matters more. Even with a moderate vocabulary, a good bridge sentence solves 70–80% of the analogies on offer. Strong vocabulary on professions, animals, geography, instruments and tools accelerates the process, but it is not a substitute for the bridge.

A second misconception: students sometimes try to "feel" the relationship instead of writing it. In high-pressure exam halls, feelings drift. A one-line sentence is concrete; it forces you to fix the exact relationship before scanning the options.

Worked example

Question: Carpenter : Wood :: Mason : ?
Options: (a) Stone (b) Brick (c) Cement (d) Trowel

Solution:
Step 1: Build the bridge sentence. "A carpenter works with wood as the main raw material."
Step 2: Fix direction: profession → main raw material.
Step 3: Test each option in the same template. "A mason works with stone as the main raw material" ✓. "A mason works with brick as the main raw material" ✓. "A mason works with cement as the main raw material" — partly true, but cement is a binder, not the main material. "A mason works with a trowel" — trowel is a tool, not raw material; relationship breaks.
Step 4: Now use the specificity tie-breaker. Mason is most directly associated with brick in Indian context (and in standard RPF answer keys) — brick is the most distinctive raw material of a mason, just as wood is the most distinctive raw material of a carpenter.
Conclusion: The best answer is Brick.

A direction-trap example

Question: Cure : Disease :: Remedy : ?
Options: (a) Problem (b) Doctor (c) Hospital (d) Solution

Solution:
Step 1: Bridge: "A cure removes a disease." Direction: action → thing it removes.
Step 2: For Remedy : ? — "A remedy removes a problem." ✓
Step 3: "Solution" looks tempting but the relationship is different — solution and remedy are synonyms, not action-and-target. So that breaks the bridge.
Conclusion: Problem.

:::compare

Common analogy types	Bridge sentence template	Example
Worker : Workplace	"X works in Y"	Doctor : Hospital, Teacher : School
Tool : Function	"X is used to Y"	Pen : Write, Knife : Cut
Animal : Young	"X is the young one of Y"	Calf : Cow, Cub : Lion
Animal : Sound	"X is the sound made by Y"	Bark : Dog, Roar : Lion
Whole : Part	"Y is a part of X"	Tree : Branch, Car : Wheel
Worker : Raw material	"X works with Y"	Carpenter : Wood, Mason : Brick
Country : Capital	"Y is the capital of X"	India : New Delhi
Cause : Effect	"X leads to Y"	Hard work : Success
:::

:::keypoints

• Build a one-line bridge sentence in plain English between the two given words.
• Substitute each option into the same template; the right answer fits cleanly.
• Add qualifiers like "primarily," "is the place where," "is the sound of" to break ties.
• Preserve the direction: object→place is not the same as place→object.
• Eliminate options that change the kind of relationship (function → attribute, etc.).
• Vocabulary helps speed; method controls accuracy.
• Practise standard categories: profession, animals, geography, tools, raw materials.
  :::

:::memory
BRIDGE-DIRECTION-TIE. Build the BRIDGE; fix the DIRECTION; break TIEs with a sharper qualifier. Three checks, every analogy.
:::

:::recap

• The sentence-bridge method turns a vague analogy into a concrete test.
• Direction of the relationship must match between the given pair and the answer pair.
• Watch for topically related but relationally wrong traps (Knife : Sharp instead of Knife : Cut).
• A good bridge plus a strong vocabulary on standard categories locks down full marks in this section.
  :::

Q: Pride : Lions :: ? : Wolves. Bridge: 'A pride is a group of lions.' A group of wolves is a Pack. Answer: Pack. Q: Optimist : Cheerful :: Pessimist : ? Bridge: an optimist is characterised by being cheerful; a pessimist is characterised by being Gloomy. Answer: Gloomy. Q: Painter : Brush :: Blacksmith : ? Bridge: a painter works with a brush (his tool); a blacksmith works with a Hammer. Answer: Hammer. NOTE the trap option 'Iron' — iron is the material, not the tool, so the direction breaks. Always confirm the option matches the EXACT role (tool, product, place) established by the first pair.

Classification — popularly called "odd one out" — is one of the highest-frequency topics in RPF Sub-Inspector reasoning. Out of roughly 35 reasoning questions, you can expect 3 to 5 from this single chapter. The questions look like a quick visual check, but they reward speed only if you know exactly which rule the setter is applying. The candidate who scans for one specific pattern at a time, instead of looking at the whole set vaguely, finishes the question in 10–15 seconds.

Definition: A classification question presents four or five items and asks you to identify the one that does not share the property common to the others. The "odd" item is the answer; the others are linked by a rule you must first identify.

Why this topic is in the syllabus

Classification tests two narrow but important reasoning skills: pattern recognition under time pressure and the willingness to discard a partial match. In railway operations — RPF SI's professional context — staff must repeatedly identify the exception in a list (the suspicious parcel, the misplaced rake, the unlogged passenger). The exam mirrors that skill on paper.

Why it matters: A 10-second classification answer banks time you will need on the harder syllogisms and seating arrangements later in the paper. Three confident classification answers in 30 seconds is a candidate's quickest 3-mark cushion.

The four families RPF SI loves

Definition: A category family is the underlying type of relationship the setter has built into the four "matching" items. RPF SI questions almost always come from one of four families.

Family 1: Living and non-living groupings

Items that belong to broad biological or material categories: animals, birds, insects, fishes, vegetables, fruits, flowers, metals, gases, instruments, professions, vehicles. The odd one is usually a closely related impostor: in {Tiger, Lion, Leopard, Wolf}, all are big cats except Wolf (a canid). In {Lily, Rose, Marigold, Bamboo}, all are flowers except Bamboo (a grass).

The trap: an impostor that looks like a member of the group. Sparrow, parrot, ostrich, bat — three are birds, but the bat is a mammal. The setter relies on the candidate's casual classification.

Family 2: Mathematical properties

Numbers form most of the high-scoring classification items. Common rules:

• Primes vs composites: {7, 11, 13, 15} — fifteen is composite.
• Perfect squares: {16, 25, 49, 50} — fifty is not.
• Perfect cubes: {8, 27, 64, 100} — hundred is not.
• Multiples: {12, 24, 36, 50} — fifty is not a multiple of 12.
• Even/odd: {3, 5, 7, 8} — eight is even, the rest odd.
• Sum or product of digits: {12, 21, 30, 31} — three of them have digit-sum 3.
• Two-digit reversals: {12, 21, 34, 43} — usually paired.

Quick scan order: check digit sum, then primeness, then squareness, then divisibility by 2/3/5. Whichever check splits the set 3-vs-1 is your rule.

Family 3: Letter and alphabet patterns

Letters use rules that the alphabet itself enforces:

• Vowel position: {AEI, OUE, KMP, IOU} — three have only vowels, KMP has only consonants.
• Equal gap: in {ACE, GIK, MOQ, SUV}, three follow the rule "skip one letter each time" (gap of 2) but SUV has a 2-then-1 gap.
• Consonant clusters: similar to the gap rule but with consonants only.
• Reverse alphabet pairs: items where letters are positioned symmetrically about the centre (A-Z, B-Y, C-X, etc.).
• Mirror in keyboard or alphabet half: occasional, but appears in advanced sets.

Speed habit: write down each item's letter positions (A=1, B=2 ... Z=26) and compute the differences. Three items with the same difference pattern give the rule; the fourth breaks it.

Family 4: Word meaning groups

Words tied by meaning, not letters. Subcategories:

• Metals: {Iron, Copper, Silver, Marble} — marble is a rock.
• Instruments: {Sitar, Violin, Tabla, Flute} — three are strings/wind, Tabla is percussion. (Or sometimes three are Indian, one is foreign.)
• Professions: {Doctor, Lawyer, Architect, Patient} — patient is a recipient, not a profession.
• States/UTs of India: {Goa, Sikkim, Delhi, Mizoram} — Delhi is a Union Territory; rest are states.
• Continents, oceans, languages: similar pattern questions.

The PAGE memory aid

A reliable scan order for any classification item:

• P — Primes / Perfect squares. First number-only check.
• A — Alphabet gap. For letter sets, compute differences.
• G — Group / Category. For words, recall the broad category.
• E — Even/Odd or End-letter. Last quick split for both numbers and words.

Run these checks in order. The moment a check produces a 3-vs-1 split, you have the rule. If none works, look for sum-of-digits or reverse-alphabet positions before guessing.

Why it matters: A defined scan order prevents the worst classification habit — staring at the four items and "feeling" the odd one. Feeling fails on lookalike sets; systematic checking does not.

The double-trap problem

Definition: A double trap is a classification set where two of the items seem to break a rule, forcing you to pick the more fundamental break.

Example: {12, 16, 25, 36}. At first glance, 25 looks odd because it is the only odd number. But 12 is the only one that is not a perfect square. The setter expects the candidate to pick 25; the correct answer is 12, because being a perfect square is the deeper, defining rule shared by 16, 25 and 36.

How to handle double traps: rank the rule strengths. Mathematical category > digit-sum coincidence > even/odd > position curiosities. Pick the option that breaks the most defining rule.

Common misconception: That the first odd-looking option is the answer. RPF SI specifically sets these traps. Read the option matrix calmly and check both possible rules before locking in.

Real-world example: When a railway control room scans a list of cargo entries, several may look suspicious — undocumented weight, mismatched destination, unusual labelling. The senior controller is trained to focus on the most fundamental anomaly. Classification is the paper version of that habit.

Worked example:

Question: Find the odd one out: 144, 169, 196, 200.

Solution:
Step 1: Check even/odd — all are even, so this rule does not split.
Step 2: Check perfect squares — 144 = 12², 169 = 13², 196 = 14². 200 is not a perfect square.
Step 3: Confirm there is no stronger rule the squares break.
Conclusion: The odd one is 200.

Worked example (letters):

Question: Find the odd one out: BD, FH, JL, NQ.

Solution:
Step 1: Compute alphabet positions. B=2, D=4 → gap 2; F=6, H=8 → gap 2; J=10, L=12 → gap 2; N=14, Q=17 → gap 3.
Step 2: The first three pairs have a gap of 2; NQ has a gap of 3.
Conclusion: NQ is the odd one out.

Worked example (words):

Question: Find the odd one out: Mumbai, Chennai, Kolkata, Bengaluru.

Solution:
Step 1: All four are major Indian metros.
Step 2: Mumbai, Chennai and Kolkata are coastal port cities; Bengaluru is inland.
Conclusion: Bengaluru is the odd one out.

Final habits that save marks

1. Never spend more than 20 seconds on a classification item. If the rule does not emerge, mark and move.
2. Verify your candidate by reading the rule the other three share, not by why your pick is odd. If you can express the shared rule cleanly, you are right.
3. Beware brand-new option formats. Recent RPF SI papers have inserted Hindi alphabet sets and Roman numeral sets. The rules above still apply; only the surface changes.

:::compare

Family	Typical setter rule	Quick check
Living / non-living	Same kingdom or class	Look for the impostor (bat in birds)
Mathematical	Primes, squares, cubes, multiples	Run PAGE on digits and divisibility
Letters	Alphabet gap, vowel-consonant	Compute A=1, B=2 differences
Word meaning	Metals, instruments, professions	Name the shared category in one word
:::

:::keypoints

• Classification rewards quick rule identification, not deep analysis.
• Use the PAGE order: Primes/squares → Alphabet gap → Group → Even/odd.
• In double traps, the deeper structural rule wins.
• Verify by stating the rule the other three share.
• 10–15 seconds is the target time per classification question.
• Letter questions are solved by mapping letters to numbers and checking gaps.
• Word questions often hide impostors — bat among birds, Delhi among states.
• Never lock in a guess unless one rule cleanly splits the set 3-vs-1.
  :::

:::memory
"PAGE" — Primes/squares, Alphabet gap, Group/category, Even-odd. Run the scan in this order; the first check that produces a 3-vs-1 split is your rule. For double traps, remember "DEEPER WINS" — pick the option breaking the more fundamental rule.
:::

:::recap

• Classification asks for the one item that does not share the common rule.
• Four families: living/non-living, mathematical, letter-pattern, word-meaning.
• Scan with the PAGE order; the first split rule is usually correct.
• Double traps pick the deeper rule, not the first odd-looking option.
  :::

Number classification questions in RPF Sub-Inspector look harmless — four numbers, pick the odd one out — yet they trap thousands of aspirants every shift because the rule that seems obvious is often the trap. A systematic checklist beats inspiration, every time.

Definition: A number classification (or "odd one out") problem gives four or five numbers and asks which one does not share a hidden property with the rest. The property may be parity, divisibility, primeness, being a perfect power, or a digit-based rule.

The Fixed Six-Step Checklist

When you see four numbers in an RPF SI question, do not stare and "feel" for the answer. Run the same six tests in the same order, every single time. This is muscle memory, not creativity.

Test 1 — Primes vs composites. Are most of them prime (2, 3, 5, 7, 11, 13, 17, 19, 23, 29 …)? If three are prime, the composite is your odd one out. If three are composite, the prime is odd. Memorise primes up to 50 cold — RPF SI almost always picks from that range.

Test 2 — Perfect squares. Are most of them perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225)? If yes, the non-square is your answer.

Test 3 — Perfect cubes. Are most of them perfect cubes (1, 8, 27, 64, 125, 216, 343)? If yes, the non-cube is the answer. Watch out — 64 is both a square (8²) and a cube (4³), so 64 can sit in either group depending on what the other numbers are.

Test 4 — Parity (even vs odd). Are all of them even except one, or all odd except one? This is the simplest test, so it should actually be your first sanity check. If three are even and one is odd, you almost always have your answer.

Test 5 — Multiples of a fixed number. Are most of them multiples of 5, 7, 11, or 13? Try a small set of common factors (3, 5, 7, 11). Three numbers from a multiplication table with one outsider is a very common pattern.

Test 6 — Digit-based rules. Sum of digits, product of digits, digit-reversal property (palindromes), or alternating digits. Try this last, only if Tests 1–5 fail.

Definition: A prime number is a natural number greater than 1 that has exactly two distinct positive divisors — 1 and itself. A composite number has more than two divisors. Note carefully: 1 is neither prime nor composite — it is the unit. This is a textbook trap that examiners exploit relentlessly.

Trap Rules You Must Know Cold

• 1 is neither prime nor composite. A set like {1, 2, 3, 5} looks like "four small primes" but 1 is the imposter.
• 2 is the only even prime. A set like {2, 4, 6, 8} has 2 as the odd one not because of size but because three of the four are composite while 2 is prime; or in a set like {2, 3, 5, 7}, 2 is the only even — both interpretations are valid, so a careful examiner will design only one to fit perfectly.
• 64 is the only number ≤ 100 that is both a perfect square and a perfect cube (since 64 = 8² = 4³ = 2⁶). Other dual-power numbers (1, 729 = 27² = 9³) lie outside common RPF ranges.
• Confirm by counting. A valid odd-one-out question must have exactly three numbers sharing a property and exactly one breaking it. If two-and-two share a property, you have misidentified the rule — try the next test.

Why It Matters

In RPF SI Phase I, three to four marks of Reasoning come from classification — pure speed marks. A trained candidate solves each in 15 seconds; an untrained one wastes a minute and still picks wrong. Over the full paper, that is two extra minutes for arithmetic or general awareness, and arithmetic at the cutoff is what decides selection.

Real-world example: When the railway recruitment cell tabulates candidate roll numbers and flags duplicates, the underlying logic is the same — find the entry that breaks the pattern shared by the rest. The reasoning syllabus is training a skill the service actually uses on the job: spotting the outlier in a clean dataset.

Common misconception: Many students believe the "harder" the rule, the more likely it is the answer — so they jump to digit-sum or some clever cubic relation. In reality, the simplest rule that fits three numbers is almost always the intended one. If even/odd already explains the split, do not look for cubes. Occam's razor wins in RPF reasoning.

Question: Find the odd one out — (8, 27, 64, 100).

Solution:
Step 1: Apply Test 4 (parity) — 8, 64, 100 are even; 27 is odd. Three even, one odd. So 27 could be the answer.
Step 2: Apply Test 3 (cubes) — 8 = 2³, 27 = 3³, 64 = 4³ are perfect cubes; 100 = 10² is not a cube. Three cubes, one non-cube. So 100 could also be the answer.
Step 3: When two tests give two different answers, pick the rule that uses a stronger, more specific property. Cubes are a tighter property than parity (parity is true for half of all numbers; cubes are rare). So the intended classifier is cubes.
Conclusion: 100 is the odd one out — it is a perfect square but not a perfect cube, while the other three are perfect cubes.

Question: Find the odd one out — (15, 25, 35, 45).

Solution:
Step 1: Test 4 (parity) — all four are odd. No split. Move on.
Step 2: Test 5 (multiples) — all four are multiples of 5. No split. Move on.
Step 3: Test 1 (composite check) — 15 = 3×5, 35 = 5×7, 45 = 9×5 each have two distinct prime factors; 25 = 5×5 has only one distinct prime factor.
Conclusion: 25 is the odd one — it is a perfect square (5²) and has only one distinct prime factor, unlike the other three.

How to Drill This

In your last 30 days before the exam, do two minutes of classification a day — twenty questions, timed. Track the test number that solved each one. Within two weeks you will discover that Tests 1 and 4 alone solve 70 percent of all RPF SI classification questions. That data tells you where to look first when the clock is running.

:::compare

Test	Property checked	Frequency in RPF SI	Time to run
Test 1	Prime vs composite	High	10 sec
Test 2	Perfect squares	High	5 sec
Test 3	Perfect cubes	Medium	5 sec
Test 4	Even vs odd	Very high	2 sec
Test 5	Multiples of a fixed number	Medium	10 sec
Test 6	Digit-sum / reversal	Low	15 sec
:::

:::keypoints

• Always run the six-test checklist in order — parity first, digit-rules last.
• 1 is neither prime nor composite.
• 2 is the only even prime.
• 64 is both a perfect square and a perfect cube — handle with care.
• A valid question must have exactly three numbers sharing the rule.
• If two rules both seem to fit, pick the rarer (more specific) one.
• Memorise primes up to 50 and squares/cubes up to 225.
  :::

:::memory
PSEC-MD: Primes, Squares, cEubes (yes — pronounce it "EE-cubes" to keep order), pariTy, Multiples, Digits. Or use the simpler English chant: "Prime, Square, Cube, Even, Multiple, Digit". The first letters spell PSCEMD — say it before each set and you will never skip a test.
:::

:::recap

• Classification is a checklist exercise, not a flash of insight.
• The simplest rule that fits three of four numbers is the right one.
• Trap numbers — 1, 2, 64 — appear in roughly one in five RPF SI questions.
• Two minutes of daily timed practice will lock the method in for exam day.
  :::

Q: (a) Rose (b) Lotus (c) Marigold (d) Mango. Three are flowers; Mango is a fruit -> answer (d). Q: (a) 8 (b) 27 (c) 64 (d) 81. 8=2^3, 27=3^3, 64=4^3 are cubes; 81=3^4 (or 9^2) is not a cube -> answer (d). Q: (a) BD (b) FH (c) JM (d) PR. Gaps: B-D=1 skip, F-H=1 skip, P-R=1 skip, but J-M has 2 letters skipped (J,K,L,M) -> JM is odd, answer (c). TIP: when 3 options have an equal alphabet gap, the one with a different gap is the misfit. Always count gaps using position numbers to avoid careless errors.

This variant gives a stated pair and asks which OPTION PAIR shares the same relationship. Steps: (1) Define the precise relation of the given pair as a bridge sentence. (2) Note the DIRECTION (A causes B, A is part of B, etc.). (3) Test each option pair against the SAME bridge; the matching one wins. MEMORY AID 'DBR': Define-Bridge-Reject. Watch for reversed pairs — if given is Tool:Worker, a Worker:Tool option is wrong even if related. Also check the LEVEL of relation: Synonym vs near-synonym, whole-part vs part-part. If two options pass, tighten the bridge (degree, material, function). Eliminate distractors that are merely 'same category' but lack the specific link.

Almost every metal you touch in daily life — the steel of a bridge, the aluminium of a window frame, the copper inside a wire, the gold in a wedding ring — began life as a dull lump of rock in a mine. The journey from rock to shining metal is metallurgy, and the chemistry of that journey is decided by one master idea: how reactive the metal is.

Definition: Metallurgy is the entire process of extracting a metal from its ore and refining it to obtain the pure metal. The choice of extraction method is governed almost entirely by the metal's position in the reactivity series.

Minerals, Ores and Gangue

Definition: A mineral is any naturally occurring compound or element containing the metal. An ore is a mineral from which the metal can be profitably and conveniently extracted. Every ore is a mineral, but not every mineral is an ore.

The earthy and rocky impurities mixed with an ore are called gangue. Before extraction, the crushed ore is enriched (concentrated) to remove most of the gangue. Common enrichment methods you should recognise from your NCERT textbook include hand-picking, washing/hydraulic separation (using density differences), magnetic separation (for magnetic ores like magnetite), and froth flotation (for sulphide ores, which become wet by oil but not water).

Extraction by Reactivity — The Three Tiers

The reactivity series splits metals into three practical groups, and each group needs a different extraction strategy.

Tier 1 — Highly Reactive Metals (K, Na, Ca, Mg, Al)

These metals hold on to oxygen and chlorine so tightly that no ordinary reducing agent (like carbon) can pull the metal out. Carbon would itself stay bonded. So we use the brute force of electricity.

Definition: Electrolysis of the molten salt (chloride or oxide) is the standard method here. The metal is deposited at the cathode and the non-metal at the anode.

• Sodium is obtained by electrolysis of molten NaCl (Down's cell).
  At the cathode: Na⁺ + e⁻ → Na.
  At the anode: 2Cl⁻ → Cl₂ + 2e⁻.
• Aluminium is obtained by electrolysis of molten Al₂O₃ (Hall-Héroult process). Cryolite is added to lower the melting point.

Tier 2 — Moderately Reactive Metals (Zn, Fe, Pb, Cu)

These metals can be reduced from their oxides using carbon (coke). But their natural ores are often sulphides or carbonates, not oxides. So a preliminary step converts the ore into the oxide first.

Definition: Roasting is heating a sulphide ore strongly in the presence of excess air to convert it to the metal oxide. Sulphur dioxide is released.

Example: 2ZnS + 3O₂ → 2ZnO + 2SO₂ (zinc blende → zinc oxide).

Definition: Calcination is heating a carbonate ore strongly in the absence (or limited supply) of air to convert it to the metal oxide. Carbon dioxide is released.

Example: ZnCO₃ → ZnO + CO₂ (calamine → zinc oxide).

Then the oxide is reduced with carbon:

ZnO + C → Zn + CO
Fe₂O₃ + 3C → 2Fe + 3CO

In some cases (where the metal is more reactive than carbon allows for cleanly), a more reactive metal acts as the reducing agent — this is the thermite reaction used to weld railway tracks:
Fe₂O₃ + 2Al → 2Fe + Al₂O₃ + heat.

Tier 3 — Least Reactive Metals (Hg, Ag, sometimes Cu)

These metals are so unreactive that simply heating the ore in air releases the metal. No carbon, no electricity.

Example with cinnabar (HgS, mercury ore):

• Roasting: 2HgS + 3O₂ → 2HgO + 2SO₂.
• Self-reduction on further heating: 2HgO → 2Hg + O₂.

The same logic applies to silver and to some copper ores.

Refining the Crude Metal

The metal you obtain straight from extraction is impure. The standard purification method is electrolytic refining.

Definition: In electrolytic refining, the impure metal is made the anode, a thin strip of pure metal is the cathode, and the electrolyte is a salt solution of the metal. On passing current, pure metal dissolves from the anode, travels through the electrolyte, and deposits on the cathode. Soluble impurities (like Zn, Fe in crude copper) stay dissolved in the electrolyte; insoluble impurities (silver, gold, platinum) sink to the bottom of the cell as anode mud — and are themselves valuable.

Electrolytic refining is used routinely for copper, zinc, tin, lead, gold and silver.

Corrosion — Why Metals Slowly "Die"

Definition: Corrosion is the slow eating away of a metal due to the action of air, moisture or chemicals on its surface.

Common examples:

• Iron forms reddish-brown rust (Fe₂O₃·xH₂O). Both oxygen AND water are required — iron does not rust in pure dry air or in pure boiled water.
• Copper develops a green coating of basic copper carbonate (CuCO₃·Cu(OH)₂), seen on old copper temple roofs.
• Silver turns black due to silver sulphide (Ag₂S) formed by reacting with hydrogen sulphide in the air.

Preventing Corrosion

• Painting / oiling / greasing: physical barrier between metal and air-moisture.
• Galvanisation: coating iron with a thin layer of zinc. Zinc is more reactive and protects iron even when scratched (sacrificial protection).
• Tin plating and chromium plating: protective coatings on iron and steel.
• Alloying: e.g. stainless steel (iron + chromium + nickel) resists corrosion because the chromium forms a self-healing protective oxide layer.

Why It Matters

Without metallurgy there is no civil construction (steel), no electrification (copper), no aviation (aluminium), no electronics (silicon and gold contacts) and no renewable energy (rare earth magnets). Corrosion alone costs the world economy hundreds of billions of dollars a year — preventing rust is not a textbook curiosity, it is a multi-trillion-rupee industry.

Real-world example: The Statue of Unity in Gujarat is clad in bronze panels, but its core structure is galvanised steel. The zinc layer on the steel members is what keeps the structure corrosion-free in the open monsoon environment — the same chemistry as the corrugated tin sheets on countless village roofs, which are actually steel sheets dipped in molten zinc.

Common misconception: Students confuse roasting and calcination. The clean rule: roasting is for sulphide ores in excess air (gives SO₂); calcination is for carbonate ores with limited or no air (gives CO₂). A second common slip is forgetting that rust needs both air and water — iron exposed only to dry air (in deserts) or only to boiled, oxygen-free water does not rust.

A Worked Example

Question: A reddish-brown metal M is found in nature mainly as its sulphide ore. Outline the steps to obtain pure M, identify it, and explain why one specific step is needed.

Solution:

Step 1: A reddish-brown metal extracted mainly from sulphide ore points to copper (M = Cu); the ore is copper pyrite (CuFeS₂) or copper glance (Cu₂S).

Step 2: Concentrate the ore by froth flotation (sulphide ores wet with oil; gangue wets with water).

Step 3: Roast the concentrated sulphide ore in excess air to convert it to the oxide:
2Cu₂S + 3O₂ → 2Cu₂O + 2SO₂.

Step 4: Reduce the oxide with the residual sulphide (self-reduction):
2Cu₂O + Cu₂S → 6Cu + SO₂.

Step 5: The "blister copper" obtained is impure; refine it by electrolytic refining — impure copper as anode, pure copper as cathode, copper(II) sulphate solution as electrolyte.

Conclusion: Pure copper is obtained, and the roasting step is essential because the oxide is much easier to reduce than the sulphide. The valuable silver and gold impurities collect as anode mud during the final electrolytic refining.

:::compare

Process	Type of Ore	Air Supply	Product	Gas Released
Roasting	Sulphide	Excess air	Metal oxide	SO₂
Calcination	Carbonate	Limited / no air	Metal oxide	CO₂
Electrolysis	(oxide/chloride of very reactive metals)	Not relevant	Pure metal	Cl₂ or O₂ at anode
Heating alone	Sulphides of very unreactive metals	Air	Pure metal directly	SO₂ then O₂
:::

:::compare

Reactivity Tier	Examples	Extraction Method
Highly reactive	K, Na, Ca, Mg, Al	Electrolysis of molten salt/oxide
Moderately reactive	Zn, Fe, Pb, Cu	Roast/calcinate, then reduce with carbon (or thermite)
Least reactive	Hg, Ag, sometimes Cu	Heating ore in air (self-reduction)
:::

:::keypoints

• Metallurgy: concentration → conversion to oxide → reduction → refining.
• Method of extraction depends strictly on the metal's reactivity.
• Roasting (sulphide + excess air) and calcination (carbonate + limited air) both give the metal oxide.
• Electrolytic refining: impure metal at anode, pure metal at cathode, salt of the metal as electrolyte; gold/silver collect in the anode mud.
• Rust = Fe₂O₃·xH₂O; requires BOTH oxygen and water.
• Galvanisation gives sacrificial protection because zinc is more reactive than iron.
• Stainless steel = iron + chromium + nickel; resists corrosion through a passive chromium-oxide film.
  :::

:::memory
"SRC" — Sulphide → Roast (air excess); Carbonate → Calcine (no air). Two letters, two ores, two conditions.
:::

:::recap

• Reactivity decides the method: electrolysis for the top, carbon reduction for the middle, simple heating for the bottom.
• Roasting and calcination are different in both substrate and air supply; do not swap them.
• Electrolytic refining is the universal purification step, with valuable by-products in the anode mud.
• Rust prevention is mostly about cutting off air or water, or coating with a more reactive metal.
  :::

Analogy questions in RPF SI reasoning look deceptively easy — yet most candidates lose 1–2 marks here because they pick the "felt right" option instead of the one that survives the bridge test. The trick is mechanical: build a sentence-bridge, then plug each option into the same bridge.

Definition: An analogy is a logical relationship between two words. In an analogy question, you must identify the relationship in the given pair and pick the option pair that shares the same relationship in the same direction.

The bridge method — the only reliable technique

Step zero of every analogy question is to state the relationship between the given pair as a full sentence (the "bridge"). A good bridge has three properties:

1. It uses the exact words from the pair.
2. It captures the direction (A → B, not B → A).
3. It is specific — "is related to" is too vague; "uses … as a professional tool" is specific.

Once the bridge is built, drop each option into the same sentence, swapping in the option words. The option that fits word-for-word with the same direction is the answer.

Worked example 1 — Worker : Tool

Question: Doctor : Stethoscope :: ? : ?
Options: (a) Farmer : Plough (b) Singer : Song (c) Student : School

Build the bridge: "A doctor uses a stethoscope as a professional tool."

Now test each option in the exact same sentence:

• (a) A farmer uses a plough as a professional tool. ✔ Fits perfectly — same relationship (worker:tool), same direction.
• (b) A singer uses a song as a professional tool. ✘ A song is the product of a singer, not the tool. Wrong relationship (worker:product).
• (c) A student uses a school as a professional tool. ✘ A school is the workplace, not the tool. Wrong relationship (person:place).

Answer: (a) Farmer : Plough.

Notice how (b) Singer : Song would have looked tempting if you only asked "is there a connection?" — there obviously is, because singers make songs. But the bridge "uses … as a tool" exposes that the direction and type of the relationship is different.

Worked example 2 — Pure antonyms

Question: Day : Night :: ? : ?
Options: (a) Sun : Moon (b) Up : Down (c) Cat : Dog

Build the bridge: "Day and night are direct opposites (antonyms)."

Test each option:

• (a) Sun and Moon are direct opposites. ✘ Sun and Moon are related celestial objects, not antonyms. The Moon is not the opposite of the Sun.
• (b) Up and Down are direct opposites. ✔ Perfect antonym pair — same relationship.
• (c) Cat and Dog are direct opposites. ✘ Cats and dogs are not antonyms; they are two animals, often contrasted but not opposite by definition.

Answer: (b) Up : Down.

The classic mistake here is choosing Sun:Moon because day relates to sun and night relates to moon. But the relationship within the pair is what matters, not the relationship between pairs. Day and Night are themselves opposites; therefore the answer pair must itself be a pair of opposites.

Why precision beats intuition

In analogy questions, two options often look "right" on first read. The bridge method forces you to choose the one that is precisely right. Without a written bridge, candidates fall for near-miss relationships — worker:product instead of worker:tool, related-thing instead of opposite, part instead of whole.

A second discipline is to check direction. "Doctor : Stethoscope" puts the worker first and the tool second. So your answer must also be worker first, tool second — not "Plough : Farmer".

Why it matters: RPF SI, SSC CGL, RRB NTPC and most state-level competitive reasoning sections carry 4–8 analogy questions per paper. The bridge method converts these from "I'll guess" into "I'll calculate". It also protects you from negative marking — if no option survives the bridge, you have a strong reason to skip rather than guess.

Real-world example: When the Railway Recruitment Board sets analogy questions, they often use everyday Indian contexts — "Tabla : Musician", "Constable : Lathi", "Patwari : Land record". Each of these is a clean worker:tool or person:document relationship — exactly the kind of bridge you have just learned to build.

Common misconception: "If both pairs are 'related', I'll pick one." Wrong. Related is too weak — every two words in language are related in some way. The question always rewards the option whose relationship type and direction mirror the given pair exactly.

:::compare

Pair	Relationship	Bridge sentence
Doctor : Stethoscope	Worker : Tool	A doctor uses a stethoscope as a tool
Farmer : Plough	Worker : Tool	A farmer uses a plough as a tool
Singer : Song	Worker : Product	A singer produces a song
Student : School	Person : Place	A student studies in a school
Day : Night	Antonym	Day and night are opposites
Up : Down	Antonym	Up and down are opposites
Sun : Moon	Related celestial objects	Sun and Moon both appear in the sky
:::

:::keypoints

• Always write the bridge as a full sentence before scanning options.
• A good bridge is specific ("uses as a tool"), not vague ("is related to").
• Check direction: A:B is not the same as B:A.
• Distinguish near-miss types — worker:tool vs worker:product vs person:place.
• For antonym pairs, the answer must itself be a clean antonym pair, not a related-object pair.
• If no option fits the bridge cleanly, broaden the bridge slightly; if still none fits, skip.
• Indian-context bridges (Constable : Lathi, Patwari : Record) are frequent in RPF SI.
  :::

:::memory
B-R-D: Bridge the pair → Restate with each option → Direction check. Drill this loop and analogies become arithmetic, not intuition.
:::

:::recap

• Doctor : Stethoscope = worker : tool → Farmer : Plough is the parallel pair.
• Day : Night = antonyms → Up : Down (also antonyms) wins over Sun : Moon (related, not opposite).
• The bridge sentence converts analogy from feeling-based to rule-based.
• Watch out for relationship-type traps and direction reversals.
  :::