RRB NTPC Number System Questions, Check Solved Problems With Solution

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.

What are the types of RRB NTPC Number System Questions?

There are various types of number system questions asked from topics like divisibility rules, LCM and HCF, BODMAS, and more. The RRB NTPC Notification for 2025-26 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:

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
Answer: (a) 9936

Q2. What is the unit digit of the expression
(7^1 + 7^2 + 7^3 + \dots + 7^{50})?
(a) 1
(b) 3
(c) 4
(d) 0
Answer: (d) 0

Q3. The least 5-digit number divisible by 16, 20, and 24 is - 
(a) 10080
(b) 10000
(c) 10040
(d) 10020
Answer: (a) 10080

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
Answer: (c) 7

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
Answer: (a) 270

Q6. A ball rebounds to ( \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
Answer: (d) 21.6 m

Q7. What is the remainder when ((2023^{125})^{3}) is divided by 2024?
(a) 0
(b) 1
(c) 2023
(d) 2022
Answer: (b) 1

Q8. If 742x819y is divisible by 72, what is the value of (3x + y)?
(a) 12
(b) 9
(c) 15
(d) 18
Answer: (c) 15

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
Answer: (b) 1

Q10. Find the unit digit of the product
(91 \times 92 \times 93 \times \dots \times 100).
(a) 5
(b) 0
(c) 2
(d) 6
Answer: (b) 0

Q11. If the equation (x^2 + 6x + b = 0) has equal roots, then b = ?
(a) 9
(b) 36
(c) 3
(d) 12
Answer: (a) 9

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
Answer: (b) 3

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
Answer: (c) 10000

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
Answer: (b) 2, 3, 6, 9

Q15. The face value of digit 7 in 57281 is:
(a) 7000
(b) 70
(c) 700
(d) 7
Answer: (d) 7

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
Answer: (c) 9991

Q17. The expression (6k^2 - 6k) is divisible by—
(a) 6 only
(b) 12 only
(c) 6 and 12 both
(d) 6 and 3 both
Answer: (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
Answer: (b) 18

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
Answer: (c) p = 5, q = 4

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
Answer: (a) 123456

Q21. What is the HCF of 306 and 657?
(a) 9
(b) 27
(c) 3
(d) 18
Answer: (b) 27

Q22. What is the LCM of 18, 24 and 36?
(a) 72
(b) 144
(c) 36
(d) 216
Answer: (b) 144

Q23. Find the unit digit of (17^{23}).
(a) 3
(b) 7
(c) 9
(d) 1
Answer: (a) 3

Q24. The smallest number which when divided by 8, 12 and 15 leaves remainder 1 is:
(a) 121
(b) 241
(c) 361
(d) 481
Answer: (b) 241

Q25. What is the sum of first 50 natural numbers?
(a) 1225
(b) 1250
(c) 1275
(d) 1300
Answer: (c) 1275

Q26. If x:y = 4:7 and y:z = 14:15, then x:z equals
(a) 2:5
(b) 8:15
(c) 4:15
(d) 6:15
Answer: (b) 8:15

Q27. A number is divisible by 9 if
(a) Last digit is 9
(b) Sum of digits is divisible by 9
(c) Number is even
(d) Last two digits divisible by 9
Answer: (b) Sum of digits is divisible by 9

Q28. What is the remainder when 9999 is divided by 11?
(a) 0
(b) 1
(c) 9
(d) 10
Answer: (a) 0

Q29. Find the average of first 20 even numbers.
(a) 20
(b) 21
(c) 22
(d) 19
Answer: (b) 21

Q30. The product of two consecutive odd numbers is 483. The numbers are
(a) 21, 23
(b) 19, 21
(c) 23, 25
(d) 17, 19
Answer: (a) 21, 23

Q31. What is the square root of 9409?
(a) 97
(b) 99
(c) 101
(d) 103
Answer: (a) 97

Q32. If a number is increased by 20 percent, by what percent should it be decreased to get the original number?
(a) 20 percent
(b) 16⅔ percent
(c) 18 percent
(d) 25 percent
Answer: (b) 16⅔ percent

Q33. What is the smallest prime number?
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (c) 2

Q34. How many factors does 36 have?
(a) 7
(b) 8
(c) 9
(d) 10
Answer: (c) 9

Q35. What is the cube of 7?
(a) 343
(b) 294
(c) 216
(d) 512
Answer: (a) 343

Q36. A shopkeeper gains 20 percent. If cost price is ₹500, what is the selling price?
(a) ₹550
(b) ₹600
(c) ₹620
(d) ₹580
Answer: (b) ₹600

Q37. What is the remainder when (5^{103}) is divided by 4?
(a) 1
(b) 3
(c) 0
(d) 2
Answer: (a) 1

Q38. The sum of digits of a two-digit number is 10. If digits are reversed, the number increases by 36. The number is
(a) 46
(b) 37
(c) 28
(d) 64
Answer: (a) 46

Q39. What is the value of 15 percent of 240?
(a) 30
(b) 32
(c) 36
(d) 40
Answer: (c) 36

Q40. If x = 3, find (x^3 − x).
(a) 24
(b) 18
(c) 27
(d) 21
Answer: (a) 24

Q41. How many zeroes are there in the product of first 20 natural numbers?
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (c) 5

Q42. What is the LCM of first 10 natural numbers?
(a) 2520
(b) 5040
(c) 720
(d) 1440
Answer: (a) 2520

Q43. If the perimeter of a square is 64 cm, its area is
(a) 256 cm²
(b) 144 cm²
(c) 196 cm²
(d) 128 cm²
Answer: (a) 256 cm²

Q44. Find the simple interest on ₹2000 at 10 percent per annum for 2 years.
(a) ₹200
(b) ₹300
(c) ₹400
(d) ₹500
Answer: (c) ₹400

Q45. What is the ratio of 2.5 km to 500 m?
(a) 5:1
(b) 2:1
(c) 1:5
(d) 25:5
Answer: (a) 5:1

Q46. The smallest number divisible by all numbers from 1 to 7 is
(a) 210
(b) 420
(c) 840
(d) 2520
Answer: (b) 420

Q47. What is the value of (3^4 + 4^3)?
(a) 145
(b) 81
(c) 91
(d) 128
Answer: (a) 145

Q48. If A can do a work in 10 days and B in 15 days, together they can do it in
(a) 5 days
(b) 6 days
(c) 7 days
(d) 8 days
Answer: (b) 6 days

Q49. What is the sum of angles of a triangle?
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Answer: (b) 180°

Q50. Which number is divisible by both 3 and 4?
(a) 108
(b) 116
(c) 124
(d) 132
Answer: (a) 108

Q51. If (a^2 − b^2 = 15) and (a − b = 3), find (a + b).
(a) 5
(b) 6
(c) 7
(d) 8
Answer: (a) 5

Q52. What is the decimal value of 3/8?
(a) 0.375
(b) 0.425
(c) 0.25
(d) 0.625
Answer: (a) 0.375

Q53. Find the odd one out
(a) 121
(b) 144
(c) 169
(d) 196
Answer: (b) 144

Q54. What is the value of √0.04?
(a) 0.02
(b) 0.2
(c) 0.4
(d) 0.04
Answer: (b) 0.2

Q55. The ratio of boys to girls is 5:3. If girls are 24, the total students is
(a) 64
(b) 40
(c) 48
(d) 56
Answer: (d) 56

Q56. What is the smallest composite number?
(a) 1
(b) 2
(c) 4
(d) 6
Answer: (c) 4

Q57. A train 120 m long crosses a pole in 6 seconds. Speed is
(a) 72 km/h
(b) 60 km/h
(c) 54 km/h
(d) 48 km/h
Answer: (a) 72 km/h

Q58. What is the value of 7 factorial?
(a) 720
(b) 840
(c) 5040
(d) 40320
Answer: (c) 5040

Q59. The value of 1/2 + 1/3 is
(a) 5/6
(b) 2/5
(c) 3/5
(d) 4/6
Answer: (a) 5/6

Q60. What is the unit digit of (2^{50})?
(a) 2
(b) 4
(c) 6
(d) 8
Answer: (c) 6

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Key Points - RRB NTPC Number System Questions

The key points of the article are summarised below. Check them out:

• Understand rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12.
• Essential for LCM, HCF, and factor-related questions.
• Use prime factorisation or Euclid's method.
• Key for solving problems on sharing, distribution, and ratios.
• Use prime factorisation or formula: LCM × HCF = Product of numbers.
• Frequently appears in time and work, train problems, and pattern questions.
• Natural, Whole, Integers, Rational, Irrational, Prime, Composite.
• Important for categorising numbers and applying correct properties.
• Even/Odd, Prime/Composite, Perfect Squares/Cubes.
• Knowledge of these properties helps in simplification and reasoning.
• Use the cyclicity of unit digits for powers.
• Apply modular arithmetic for remainder-related questions.
• Fraction ↔ Decimal, Decimal ↔ Percentage, Ratio ↔ Fraction.
• Critical for solving ratio, proportion, and percentage-based number problems.
• Identify arithmetic or geometric progressions.
• Common in questions involving sequences, missing numbers, and sums.
• Memorise small prime numbers, squares, cubes, and divisibility shortcuts.
• Practice mental calculations for faster problem-solving.
• Solve topic-wise questions: HCF/LCM, Divisibility, Unit Digit, Remainder.
• Gradually move to mixed sets to improve speed and accuracy.

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