Scaling Transformation

Scaling Transformation problems involve sequences where the size of a figure increases or decreases by a fixed amount (linear scaling) or fixed ratio (geometric scaling). You must identify the scaling pattern and predict the next figure's size.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

Introduction to Scaling Transformation

Scaling Transformation problems involve sequences where the size of a figure increases or decreases by a fixed amount (linear scaling) or fixed ratio (geometric scaling). You must identify the scaling pattern and predict the next figure's size.

Prerequisites

Measurement of size (radius, side length, area) Arithmetic progression concept Geometric progression concept Ratio and proportion
Why This Matters: Scaling problems appear in moderate-level non-verbal reasoning. You can expect 1-2 questions in SSC CGL, 1-2 in Banking PO, and 2-3 in Railways RRB exams.

How to Solve Scaling Transformation Problems

1

Step 1: Measure the size (radius, side length, or height) of each figure

2

Step 2: Calculate the difference between consecutive sizes for linear pattern

3

Step 3: Calculate the ratio between consecutive sizes for geometric pattern

4

Step 4: Check if the difference is constant (linear progression)

5

Step 5: Check if the ratio is constant (geometric progression)

6

Step 6: Apply the identified pattern to find the next size

7

Step 7: Draw or identify the figure with that size

Pro Strategy: Always measure a consistent dimension (radius for circles, side length for squares, height for triangles). Check both differences (for linear) and ratios (for geometric) to identify the pattern type.

Example Problem

Example: Circle radii: 10 units, 15 units, 20 units, 25 units. What is the next radius? Solution: Step 1: Sizes: 10, 15, 20, 25 Step 2: Differences: +5, +5, +5 Step 3: Constant difference = +5 (linear progression) Step 4: Next radius = 25 + 5 = 30 units Answer: 30 units

Pro Tips & Tricks

  • Linear scaling: size increases/decreases by constant amount
  • Geometric scaling: size multiplies/divides by constant factor
  • For circles, measure radius (not diameter) for consistency
  • For squares, measure side length
  • For triangles, measure height or base length
  • Watch for size changes that follow square or cube patterns

Shortcut Methods to Solve Faster

If sizes: 10, 20, 30, 40 → linear (+10), next = 50
If sizes: 5, 10, 20, 40 → geometric (×2), next = 80
If sizes: 1, 4, 9, 16 → square numbers, next = 25
If sizes: 1, 8, 27, 64 → cube numbers, next = 125

Common Mistakes to Avoid

Measuring inconsistent dimensions (diameter vs radius)
Confusing linear with geometric progression
Not checking both differences and ratios
Assuming area scaling when it's linear dimension scaling

Exam Importance

Scaling Transformation is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
UPSC
1-2 questions

Ready to Master Scaling Transformation?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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