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The RRB NTPC exam is one of the most competitive railway recruitment examinations in India, with lakhs of students appearing each year. Among the various topics asked in the Mathematics section, the Number System is one of the most fundamental yet highly scoring areas. Understanding concepts like divisibility, LCM & HCF, fractions, decimals, indices, and rational/irrational numbers is crucial for clearing the cut-off. In this article, we will provide a complete and easy-to-understand guide on RRB NTPC Number System Questions, including important concepts, formulas, sample questions, difficulty levels, and preparation tips.
Types of RRB NTPC Number System Questions
The RRB NTPC Notification has already been released for the applicants. The number system questions generally come from the following subtopics:
- Types of numbers (Natural, Whole, Integer, Rational, Irrational, Real)
- Divisibility rules
- LCM and HCF
- Fractions and decimals
- Square and cube roots
- BODMAS application
- Indices and surds
- Remainders (Basic level)
- Factorization
Topic-wise weightage of Number System Questions in RRB NTPC
Candidates must understand the difficulty level of each of the mathematics topics asked in the examination. The expected distribution of questions based on past trends is shown below:
| Topic | Expected Questions | Difficulty Level |
|---|
| Types of Numbers | 1 | Easy |
| Divisibility Rules | 1 | Easy |
| LCM & HCF | 1 | Moderate |
| Fractions & Decimals | 1 | Easy |
| Square/Cube Roots | 1 | Moderate |
| Indices & Surds | 1 | Moderate |
Sample RRB NTPC Number System Questions
In the CBT 1 examination, there are in total of 30 questions from Mathematics. On the other hand, qualifying candidates are required to answer 35 questions from the CBT 2 exam. We have provided below a set of RRB NTPC Number System Questions that will help candidates get an idea about the difficulty level:
Q1. What is the largest 4-digit number exactly divisible by 9, 12, and 18?
(a) 9936
(b) 9960
(c) 9990
(d) 9972
Q2. What is the unit digit of the expression 71+72+73+⋯+7507^1 + 7^2 + 7^3 + \dots + 7^{50}?
(a) 1
(b) 3
(c) 4
(d) 0
Q3. The least 5-digit number divisible by 16, 20, and 24 is—
(a) 10080
(b) 10000
(c) 10040
(d) 10020
Q4. If the 10-digit number 6284x179y5 is divisible by 72, what is the value of (x + y)?
(a) 5
(b) 6
(c) 7
(d) 8
Q5. A number is divided by 5, and then 15 is subtracted from the result. If the final value is 41, what was the original number?
(a) 270
(b) 280
(c) 300
(d) 250
Q6. A ball rebounds to 23\frac{2}{3} of the height it is dropped from. If dropped from 81 m, how high will it reach after the third bounce?
(a) 24 m
(b) 36 m
(c) 29.16 m
(d) 21.6 m
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Q7. What is the remainder when (2023125)3(2023^{125})^{3} is divided by 2024?
(a) 0
(b) 1
(c) 2023
(d) 2022
Q8. If 742x819y is divisible by 72, what is the value of (3x + y)?
(a) 12
(b) 9
(c) 15
(d) 18
Q9. If a number leaves a remainder of 5 when divided by 12, what is the remainder when the same number is multiplied by 3 and divided by 6?
(a) 3
(b) 1
(c) 0
(d) 2
Q10. Find the unit digit of the product 91×92×93×⋯×10091 \times 92 \times 93 \times \dots \times 100.
(a) 5
(b) 0
(c) 2
(d) 6
Q11. If the equation x2+6x+b=0x^2 + 6x + b = 0 has equal roots, then b = ?
(a) 9
(b) 36
(c) 3
(d) 12
Q12. If a number gives a remainder of 4 when divided by 9, what will be the remainder when 7 times the number is divided by 9?
(a) 1
(b) 3
(c) 7
(d) 6
Q13. A number is increased by 15% and then decreased by 15%. The result is 255 less than the original number. What was the original number?
(a) 12000
(b) 11000
(c) 10000
(d) 9000
Q14. 183960 is divisible by which of the following single-digit numbers?
(a) 2, 3, 4, 5, 6
(b) 2, 3, 6, 9
(c) 3, 4, 6
(d) 2, 3, 5, 9
Q15. The face value of digit 7 in 57281 is:
(a) 7000
(b) 70
(c) 700
(d) 7
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Q16. What is the greatest four-digit number that leaves remainders 1, 2 and 3 when divided by 3, 4 and 5 respectively?
(a) 9979
(b) 9993
(c) 9991
(d) 9995
Q17. The expression 6k2−6k6k^2 - 6k is divisible by -
(a) 6 only
(b) 12 only
(c) 6 and 12 both
(d) 6 and 3 both
Q18. If 127xy is divisible by 3, 7, and 13, what is the value of (x + 2y)?
(a) 14
(b) 18
(c) 22
(d) 12
Q19. If the number 1783pq is divisible by 11 and 13, which of the following pairs of p and q is correct?
(a) p = 6, q = 5
(b) p = 4, q = 6
(c) p = 5, q = 4
(d) p = 3, q = 6
Q20. Identify the smallest number from the following that is divisible by 3 but not by 9:
(a) 123456
(b) 999999
(c) 876543
(d) 100002
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