Study Notes: Analogy and Classification

Overview

Analogy and Classification form a critical pillar of the Logical Reasoning section in SOF IMO. These questions test your ability to recognize patterns, relationships and underlying logic among words, numbers and geometric figures. The exam typically presents 3–5 questions on this topic, and they're often considered "scoring" questions if you understand the core principles.

In analogy questions, you identify a relationship between two items and apply the same relationship to find a matching pair. In classification questions, you spot the odd one out—the element that doesn't share the common property of the others. Both question types demand quick pattern recognition and systematic elimination. Mastering these concepts not only boosts your IMO score but also sharpens logical thinking skills applicable across mathematics and verbal reasoning sections.

Students who excel here learn to look beyond surface features. A strong grasp of number properties (prime, composite, perfect square, divisibility rules), alphabet positions, geometric properties and semantic word relationships is essential.

Key Concepts

• **Analogy** means similarity or correspondence between two pairs. If A relates to B in a certain way, then C relates to D in the same way. Format: A : B :: C : ?
• **Classification** means grouping items by a common property, then identifying the element that doesn't belong. Three items share a trait; one does not.
• **Number-based patterns** include arithmetic operations (sum, difference, product), divisibility rules, squares/cubes, prime/composite classification and place-value manipulation (reverse, digit sum).
• **Alphabet-based patterns** rely on letter positions (A=1, B=2...Z=26), vowel/consonant classification, alphabetical order and letter shifts (next letter, skip patterns).
• **Word-based classification** uses semantic categories (fruits, animals, metals), part-of-speech grouping (noun, verb) or functional relationships (tool-action, animal-habitat).
• **Figure-based patterns** involve shape properties (number of sides, symmetry), shading/rotation, element count (dots, lines) and spatial transformations (mirror, rotation by 90°).
• **Systematic elimination** is your best friend: check each option against the identified rule; discard mismatches immediately.

Key Facts

• **Letter position values**: A=1, B=2, C=3...Z=26. Frequently used in alphabet analogy (e.g., C:3 :: E:5).
• **Vowels**: A, E, I, O, U. Consonants: all other 21 letters. Common classification criterion.
• **Prime numbers below 50**: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Often one number is composite in a prime group.
• **Perfect squares**: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100... Check if all numbers are squares except one.