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Square Analogy

Square Analogy problems involve number pairs where the second number is the square of the first number (A : A²). For example, 4:16 (4² = 16). You may also encounter square root relationships (A : √A) or variations like (A² : A³). These problems test knowledge of squares and square roots.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 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 Square Analogy

Square Analogy problems involve number pairs where the second number is the square of the first number (A : A²). For example, 4:16 (4² = 16). You may also encounter square root relationships (A : √A) or variations like (A² : A³). These problems test knowledge of squares and square roots.

Prerequisites

Perfect squares up to 20² = 400 Square root concepts Exponent understanding Basic multiplication
Why This Matters: Square Analogy problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test knowledge of perfect squares and exponents.

How to Solve Square Analogy Problems

1

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

2

Step 2: Check if B = A² (A squared)

3

Step 3: Alternative patterns: B = (A + k)², or A = √B

4

Step 4: Verify the pattern consistently

5

Step 5: Apply the same operation to the second pair's first number

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Step 6: For square root relationships, find √C or C² as appropriate

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Step 7: Present the answer

Pro Strategy: Check if the second number is the square of the first. Also check if the first number is the square root of the second. For variations, identify the offset pattern.

Example Problem

Example: 5 : 25 :: 8 : ? Solution: Step 1: First pair: 5 and 25 Step 2: 5² = 25 Step 3: Relationship: Square the first number Step 4: Apply to 8: 8² = 64 Answer: 64

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, etc.
  • Pattern can be (A+1)² : e.g., 3:16 (4²)
  • Pattern can be A² + A : e.g., 5:30 (25+5)
  • Pattern can be (A-1)² : e.g., 6:25 (5²)
  • Check if the relationship involves both square and addition/subtraction

Shortcut Methods to Solve Faster

If A:B, check if B = A², then ? = C²
If A:B, check if A = √B, then ? = √C (if perfect square)
Common square pairs: 2:4, 3:9, 4:16, 5:25, 6:36, 7:49, 8:64, 9:81, 10:100, 11:121, 12:144

Common Mistakes to Avoid

Confusing square with multiplication (2×2=4 is square, 2×3=6 is not)
Using square root when square is needed (or vice versa)
Not recognizing perfect squares beyond 10
Forgetting that square of a fraction yields a smaller number

Exam Importance

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 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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