Number System questions form an essential foundation for the Quantitative Aptitude section of IBPS RRB 2026 (Prelims and Mains). These questions test your calculation speed and conceptual understanding of important topics, including divisibility rules, HCF and LCM, remainders, unit digits, trailing zeros, and number properties. Practising exam-level MCQs, digit-based problems, and number system shortcuts can help you solve questions faster with better accuracy. In this article, you will get important practice questions with answers, step-by-step solutions, and useful tricks to improve your preparation for the IBPS RRB Clerk and PO exams.
Number System Questions For IBPS RRB 2026 Highlights
- Full Pattern Coverage: Includes divisibility rules, HCF and LCM, unit digits, prime factors, remainders, and missing term series.
- Exam Relevance: Designed according to the latest pattern for IBPS RRB PO (Officer Scale-I) and Office Assistant (Clerk) Prelims and Mains exams.
- Speed-Building Short Tricks: Learn digital sum methods, fast factorization formulas, and simple step-by-step solutions.
- 30 + 10 Solved Practice Questions: Features 10 main solved questions plus 30 extra practice questions for solid accuracy.
IBPS RRB Number System Questions : Attempt Quiz
IBPS RRB Quantitative Aptitude number system questions PDF solved sets help you understand how fundamental number concepts are applied under timed conditions. Studying detailed step-by-step explanations allows you to spot pattern trends quickly and reduce runtime calculations.
Total Questions: 10 | Total Marks: 10
Question 1. What is the unit digit of 2467153 × 34172?
To find the unit digit of 2467153, focus on 7153. The cyclicity of 7 is 4. Dividing 153 by 4 gives a remainder of 1 (153 = 4 × 38 + 1). Therefore, the unit digit is 71 = 7. The unit digit of 34172 is always 1 because any power of 1 ends in 1.
Required unit digit = 7 × 1 = 7.
Question 2. Find the smallest number which when divided by 12, 15, 20, and 54 leaves a remainder of 4 in each case.
The required number is the LCM of the given numbers plus the common remainder.
12 = 22 × 3, 15 = 3 × 5, 20 = 22 × 5, and 54 = 2 × 33.
LCM = 22 × 33 × 5 = 540.
Required number = 540 + 4 = 544.
Question 3. If a 5-digit number 347P2 is completely divisible by 9, what is the minimum value of digit P?
A number is divisible by 9 if the sum of its digits is a multiple of 9.
Digit sum = 3 + 4 + 7 + P + 2 = 16 + P.
The nearest multiple of 9 greater than 16 is 18.
16 + P = 18, which gives P = 2.
Therefore, the minimum value of P is 2.
Question 4. The HCF of two numbers is 12 and their product is 2160. How many such pairs of numbers are possible?
Let the two numbers be 12a and 12b, where a and b are co-prime.
12a × 12b = 2160
144ab = 2160
ab = 2160 ÷ 144 = 15.
The co-prime factor pairs of 15 are (1, 15) and (3, 5).
Therefore, exactly 2 pairs are possible.
Question 5. Find the remainder when 231 is divided by 5.
Rewrite 231 as (22)15 × 2 = 415 × 2.
Since 4 = 5 − 1, the remainder of 415 when divided by 5 is (−1)15 = −1, equivalent to 4.
Therefore, the required remainder is the remainder of 4 × 2 = 8 when divided by 5.
Required remainder = 3.
Question 6. How many total factors does the number 360 have?
Prime factorisation of 360:
360 = 23 × 32 × 51.
Formula for total factors = (a + 1)(b + 1)(c + 1).
= (3 + 1) × (2 + 1) × (1 + 1)
= 4 × 3 × 2 = 24.
Therefore, 360 has 24 factors.
Question 7. What is the sum of all prime numbers between 20 and 40?
The prime numbers between 20 and 40 are 23, 29, 31, and 37.
Their sum = 23 + 29 + 31 + 37.
= 52 + 31 + 37 = 120.
120 + 23 = 143.
Required sum = 143.
Question 8. Find the value of 1 + 2 + 3 + … + 50.
Use the formula for the sum of the first n natural numbers:
S = n(n + 1)/2.
For n = 50:
S = 50 × 51 ÷ 2
= 25 × 51 = 1275.
Required sum = 1275.
Question 9. Four bells ring together at intervals of 3, 7, 12, and 14 seconds respectively. How many times will they ring together in 42 minutes?
The bells will ring together at intervals equal to the LCM of 3, 7, 12, and 14.
LCM = 84 seconds.
Total time = 42 × 60 = 2520 seconds.
Number of times = (2520 ÷ 84) + 1
= 30 + 1 = 31.
Therefore, they will ring together 31 times, including the initial ring.
Question 10. If the sum of two numbers is 42 and their product is 437, what is the absolute difference between the numbers?
Let the two numbers be x and y.
Given: x + y = 42 and xy = 437.
Using the identity:
(x − y)2 = (x + y)2 − 4xy
= 422 − 4 × 437
= 1764 − 1748 = 16.
Therefore, |x − y| = √16 = 4.
Required absolute difference = 4.
Quiz Completed!
Congratulations!
You have successfully completed the Number System Quiz 2026.
Your Final Score: 0/10
Key Topics of Number System Questions For IBPS RRB
Review the essential breakdown of Number System topics, expected marks, and difficulty levels below:
| Topic Category | Key Concepts Covered | Expected Weightage | Difficulty Level |
| Divisibility and Remainders | Rules for 3, 7, 8, 9, 11, and Remainder Theorem | 1 – 2 Questions | Easy to Moderate |
| HCF and LCM | Product rule, circular tracks, and bell ring timing | 1 – 2 Questions | Moderate |
| Unit Digit and Factors | Power series, cyclicity, total and prime factors | 1 Question | Easy |
| Number Series and Properties | Missing terms, wrong numbers, and consecutive integers | 2 – 4 Questions | Moderate to Hard |
Number System divisibility rules and remainder theorem IBPS RRB Shortcuts
Number System divisibility rules and remainder theorem IBPS RRB shortcuts save precious time during high-pressure banking tests. Mastering these basic rules allows candidates to solve complex power and division problems directly.
Keep these core divisibility rules and remainder theorems in your daily practice notes:
- Divisibility by 7: Double the last digit and subtract it from the remaining number. If the result is divisible by 7, the entire number is divisible by 7.
- Divisibility by 11: Calculate the difference between the sum of digits at odd positions and even positions. If the difference is 0 or a multiple of 11, the number is divisible by 11.
- Remainder Theorem: If a polynomial or expression F(x) is divided by (x – a), the resulting remainder equals F(a).
- Unit Digit Cyclicity: Digits 0, 1, 5, and 6 always keep their unit digits. Digits 4 and 9 follow a 2-step power cycle. Digits 2, 3, 7, and 8 follow a 4-step power cycle.
IBPS RRB PO Number Series Missing and Wrong Term Questions Strategies
IBPS RRB PO Number Series missing and wrong term questions form a significant part of the quantitative section. Candidates must learn systematically to spot addition, multiplication, and power-based series patterns quickly.
Follow these proven steps to tackle number series patterns smoothly:
- Step 1: Check Differences. Calculate the differences between adjacent numbers. If the growth is gradual, look for simple prime number additions or basic arithmetic gaps.
- Step 2: Inspect Multiplicative Step Sizes. If numbers rise rapidly, test for multiplication or division steps paired with addition or subtraction (like * 1 + 1, * 2 + 2).
- Step 3: Analyze Squares and Cubes. Check whether the difference series follows n^2 + k, n^2 – k, n^3 + k, or n^3 – k patterns, which frequently appear in PO Prelims papers.
Unit digit and factors questions for bank exams Practice Set
Unit digit and factors questions for bank exams test your speed with exponents and prime factorizations. Knowing exact cyclicity rules eliminates tedious long multiplication during your actual exam attempt.
The reference table below highlights unit digit cyclicity rules for simple mental calculation:
| Base Digit | Cyclicity Pattern | Exponent Calculation Rule |
| 0, 1, 5, 6 | 1 (Constant unit digit) | 5^n always ends in 5 |
| 4, 9 | 2 (Odd/Even power rule) | 4^odd = 4, 4^even = 6 |
| 2, 3, 7, 8 | 4 (Divide power by 4) | 3^14 implies 14 mod 4 = 2, giving 3^2 = 9 |
Simplification and approximation based on Number System IBPS RRB
Simplification and approximation based on Number System IBPS RRB tests your fundamental calculation skills under tight deadlines. Applying BODMAS rules alongside percentage shortcuts makes large calculations simple.
Use these practical calculation shortcuts to build better attempt speed:
- Memorize Square and Cube Values: Learn square values up to 30 and cube values up to 20 by heart.
- Use Fraction Conversions: Convert percentage values into simple fractions (for example, 37.5% = 3/8, 16.66% = 1/6).
- Apply Digital Sum Methods: Verify multi-digit additions and multiplications quickly by equating digit sums on both sides of an equation.
Conclusion
Mastering Number System questions forms the backbone of a high score in the IBPS RRB Quantitative Aptitude section. Regular practice with structured quizzes and mock tests on PracticeMock builds essential speed and helps eliminate simple calculation errors. Focus on key divisibility short tricks, memorize standard square and cube tables, and practice previous year paper sets to secure maximum marks in IBPS RRB 2026.
Number System Questions For IBPS RRB 2026 FAQs
What topics are in Number System Questions For IBPS RRB 2026?
Major topics include divisibility rules, remainders, unit digits, LCM and HCF, prime factors, and number series. Mastering these core concepts helps candidates solve quantitative aptitude questions quickly across prelims and mains exams.
How many number system questions appear in IBPS RRB PO?
Candidates can expect 2 to 4 direct or indirect number system questions in PO exams. Questions cover unit digit cyclicity, remainder theorem applications, HCF-LCM word problems, and missing number series patterns.
What is the shortcut for divisibility by 11 questions?
Subtract the sum of digits at even positions from the sum of digits at odd positions. If the resulting difference is 0 or a multiple of 11, the original number is completely divisible by 11.
Are HCF and LCM word problems asked in IBPS RRB Mains?
Yes, HCF and LCM word problems feature regularly in IBPS RRB Mains quantitative sections. Common question patterns involve circular track race timings, bell ring intervals, and equal grouping distributions.
How can I improve my speed in Number System questions?
Memorize square values up to 30, cube values up to 20, and basic percentage-to-fraction conversions. Daily practice with topic-wise quizzes on PracticeMock helps apply cyclicity rules and digital sum shortcuts rapidly.
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