Number System Questions and Answers – Page 2

Number System is one of the most foundational topics in Quantitative Aptitude and forms the basis for almost every other chapter tested in SSC CGL, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, RRB NTPC, and other banking and government job examinations. This topic covers essential concepts such as natural numbers, whole numbers, integers, rational and irrational numbers, prime and composite numbers, divisibility rules, factors and multiples, LCM and HCF, and the properties of even and odd numbers. A strong command over number system concepts helps aspirants solve questions faster not only in this topic but also in simplification, percentage, and data interpretation problems. This topic page offers a thorough collection of number system questions with detailed, step-by-step solutions designed to help aspirants strengthen their conceptual understanding and boost calculation speed. The practice questions cover important variations such as divisibility tests for numbers, finding unit digits using cyclicity patterns, LCM and HCF based word problems, remainder theorem questions, and problems involving prime factorization. Each solution includes clear explanations along with shortcut tricks and formula-based methods that make solving number system problems significantly faster during the exam. Aspirants preparing for SSC, banking, and railway exams often find number system questions challenging when they involve large numbers, remainder-based problems, or unit digit calculations for numbers raised to high powers. Our practice set addresses these difficulties through clear worked examples, cyclicity-based shortcuts for finding unit digits, and quick divisibility rules that save valuable time during the exam. Regular practice with these questions will strengthen your overall Quantitative Aptitude preparation and build a solid mathematical foundation for competitive exams. Whether you are a beginner starting your preparation or an experienced aspirant refining your speed and accuracy, this number system question bank is designed to support learners at every level. Practice consistently, apply the shortcut methods provided, and use them to solve number system questions accurately and quickly in your upcoming SSC, banking, railway, and other competitive government examinations.

Exams Covered:

SSC CGL

SSC CHSL

SSC MTS

IBPS PO

IBPS Clerk

RRB NTPC

UPSC

State Exams

& More

Online Quiz Test

Find the value of 250 − 175

Which number is divisible by 12?

Find the square root of 169

Which number is divisible by 10?

Find the cube of 6

Which number is divisible by 6?

Find the square of 18

Which number is divisible by 11?

Find the value of 75% of 200

Which number is divisible by 8?

1 2 3

FAQ

Number System FAQs

Common questions and clear answers for this topic.

What is Number System in mathematics and what types of numbers are important for exams?

Number System covers Natural Numbers (1,2,3), Whole Numbers (0,1,2,3), Integers, Rational Numbers (p/q form), Irrational Numbers (like pi and root 2), and Real Numbers. For competitive exams like SSC CGL and IBPS, focus on: divisibility rules, LCM and HCF, factors, prime numbers, and unit digit calculations.

What are the important divisibility rules in Number System?

Divisibility rules: Divisible by 2 - last digit even. By 3 - sum of digits divisible by 3. By 4 - last two digits divisible by 4. By 5 - last digit 0 or 5. By 6 - divisible by both 2 and 3. By 8 - last three digits divisible by 8. By 9 - sum of digits divisible by 9. By 11 - difference of alternating digit sums divisible by 11. Mastering these rules helps solve Number System questions faster in competitive exams.

What is LCM and HCF and how are they calculated?

LCM (Least Common Multiple) is the smallest number divisible by all given numbers. HCF (Highest Common Factor) is the largest number that divides all given numbers. Methods: For HCF - prime factorization or Euclidean algorithm. For LCM - prime factorization. Key relationship: LCM x HCF = Product of two numbers (only for two numbers). LCM and HCF questions appear in all major competitive exams.

How to find the unit digit of large powers?

Unit digits follow cyclicity patterns: For 2 - cycle is 2,4,8,6 (length 4). For 3 - cycle is 3,9,7,1 (length 4). For 4 - cycle is 4,6 (length 2). For 7 - cycle is 7,9,3,1 (length 4). For 8 - cycle is 8,4,2,6 (length 4). For 0,1,5,6 - unit digit is always 0,1,5,6 regardless of power. Divide the power by the cycle length and use the remainder to find the unit digit.

What are prime numbers and composite numbers up to 100?

Prime numbers up to 100 (25 total): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. All other numbers (except 1) are composite. 1 is neither prime nor composite. 2 is the only even prime. To check if a number N is prime, check divisibility only up to the square root of N.

Which method applies to this question?

Translate the statement into integer, fraction or place-value relations and simplify systematically.

What is the verified answer?

75, option B.

What is a common error?

Changing operation order, losing a sign, or simplifying a factor where cancellation is invalid.

How can the result be checked?

Substitute it back, estimate its magnitude, or recompute using an equivalent form.

Related Practice

Parent category aur related practice pages se apni preparation continue karein.

Quantitative Aptitude ke sabhi topics dekhen Number System online test start karein Compound Interest bhi practice karein Data Interpretation bhi practice karein Percentage bhi practice karein Profit & Loss bhi practice karein

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