Hey, Railway aspirant! Ready to unlock the secrets to dominating the Numerical Ability section in the RRB NTPC exam? Your foundation must be rock-solid, and that foundation is the Number System. The Number System isn’t just one topic – it is the entire backbone of mathematics. You can expect at least 3 to 4 direct, fundamental, and highly scoring questions on concepts like divisibility, factors, remainders, and rational numbers. If you know the divisibility rules and the tricks for remainders, you can easily score good marks in this topic. In this blog, we’ve provided exam-level Number System questions for the RRB NTPC exam in a free downloadable PDF. But before you download it, take a few free Number System tests to analyze your understanding of this topic.
Concept of Number System for RRB NTPC
The Number System categorizes numbers and focuses on the rules governing them. For the RRB NTPC exam, the most critical areas involve basic properties and fast computation rules:
- Classification: Understanding the difference between Natural, Whole, Integers, Rational, and Irrational numbers.
- Divisibility Rules: Knowing the quick checks for numbers divisible by 3, 4, 8, 9, 11, etc.
- LCM and HCF: Calculating the Least Common Multiple and Highest Common Factor quickly.
- Unit Digits & Remainders: Finding the last digit of a large power and calculating the remainder after division.
Key Rules You Must Master
Success in this topic depends entirely on knowing and applying the shortcuts and rules. Memorize these essentials for the RRB NTPC exam:
| Topic Category | Essential Formulas/Concepts |
| Divisibility by 3 & 9 | A number is divisible by 3 (or 9) if the sum of its digits is divisible by 3 (or 9). |
| Divisibility by 4 & 8 | Divisible by 4 if the last two digits are divisible by 4. Divisible by 8 if the last three digits are divisible by 8. |
| Divisibility by 11 | The difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11. |
| LCM and HCF Relation | Product of two numbers = LCM x HCF |
Shortcut Tricks to Master Number System Questions
Forget long division and complex factor trees! Use these tricks to save minutes in the exam:
Shortcut 1: The Cyclicity of Unit Digits
This is perfect for finding the unit digit of large powers (e.g., 743):
| Base Unit Digit | Power Cyclicity |
| 0, 1, 5, 6 | Unit digit is always the same (e.g., 650 ends in 6). |
| 4, 9 | Cycle of 2. (Odd power -> same digit; Even power -> different digit). |
| 2, 3, 7, 8 | Cycle of 4. Divide the power by 4, and the remainder is the effective new power. |
- Example: Find the unit digit of 342.
- Divide 42 by 4. The remainder is 2.
- The unit digit is the same as 32 = 9.
Shortcut 2: Remainder Theorem (Basic)
When dividing a number by N, you can replace the number with its remainder before multiplying or adding:
- Example: Find the remainder of (25 x 26) / 5.
- Remainder of 25/5 is 0. Remainder of 26/5 is 1.
- The remainder of (0 x 1) / 5 is 0. (Faster than 650/5 remainder).
Number System Questions for RRB NTPC PDF, Download for Free
The questions asked by RRB in the Numerical Ability section are typically direct applications of rules. They require quick recall of formulas, divisibility rules, and mental calculation. They are the perfect type of question that can save you time for other time-consuming sections. To help you master these quick facts, we have provided a PDF containing the most important and frequently asked Number System questions for the exam. Click on the button given below to download the Number System Questions for RRB NTPC PDF for free.
Q1. The product of 277 and 323 is:
(a) 88471
(b) 89471
(c) 89391
(d) 91371
Correct Answer: (b) 89471
Q2. The square of 72 is equal to the product of 216 and a number. Find the number.
(a) 18
(b) 24
(c) 48
(d) 36
Correct Answer: (b) 24
Q3. Which of the following is the smallest 5-digit number that is exactly divisible by 526?
(a) 10426
(b) 10520
(c) 10516
(d) 11046
Correct Answer: (b) 10520
Q4. Find the least number divisible by 2, 3, 5, 6, 9, and 18, which is a perfect square.
(a) 400
(b) 900
(c) 3600
(d) 144
Correct Answer: (b) 900
Q5. 625+626+627+628 is divisible by:
(a) 254
(b) 256
(c) 259
(d) 255
Correct Answer: (c) 259
Q6. Which of the following numbers is divisible by 24?
(a) 26968
(b) 49512
(c) 64760
(d) 52668
Correct Answer: (b) 49512
Q7. An 11-digit number 7823326867X is divisible by 18. What is the value of X?
(a) 8
(b) 4
(c) 2
(d) 6
Correct Answer: (c) 2
Q8. Find the remainder when 88+ 6 is divided by 7.
(a) 1
(b) 2
(c) 3
(d) 0
Correct Answer: (d) 0
Q9. When a number is divided by 45, the remainder is 21. What will be the remainder when the number is divided by 15?
(a) 6
(b) 3
(c) 0
(d) 5
Correct Answer: (a) 6
Q10. When m is divided by 7, the remainder is 5. When 3m is divided by 7, the remainder is:
(a) 1
(b) 2
(c) 3
(d) 0
Correct Answer: (a) 1
Preparation Tips for RRB NTPC Number System
The Number System is the foundation of your Quant score. Use these tips to maximize your preparation:
- Master Divisibility Rules: Practice the divisibility rules for 11, 8, and 9 daily. These are the most frequently tested rules in RRB exams.
- Create a Formula Sheet: Write down all your LCM/HCF relations and unit digit cyclicity on a single sheet. Revise this chart every morning before starting your practice.
- Use Options to Check: When solving a divisibility question, use the rules to test the given options immediately. Often, you can eliminate three options quickly and save time.
- Practice High Volume: The Number System requires high repetition to build speed at pattern recognition. Solve a dedicated set of 10-15 questions daily using our free topic tests.
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FAQs: Number System Questions for RRB NTPC
You can generally expect 3 to 4 direct, fundamental questions from the Number System in the Numerical Ability section.
Divisibility Rules and LCM/HCF are considered the most important and frequently asked sub-topics.
The best way is to memorize the cyclicity of unit digits and practice applying the divisibility rules mentally without writing too many steps.
You can download the free PDF containing solved, practice-based Number System questions directly from the link in this blog.
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