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Century Problems

Century Problems involve identifying which century a year belongs to, or the first and last years of a century. These problems test your understanding of how centuries are numbered and the special rules for century leap years.

10Worksheets
200+Practice Questions
BeginnerDifficulty
30-45 minutesHours 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 Century Problems

Century Problems involve identifying which century a year belongs to, or the first and last years of a century. These problems test your understanding of how centuries are numbered and the special rules for century leap years.

Prerequisites

Understanding of century concept (100 years) Year numbering (1-100 = 1st century) Leap year rules for century years
Why This Matters: Century Problems appear in 1-2 questions in SSC CGL and Banking exams. They test basic knowledge of century numbering.

How to Solve Century Problems Problems

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Step 1: Identify the given year

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Step 2: To find the century: divide the year by 100 and round up

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Step 3: Formula: Century = floor((year - 1) / 100) + 1

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Step 4: The 1st century covers years 1-100, 2nd century covers 101-200, etc.

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Step 5: For century years (ending with 00), they are leap only if divisible by 400

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Step 6: The last year of a century is a multiple of 100

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Step 7: Present the answer as ordinal (1st, 2nd, 3rd, ...) or numeric

Pro Strategy: Remember that the 1st century started with year 1, not year 0. So years 1-100 = 1st century, 101-200 = 2nd century, etc. The nth century covers years (100n - 99) to (100n).

Example Problem

Example 1: Which century does the year 2024 belong to? Solution: Step 1: Year = 2024 Step 2: (2024 - 1) / 100 = 2023 / 100 = 20.23 Step 3: floor(20.23) = 20, then +1 = 21 Step 4: 2024 is in the 21st century Answer: 21st century Example 2: What is the last year of the 20th century? Solution: 20th century covers years 1901-2000 (or 1900-1999? Depends on definition). Standard: 20th century = 1901-2000. Last year = 2000 Answer: 2000

Pro Tips & Tricks

  • Century = (year + 99) // 100 (integer division)
  • The 21st century started on Jan 1, 2001 (not 2000)
  • 1900 is in the 19th century? Actually 1900 is in 19th century? 19th century = 1801-1900, so 1900 is the last year of 19th century
  • 2000 is the last year of the 20th century, 2001 is first year of 21st century
  • Century years (1900, 2000, 2100) are NOT all leap years (only those divisible by 400)
  • The year 2000 was a leap year (divisible by 400)

Shortcut Methods to Solve Faster

Century = (year - 1) // 100 + 1
The nth century begins in year (100n - 99) and ends in year (100n)
To check if a century year is leap: year % 400 == 0
First year of 21st century = 2001, Last year = 2100

Common Mistakes to Avoid

Thinking century years always start with the same hundreds (e.g., 1900s = 20th century? Actually 1900s = 20th century? Need careful)
Confusing '19th century' with '1900s'
Forgetting that year 0 doesn't exist (1 AD to 100 AD is 1st century)
Assuming all century years are leap years

Exam Importance

Century Problems 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
0-1 questions
INSURANCE
1-2 questions

Ready to Master Century Problems?

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

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now