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Factorial Analogy

Factorial Analogy problems involve number pairs where the second number is the factorial of the first number. For example, in the pair 5:120 (5! = 5×4×3×2×1 = 120). You may also encounter factorial of (A+k) or variations. These problems test knowledge of factorial values.

10Worksheets
200+Practice Questions
AdvancedDifficulty
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 Factorial Analogy

Factorial Analogy problems involve number pairs where the second number is the factorial of the first number. For example, in the pair 5:120 (5! = 5×4×3×2×1 = 120). You may also encounter factorial of (A+k) or variations. These problems test knowledge of factorial values.

Prerequisites

Factorial concept (n! = product of numbers 1 to n) Factorial values up to 10! Basic multiplication Pattern recognition
Why This Matters: Factorial Analogy problems appear in 0-1 questions in advanced exams like CAT and Banking PO mains. They test knowledge of factorials.

How to Solve Factorial Analogy Problems

1

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

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Step 2: Calculate the factorial of A: A! = 1×2×3×...×A

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Step 3: Check if B equals A! (or (A+k)!)

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Step 4: Common variations: B = A! + k, B = (A+1)!, etc.

5

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

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Step 6: Verify the pattern with all given examples

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Step 7: Present the answer

Pro Strategy: Memorize factorial values: 0! = 1, 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720, 7! = 5040, 8! = 40320, 9! = 362880, 10! = 3628800. Apply the factorial operation to the second pair.

Example Problem

Example: 4 : 24 :: 5 : ? Solution: Step 1: First pair: 4 and 24 Step 2: 4! = 4×3×2×1 = 24 Step 3: Relationship: Second number = factorial of first Step 4: Apply to 5: 5! = 5×4×3×2×1 = 120 Answer: 120

Pro Tips & Tricks

  • 0! = 1 (special case)
  • 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720
  • 7! = 5040, 8! = 40320, 9! = 362880, 10! = 3628800
  • Factorial grows very fast - answer will be large for A ≥ 5
  • Variation: (A+1)! = (A+1) × A!
  • Variation: A! × A = (A+1)! - A!

Shortcut Methods to Solve Faster

If A:B with B = A!, then answer = C!
Factorial values: memorize up to 7! for quick recall
For large numbers, pattern may be factorial of (A+k) or (A-k)

Common Mistakes to Avoid

Confusing factorial with exponent (2⁴=16 vs 4!=24)
Forgetting that 0! = 1 (not 0)
Using multiplication instead of factorial (5×4=20 vs 5!=120)
Not recognizing that factorial values grow rapidly

Exam Importance

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

SSC CGL
0-1 questions
BANKING PO
0-1 questions
RAILWAYS RRB
0-1 questions
CAT
1-2 questions
INSURANCE
0-1 questions

Ready to Master Factorial 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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