Analogy Test — Study Notes
Overview
Analogy questions test your ability to identify logical relationships between pairs of numbers, figures, or objects and apply that same relationship to find a missing element or odd one out. In the UP Police Constable exam, you can expect 3–5 questions from this topic, making it a moderate-weightage area that's also relatively scoring if you master the pattern recognition skills.
The core principle is simple: **A is to B as C is to D**. You must identify how A relates to B, then apply that exact relationship to find what D should be when given C. For numerical analogies, relationships can be arithmetic (addition, multiplication, squares, cubes) or positional (digits, place values). For figural analogies, you look for changes in shape, size, rotation, shading, number of elements, or position. Mastering 8–10 common relationship patterns will help you solve 90% of analogy questions within 30–45 seconds each.
Analogy questions also overlap with classification (odd one out), where instead of completing a relationship, you identify which element doesn't follow the pattern. Both question types reward the same skill: **quick pattern recognition and logical reasoning**.
Key Concepts
- **Direct relationship identification**: The first pair establishes a rule (e.g., "multiply by 3" or "rotate 90° clockwise"). Your job is to decode this rule and apply it to the second pair.
- **Numerical analogies**: Common patterns include arithmetic operations (addition, subtraction, multiplication, division), exponential relationships (squares, cubes, square roots), digit manipulation (sum of digits, product of digits, reverse), and positional patterns (prime numbers, even-odd sequences).
- **Figural analogies**: Look for transformations like rotation (clockwise/anticlockwise), reflection (horizontal/vertical mirror), size changes (enlargement/reduction), shading changes (filled to unfilled), addition/removal of elements, or positional shifts of internal components.
- **Odd one out**: Instead of completing a pair, you identify which of 4–5 given options doesn't follow the same relationship pattern as the others. Test each option against a hypothesis about the common rule.
- **Multiple operations**: Some analogies involve two-step relationships (e.g., "add 5, then multiply by 2" or "rotate 45°, then add one element"). Always check if a single operation doesn't explain the relationship.
- **Elimination strategy**: In figural analogies, eliminate options that violate the most obvious transformation first (wrong rotation direction, wrong number of elements), then check finer details (shading, internal positioning).
Formulas / Key Facts
**Numerical Analogy Patterns (Common Types)**
1. **Arithmetic operations**: 4 : 16 :: 7 : 28 → multiply by 4 2. **Squares and cubes**: 3 : 9 :: 5 : 25 → square the number 3. **Sum/product of digits**: 23 : 5 :: 34 : 7 → sum of digits (2+3=5, 3+4=7) 4. **Reverse digits**: 12 : 21 :: 45 : 54 → reverse the two-digit number 5. **Predecessor/successor**: 7 : 8 :: 15 : 16 → next consecutive number 6. **Prime-composite pairs**: 2 : 4 :: 3 : 6 → prime × 2 = composite 7. **Position in series**: 1st prime : 2, 2nd prime : 3, 3rd prime : 5 8. **Exponential patterns**: 2 : 8 :: 3 : 27 → cube the number
**Figural Analogy Transformations**
- Rotation: 45°, 90°, 180° clockwise or anticlockwise
- Reflection: Horizontal flip, vertical flip, or both
- Shading: Filled ↔ unfilled, or partial shading patterns
- Element count: Add/remove lines, dots, shapes
- Size change: Enlarge, reduce, or maintain size
- Position: Internal elements shift left/right, up/down, or swap places
Worked Examples
**Example 1: Numerical Analogy — Arithmetic Pattern**
**Question**: 6 : 36 :: 9 : ? (a) 72 (b) 81 (c) 63 (d) 90
**Solution**: Step 1: Identify the relationship between 6 and 36. 6² = 36 (the number is squared).
Step 2: Apply the same operation to 9. 9² = 81.
**Answer**: (b) 81
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**Example 2: Numerical Analogy — Digit Manipulation**
**Question**: 24 : 6 :: 63 : ? (a) 9 (b) 18 (c) 12 (d) 15
**Solution**: Step 1: Check the relationship. 2 + 4 = 6 (sum of digits).
Step 2: Apply to 63. 6 + 3 = 9.
**Answer**: (a) 9
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**Example 3: Figural Analogy — Rotation**
**Question**: In the first pair, a triangle pointing upward becomes a triangle pointing to the right. What happens to a square in the second pair?
**Solution**: Step 1: The triangle rotated 90° clockwise.
Step 2: Apply the same rotation to the square. If the square has a distinctive mark (e.g., a dot in the top-left corner), after 90° clockwise rotation, the dot moves to the top-right corner.
**Answer**: Select the option showing the square rotated 90° clockwise with the internal mark in the correct new position.
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**Example 4: Odd One Out — Numerical**
**Question**: Find the odd one: 8, 27, 64, 125, 144 (a) 8 (b) 27 (c) 64 (d) 144
**Solution**: Check if all are perfect cubes:
- 8 = 2³
- 27 = 3³
- 64 = 4³
- 125 = 5³
- 144 = 12² (perfect square, not cube)
**Answer**: (d) 144 is the odd one out.
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**Example 5: Figural Odd One Out**
**Question**: Four figures show circles with internal lines. Three have 3 lines, one has 4 lines. Which is the odd one?
**Solution**: Step 1: Count internal elements. Three figures have 3 lines each; one has 4 lines.
Step 2: The figure with 4 lines breaks the pattern.
**Answer**: The figure with 4 internal lines is the odd one out.
Common Mistakes
1. **Assuming only one operation**: Students often try a single arithmetic operation (like addition) and stop. **Fix**: Always test 2–3 common operations (square, cube, digit sum, multiplication) before concluding.
2. **Ignoring digit-level patterns**: In numbers like 23 : 5, students miss that 2+3=5. **Fix**: When direct arithmetic doesn't work, immediately check sum of digits, product of digits, or digit reversal.
3. **Not checking all transformations in figural analogies**: Students see rotation and stop, missing that shading also changed. **Fix**: Use a mental checklist — rotation, reflection, size, shading, element count, position — and verify each.
4. **Picking the visually similar option instead of the logically consistent one**: In figural analogies, an option may look "close" but violate the transformation rule. **Fix**: Apply the rule strictly; eliminate options that break even one aspect of the pattern.
5. **Confusing odd-one-out with analogy completion**: In odd-one-out, you're finding the exception, not completing a pair. **Fix**: Read the question type carefully. For odd-one-out, test what rule the majority follow, then find which one doesn't.
Quick Reference
- **A : B :: C : D** → Decode the A→B transformation, apply to C to find D.
- **Top 5 numerical patterns**: Squares, cubes, digit sum, multiply by constant, reverse digits.
- **Top 5 figural patterns**: 90° rotation, horizontal/vertical flip, shading change, element addition, position swap.
- **Odd one out strategy**: Find the common property in 3–4 items, identify which item lacks it.
- **Time management**: Spend max 45 seconds per analogy; if stuck after testing 3 patterns, mark for review and move on.
- **Elimination works**: In figural analogies, eliminating 2 obviously wrong options increases your guess success to 50%.