Problem on Numbers
📋 Quick-reference guides with key formulas and must-know concepts. Perfect for daily practice, last-minute revision, and on-the-go learning.
Cheat Sheets
Study MaterialProblem on Numbers Cheat Sheet
Problems on Numbers is one of the most important and frequently asked topics in Quantitative Aptitude for SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates understand digit-based problems, number formation, remainder concepts, divisibility rules, consecutive numbers, factors and multiples, linear equation-based number problems, and shortcut methods for solving questions quickly and accurately in exams.
About This Cheat Sheet
Complete guide to Problems on Numbers for competitive exams:
Two & Three Digit Numbers
- Formation of Numbers
- Digit Place Values
- Two-digit Number Concepts
- Three-digit Number Problems
Digit Interchanging
- Reversing Digits
- Difference Between Number & Reverse
- Interchange of Digits
- Digit Transformation Tricks
Digit Sum Problems
- Sum of Digits
- Repeated Digit Sum
- Cyclic Digit Patterns
- Digital Root Concepts
Number Algebra
Consecutive numbers, even and odd numbers, prime numbers, and number relationships.
Remainder Problems
- Remainder Theorem
- Modular Arithmetic
- Cyclic Remainders
- Division Based Questions
Factors & Multiples
- Number of Factors
- Prime Factorization
- Multiples Concepts
- LCM & HCF Applications
Word Problems on Numbers
- Linear Equation Problems
- Ratio Based Numbers
- Fraction & Decimal Numbers
- Condition Based Questions
Shortcut Tricks
Fast solving techniques, divisibility shortcuts, and exam-oriented number tricks.
Topics Covered
| Topic | Description |
|---|---|
| Two-digit Numbers | Representation using tens and units digits |
| Three-digit Numbers | Representation using hundreds, tens, and units |
| Digit Reversal | Problems involving reversing digits |
| Difference Problems | Difference between number and reversed number |
| Sum of Digits | Digit addition and cyclic sum concepts |
| Consecutive Numbers | Even, odd, and natural number problems |
| Prime Numbers | Questions involving prime number concepts |
| Divisibility Rules | Shortcut methods for divisibility checks |
| Remainder Theorem | Problems based on division remainders |
| Factors & Multiples | Finding factors, multiples, and divisors |
| LCM & HCF Problems | Applications in number problems |
| Ratio Based Numbers | Number formation using ratios |
| Linear Equation Problems | Word problems solved using equations |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand Number Concepts
↓
Improve Logical Thinking
↓
Apply Shortcut Techniques
↓
Solve Complex Problems Faster
↓
Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Example
Example:
The sum of digits of a two-digit number is 11. If digits are reversed, the new number becomes 27 less than the original number. Find the number.
Let the tens digit = x
Let the units digit = y
According to question:
x + y = 11
Original number = 10x + y
Reversed number = 10y + x
(10x + y) − (10y + x) = 27
9x − 9y = 27
x − y = 3
Solving:
x = 7 and y = 4
Required number = 74
Final Takeaway
This Problem on Numbers Cheat Sheet provides complete revision material for all important concepts frequently asked in competitive examinations. Regular practice of digit problems, divisibility rules, remainder concepts, factors and multiples, and shortcut techniques can significantly improve speed, accuracy, and analytical thinking in exams.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
View Full Cheat Sheet
Learn Smart. Score High.
Complete Quick Revision Material for Competitive Exams
View Problem on Numbers Cheat Sheet