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Perfect Square Analogy

Perfect Square Analogy problems involve number pairs where the second number is a perfect square of the first or related to squares. Common patterns include: A : A², A : (A+1)², A : A² + k, or square root relationships. These problems test knowledge of perfect squares and square roots.

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

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Perfect Square Analogy

Perfect Square Analogy problems involve number pairs where the second number is a perfect square of the first or related to squares. Common patterns include: A : A², A : (A+1)², A : A² + k, or square root relationships. These problems test knowledge of perfect squares and square roots.

Prerequisites

Perfect squares up to 20² = 400 Square root concepts Square numbers pattern Basic arithmetic
Why This Matters: Perfect Square Analogy problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test knowledge of squares and square roots.

How to Solve Perfect Square Analogy Problems

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Step 1: Identify the two numbers in the given analogy pair (A:B)

2

Step 2: Check if B = A² (A squared)

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Step 3: Check if B = (A+1)² or (A-1)²

4

Step 4: Check if B = A² ± k

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Step 5: Alternative: A = √B (A is square root of B)

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Step 6: Apply the same operation to the second pair's first number

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Step 7: Present the answer

Pro Strategy: Check if the second number is a perfect square. If so, find its square root. Common patterns involve squares of the first number, squares of (first ± k), or square plus constant.

Example Problem

Example: 5 : 25 :: 7 : ? Solution: Step 1: First pair: 5 and 25 Step 2: 5² = 25 Step 3: Relationship: Second number = square of first Step 4: Apply to 7: 7² = 49 Answer: 49

Pro Tips & Tricks

  • Perfect squares: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400
  • Square root: √25 = 5, √36 = 6, √49 = 7, √64 = 8, etc.
  • Pattern: A : A² is the most common
  • Pattern: A : (A+1)² e.g., 3:16 (4²)
  • Pattern: A : (A-1)² e.g., 5:16 (4²)
  • Pattern: A : A² + A e.g., 5:30 (25+5)

Shortcut Methods to Solve Faster

If A:B with B = A², then answer = C²
If A:B with A = √B, then answer = √C (if perfect square)
Consecutive squares: (n+1)² - n² = 2n+1 (odd numbers)
Square of sum: (a+b)² = a² + 2ab + b²

Common Mistakes to Avoid

Confusing square with multiplication (2×3=6 vs 3²=9)
Not recognizing perfect squares beyond 10
Forgetting that square of a number can be large
Using square when square root is needed (or vice versa)

Exam Importance

Perfect Square Analogy 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
1-2 questions
CAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Perfect Square Analogy?

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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