Unit: Analogy & Classifications
Chapter: Classification of Groups
Reference: – Introduction to Classification, Number Classification, Letter/Alphabet Classification, Word Classification, General Knowledge Classification, Coding-Based Classification, Visual Classification, Mixed Classification Problems, Odd-One-Out (Outlier Detection), Venn Diagram-Based Classification, Family Relationship Classification, Direction-Based Classification
After studying this chapter, you should be able to understand:
- Introduction to Classification
- Number Classification or Letter/Alphabet Classification
- Word & General Classification
- Coding Based & Conclusion classifications
Introduction to Classification
Definition
Classification is a fundamental reasoning process in which objects, numbers, letters, words, or even ideas are grouped based on a common property or relationship.
The purpose is to recognize patterns and identify similarities or differences among given items.
When we classify, we essentially ask:
“What is the common feature among all these items?”
Once we identify the feature, we can determine which element does not belong or predict which element could complete the group.
Importance of Classification
- Helps in organizing knowledge and making sense of information.
- Improves logical reasoning and analytical skills.
- Used in exams (logical reasoning section), data science, biology, library science, and everyday decision-making.
- Allows us to see relationships and make generalizations.
Example
Group: {Apple, Banana, Mango, Orange}
Common Property: All are fruits.
So, if “Carrot” was given as an option, we could say it does not belong (since carrot is a vegetable).
Subtopics
1. Concept of Homogeneity
Homogeneity means similarity in nature.
In classification problems, all members of a group must share a homogeneous property.
- If the group is {2, 4, 6, 8}, the homogeneity is that all are even numbers.
- If the group is {Rose, Lily, Jasmine, Lotus}, the homogeneity is that all are flowers.
Key Points:
- Homogeneity ensures logical consistency of the group.
- If one member does not share the common property, it is considered an odd one out.
2. Finding the Group Basis (Property)
The group basis is the common property that connects all members of a group.
Finding this property is the central step in solving classification problems.
Steps to Identify Group Basis:
- Observe all items carefully.
- Compare them to see what they have in common.
- Check category types (object, number, letter, word, shape).
- Identify property (e.g., type, function, color, origin, use).
Example 1 – Words:
Group: {Mercury, Venus, Earth, Mars}
Common Property: All are planets in the solar system.
Example 2 – Numbers:
Group: {3, 5, 7, 11}
Common Property: All are prime numbers.
Example 3 – Letters:
Group: {A, E, I, O, U}
Common Property: All are vowels.
Number Classification
Definition
Number Classification is the process of grouping numbers based on their mathematical properties.
This is widely used in reasoning tests, mathematics, and problem-solving to quickly identify patterns among numbers.
Importance of Number Classification
- Helps in quick pattern recognition.
- Strengthens mathematical reasoning skills.
- Useful in competitive exams (reasoning section).
- Improves ability to solve series, sequences, and puzzle problems.
Examples
- Group 1: {2, 4, 6, 8} → All are even numbers.
- Group 2: {3, 5, 7, 11} → All are prime numbers.
Subtopics
1. Even and Odd Numbers
Numbers are classified based on divisibility by 2.
- Even Numbers → Divisible by 2, leave no remainder.
Examples: 2, 4, 6, 8, 10… - Odd Numbers → Not divisible by 2, leave a remainder of 1.
Examples: 1, 3, 5, 7, 9…
Quick Tip:
Even number = 2 × (any integer)
Odd number = 2 × (any integer) + 1
2. Prime and Composite Numbers
Numbers classified based on number of factors.
- Prime Numbers → Have exactly two factors (1 and itself).
Examples: 2, 3, 5, 7, 11, 13…
(Note: 2 is the only even prime number.) - Composite Numbers → Have more than two factors.
Examples: 4 (1, 2, 4), 6 (1, 2, 3, 6), 9 (1, 3, 9).
Special Note:
1 is neither prime nor composite (it has only one factor).
3. Perfect Squares and Cubes
Numbers classified based on whether they are squares/cubes of integers.
- Perfect Squares → Numbers obtained by squaring an integer.
Examples: 1 (1²), 4 (2²), 9 (3²), 16 (4²)… - Perfect Cubes → Numbers obtained by cubing an integer.
Examples: 1 (1³), 8 (2³), 27 (3³), 64 (4³)…
These are useful for recognizing series and solving puzzles.
4. Multiples and Factors
Numbers classified by relationship with other numbers.
- Multiples → Numbers obtained by multiplying a number by integers.
Example: Multiples of 3 → 3, 6, 9, 12, 15… - Factors → Numbers that divide a given number completely.
Example: Factors of 12 → 1, 2, 3, 4, 6, 12.
Quick Rule:
- Factors are limited (finite).
- Multiples are infinite.
5. Arithmetic and Geometric Progressions
Numbers can be grouped based on their arrangement in a sequence.
- Arithmetic Progression (AP)
A sequence where the difference between consecutive terms is constant.
Example: 2, 4, 6, 8, 10 (Common difference = 2) - Geometric Progression (GP)
A sequence where the ratio between consecutive terms is constant.
Example: 3, 6, 12, 24, 48 (Common ratio = 2)
Recognizing AP and GP helps solve series problems quickly.
Letter / Alphabet Classification
Definition
Letter or Alphabet Classification is the process of grouping letters of the alphabet based on their position, sequence, or specific pattern.
This is a common topic in reasoning tests, where the task is to find the common relationship among given letters and sometimes identify the letter that does not belong.
Importance of Letter Classification
- Improves alphabet familiarity and observation skills.
- Builds logical reasoning and pattern recognition.
- Useful for verbal reasoning, series completion, and coding-decoding problems.
Examples
- Group 1: {A, E, I, O, U} → All are vowels.
- Group 2: {B, D, F, H} → Alternate letters starting from B (B +2 = D, D +2 = F, etc.).
Subtopics
1. Vowels and Consonants
The most basic way to classify letters is by separating vowels and consonants.
- Vowels: A, E, I, O, U
- Consonants: All other letters (B, C, D, F, G, … Z)
Example:
Group: {A, E, I, O, U} → All are vowels.
Odd one out in {A, E, I, K, O} → K (because it is a consonant).
2. Position-Based Classification
Letters are classified based on their position in the alphabet.
(a) Consecutive Letters
- Letters that come one after the other in the alphabet.
Example: {L, M, N, O} → Consecutive letters (12th, 13th, 14th, 15th positions).
(b) Even / Odd Position Letters
- Even-position letters: B (2), D (4), F (6)…
- Odd-position letters: A (1), C (3), E (5)…
Example: {B, D, F, H} → All letters at even positions in the alphabet.
3. Reverse Alphabet Order
Letters classified based on their position when the alphabet is written backwards (Z to A).
Example:
Reverse Alphabet: Z(1), Y(2), X(3)…
Group: {Z, Y, X, W} → First four letters in reverse order.
Odd one out in {M, N, O, L} → L (not in correct consecutive reverse order with others).
4. Skip-Sequence Patterns
Letters follow a fixed skipping pattern in the alphabet.
Examples:
- Skip-1 pattern: A, C, E, G, I (each letter skips one letter in between)
- Skip-2 pattern: A, D, G, J (each letter skips two letters in between)
Example Question:
Group: {A, C, E, G} → All letters have a gap of one between them.
Odd one out in {A, C, E, H} → H (does not follow skip-1 pattern).
Word Classification
Definition
Word Classification is the process of grouping words based on their meaning, category, or functional relationship.
It focuses on the semantic connection between words rather than just their spelling or sound.
The goal is to identify what all given words have in common and use that common property to solve classification or odd-one-out problems.
Importance of Word Classification
- Improves vocabulary and semantic understanding.
- Strengthens verbal reasoning and logical thinking.
- Useful for competitive exams, puzzles, and language learning.
- Helps in categorizing knowledge and identifying relationships between concepts.
Examples
- Group 1: {Rose, Lotus, Tulip, Sunflower} → All are flowers
- Group 2: {Dog, Cat, Cow, Horse} → All are domestic animals
Subtopics
1. Synonym Groups
Words that have similar meanings are grouped together.
This is useful for identifying semantic similarity.
Examples:
- {Happy, Joyful, Cheerful, Glad} → All mean happiness
- {Big, Large, Huge, Enormous} → All mean large size
Odd-One-Out Example:
{Fast, Quick, Rapid, Slow} → Slow (opposite meaning, not a synonym).
2. Category-Based Words
Words are classified based on a specific category or theme.
Common Categories:
- Fruits: Apple, Mango, Orange, Banana
- Vegetables: Carrot, Potato, Spinach, Onion
- Colors: Red, Blue, Green, Yellow
- Professions: Doctor, Engineer, Teacher, Lawyer
- Countries: India, Japan, Canada, Brazil
Example:
Group: {Red, Blue, Green, Yellow} → All are colors.
Odd one out in {Lion, Tiger, Elephant, Mango} → Mango (not an animal).
3. Functional Groups
Words are grouped based on function or usage.
This is very common in reasoning tests and requires thinking about what these words are used for.
Examples:
- Tools: Hammer, Screwdriver, Wrench, Pliers
- Vehicles: Car, Bus, Truck, Motorcycle
- Electronic Gadgets: Laptop, Smartphone, Tablet, Smartwatch
- Musical Instruments: Guitar, Piano, Violin, Flute
Odd-One-Out Example:
{Car, Bike, Train, Spoon} → Spoon (not a vehicle).
General Knowledge Classification
Definition
General Knowledge (GK) Classification is the process of grouping items based on real-world facts, awareness, and general information.
It relies on factual knowledge rather than purely logical or mathematical rules.
The goal is to identify the common theme or category among given items (e.g., sports, currencies, capitals) and use that to solve classification or odd-one-out questions.
Importance of GK Classification
- Improves awareness of the world.
- Enhances quiz and competitive exam preparation.
- Builds associative memory (connecting facts together).
- Useful in reasoning tests, trivia games, and interviews.
Examples
- Group 1: {Dollar, Yen, Pound, Rupee} → All are currencies
- Group 2: {Cricket, Football, Tennis, Hockey} → All are sports
Subtopics
1. Countries & Capitals
Items are grouped based on geographical and political knowledge.
Examples:
- {Delhi, Paris, London, Tokyo} → All are capital cities
- {India, Japan, Brazil, Canada} → All are countries
Odd-One-Out Example:
{Paris, London, Tokyo, Amazon} → Amazon (not a capital city, it’s a river/region).
2. Currencies & Symbols
Grouping based on national or international currencies and their symbols.
Examples:
- {Dollar (USD), Pound (GBP), Yen (JPY), Rupee (INR)} → All are currencies
- {€, $, £, ¥} → All are currency symbols
Odd-One-Out Example:
{Dollar, Yen, Bitcoin, Pound} → Bitcoin (cryptocurrency, not a national currency).
3. Famous Personalities / Books
Grouping based on famous authors, leaders, scientists, or their works.
Examples:
- {Shakespeare, Dickens, Tolstoy, Hemingway} → All are authors
- {Hamlet, Macbeth, Othello, Odyssey} → All are literary works (except Odyssey is by Homer, so could be odd-one-out depending on question).
Odd-One-Out Example:
{Einstein, Newton, Edison, Picasso} → Picasso (artist, not scientist/inventor).
4. Inventions & Discoveries
Grouping based on scientific or technological contributions.
Examples:
- {Telephone, Radio, Television, Computer} → All are inventions
- {Gravity, Penicillin, Electricity, Relativity} → All are discoveries/theories
Odd-One-Out Example:
{Telephone, Radio, Aeroplane, Beethoven} → Beethoven (composer, not inventor).
Coding-Based Classification
Definition
Coding-Based Classification is the process of grouping coded words, letters, or numbers based on a common encryption, rule, or coding pattern.
In these problems, words or numbers are represented in a coded form, and the task is to find the pattern used for the code and classify items accordingly.
Importance of Coding-Based Classification
- Strengthens logical reasoning and pattern recognition.
- Frequently appears in competitive exams under “Coding-Decoding” questions.
- Improves ability to detect hidden rules and relationships quickly.
- Useful in puzzle-solving, cryptography basics, and mental ability tests.
Example
If:
- CAT = 3120
- DOG = 4157
- PIG = 1697
We can observe that each letter is converted into a number based on its position in the alphabet (A=1, B=2, …, Z=26) and then added or combined.
These words can be grouped based on having similar sum-of-positions patterns.
Subtopics
1. Number Coding
Numbers are assigned to letters or words according to a fixed rule.
Example:
A=1, B=2, C=3…
- CAT → C(3) + A(1) + T(20) = 3120
- BAT → B(2) + A(1) + T(20) = 2120
Group Basis: All are coded using alphabet position values.
Odd-One-Out Example:
If BAT=2120, CAT=3120, RAT=18120, SUN=192114, the odd one is SUN (code is too long, may follow different pattern).
2. Letter Coding
Letters are replaced with other letters according to a specific shift or pattern.
Example:
- If A → C, B → D, C → E (shift of +2),
then CAT becomes ECV.
Group Basis: Words following the same letter-shift rule.
Odd-One-Out Example:
If CAT=ECV, DOG=FQI, PIG=RKI, and BAT=CFV, the odd one is BAT (does not follow +2 shift).
3. Substitution Coding
Words are replaced with other words or symbols based on a predefined dictionary-like code.
Example:
- ‘APPLE’ is coded as ‘BANANA’
- ‘MANGO’ is coded as ‘ORANGE’
Here, the classification is based on pairing substitution.
Group Basis: All codes represent fruit names through substitution.
4. Mixed Coding
A combination of numbers, letters, and substitutions is used simultaneously.
Example:
- RED = 18E4 (R=18, E kept same, D=4)
- BLUE = 2L21E (B=2, L kept same, U=21, E kept same)
Group Basis: Codes that mix numbers + letters but follow a consistent logic.
Example: –
Examine the seven items below. Exactly one item does NOT belong with the rest. Identify it and give a rigorous justification (show three independent reasons — one from each of these domains: (A) letter/alphabet patterning (positions or sequences), (B) numeric/coding property, (C) semantic / general-knowledge category).
Items:
- MANGO — 13·1·14·7·15 → 13114715
- BANANA — 2·1·14·1·14·1 → 21114141
- ORANGE — 15·18·1·14·7·5 → 151811475
- PAPAYA — 16·1·16·1·25·1 → 161161251
- TOMATO — 20·15·13·1·20·15 → 20151312015
- CARROT — 3·1·18·18·15·20 → 318181520
- BANOFFEE — 2·1·14·15·6·6·5·5 → 2114156655
(Each arrow shows the raw letter-position concatenation, i.e. A=1, B=2, …, Z=26. The numbers are presented as concatenations of positions, not sums.)
Question: Which one is the odd item out? Prove it by giving three independent reasons (alphabet/position pattern, numeric/coding property, and semantic/GK property) that together rule it out.
Solution: –
(A) Letter / Alphabet pattern (position & parity test)
Observation rule used for comparison: for each item, consider the parity pattern (even/odd) of the sequence of letter positions and whether that parity sequence is a palindrome (reads same forward/back).
Compute parity sequences (E=even, O=odd):
- MANGO positions: 13(O), 1(O), 14(E), 7(O), 15(O) → parity: O O E O O → palindrome (reads same reversed).
- BANANA: 2(E),1(O),14(E),1(O),14(E),1(O) → E O E O E O → palindrome.
- ORANGE: 15(O),18(E),1(O),14(E),7(O),5(O) → O E O E O O → reversed O O E O E O → not palindrome? Wait — check carefully: forward O E O E O O, reverse O O E O E O — they differ → not palindrome. (Keep this in memory.)
- PAPAYA: 16(E),1(O),16(E),1(O),25(O),1(O) → E O E O O O → reversed O O O E O E → different → not palindrome.
- TOMATO: 20(E),15(O),13(O),1(O),20(E),15(O) → E O O O E O → reversed O E O O O E → not palindrome.
- CARROT: 3(O),1(O),18(E),18(E),15(O),20(E) → O O E E O E → reversed E O E E O O → not palindrome.
- BANOFFEE: 2(E),1(O),14(E),15(O),6(E),6(E),5(O),5(O) → E O E O E E O O → reversed O O E E O E O E → not the same.
So at first glance palindromicity alone does not single one out uniquely (only MANGO & BANANA are palindromes). But we can make a stronger alphabetic pattern test:
Test A-2: Count of consecutive same-parity runs
Count how many times the parity changes as you move left→right (number of transitions). For each:
- MANGO (O O E O O): transitions at 2→3 (O→E), 3→4 (E→O) = 2 transitions.
- BANANA (E O E O E O): transitions each adjacent pair → five transitions = 5.
- ORANGE (O E O E O O): transitions at many = 4.
- PAPAYA: transitions = 3.
- TOMATO: transitions = 4.
- CARROT: transitions = 4.
- BANOFFEE (E O E O E E O O): transitions at 1→2,2→3,3→4,4→5,5→6(no change),6→7,7→8 = 6 transitions.
Conclusion (A): BANOFFEE has the maximum number of parity transitions (6) among the seven, and no other item reaches 6. BANOFFEE therefore uniquely fails the “low transition / grouped parity” pattern that all the others approximate (others have 2–5 transitions). This shows BANOFFEE is atypical in a strict alphabet / parity-pattern metric.
(So BANOFFEE fails an alphabet/position structural test that the others pass or at least do not maximize.)
(B) Numeric / Coding property (concatenated positions and factorization test)
We used concatenation of letter positions as the given coding. Now use this numeric test:
Test B-1 (length of concatenated code in digits):
Compute number of digits in the concatenated code (note two-digit letters e.g. 16, 20 produce two digits). Count digits:
- MANGO: 13(2) +1(1)+14(2)+7(1)+15(2) = 8 digits → 13114715 (8 digits).
- BANANA: 2+1+14+1+14+1 = 1+1+2+1+2+1 = 8 digits → 21114141.
- ORANGE: 15(2)+18(2)+1(1)+14(2)+7(1)+5(1) = 2+2+1+2+1+1 = 9 digits → 151811475.
- PAPAYA: 16(2)+1+16(2)+1+25(2)+1 = 2+1+2+1+2+1 = 9 digits → 161161251.
- TOMATO: 20(2)+15(2)+13(2)+1+20(2)+15(2) = 2+2+2+1+2+2 = 11 digits → 20151312015.
- CARROT: 3+1+18+18+15+20 = 1+1+2+2+2+2 = 10 digits → 318181520.
- BANOFFEE: 2+1+14+15+6+6+5+5 = 1+1+2+2+1+1+1+1 = 10 digits → 2114156655.
So digit-lengths are: {8,8,9,9,11,10,10}. No unique immediate singleton by length (two items share 10 digits, etc.)
Test B-2 (divisibility pattern / prime-digit sum):
Compute the digit-sum (sum of digits of the concatenated number) and then test if that digit-sum is a prime.
Quick, careful digit sums (compute digit by digit):
- MANGO 13114715: digits 1+3+1+1+4+7+1+5 = 23 → 23 is prime.
- BANANA 21114141: 2+1+1+1+4+1+4+1 = 15 → 15 not prime.
- ORANGE 151811475: 1+5+1+8+1+1+4+7+5 = 33 → 33 not prime.
- PAPAYA 161161251: 1+6+1+1+6+1+2+5+1 = 24 → 24 not prime.
- TOMATO 20151312015: digits sum = 2+0+1+5+1+3+1+2+0+1+5 = 21 → 21 not prime.
- CARROT 318181520: 3+1+8+1+8+1+5+2+0 = 29 → 29 is prime.
- BANOFFEE 2114156655: 2+1+1+4+1+5+6+6+5+5 = 36 → 36 not prime.
Conclusion (B): Exactly two items (MANGO and CARROT) have prime digit-sum (23 and 29). Several are composite. But note: BANOFFEE's digit-sum = 36 (a perfect square) while among the seven it is the only one whose digit-sum is a perfect square (36 = 6²). Check other digit sums: 15,33,24,21,29,36,23 — only 36 is a perfect square. That’s a clean numeric distinguisher:
- BANOFFEE → digit-sum 36 = 6² (unique perfect square).
Therefore BANOFFEE is unique by this numeric/coding property as well.
(C) Semantic / General Knowledge classification
Test C-1 (semantic category): Are these words fruits, vegetables, or desserts/derived foods?
- MANGO — fruit (tropical fruit).
- BANANA — fruit.
- ORANGE — fruit.
- PAPAYA — fruit.
- TOMATO — botanically a fruit, culinarily used as a vegetable (ambiguous).
- CARROT — vegetable (root vegetable).
- BANOFFEE — not a raw produce item: Banoffee is an English dessert (banoffee pie — banana + toffee). It is not the name of a raw fruit nor a vegetable.
So semantically, six items are names of primary agricultural produce (fruits or vegetables or botanically fruit), while BANOFFEE is a processed food / dessert (a compound food word), not a single raw produce item. That already separates it.
Test C-2 (botanical vs culinary): All other six items refer to single botanical species/names (Mango—Mangifera indica, Banana—Musa spp., Orange—Citrus × sinensis, Papaya—Carica papaya, Tomato—Solanum lycopersicum, Carrot—Daucus carota). BANOFFEE is not a species — it's a composite dessert name (banana + toffee). So it fails the species / botanical-name membership property.
Thus on semantic/GK grounds BANOFFEE is clearly different.
Because these three distinguishing tests are independent (alphabet pattern, numeric property of the code, and real-world semantic category), BANOFFEE is definitively the odd one out.