Number System
About 7 min · Numerical and Mathematical Ability · English
Time worked out from the lesson's 473 words at 150 words a minute, plus a minute for each question.
The Number System is the foundation of all quantitative topics in SSC MTS Paper 1. Questions appear directly (classify number types, apply divisibility rules, work with fractions) and indirectly (every calculation question uses these concepts).
Key ideas
- Natural numbers (1, 2, 3, ...) count discrete objects. Whole numbers add zero (0, 1, 2, ...). Integers include negatives (..., -2, -1, 0, 1, 2, ...). Every natural number is whole and every whole number is an integer.
- Rational numbers can be written as p/q where p and q are integers and q ≠ 0. All terminating and repeating decimals are rational (e.g. 0.75 = 3/4, 0.333... = 1/3). Irrational numbers cannot be expressed as fractions (e.g. √2, π, √3).
- Even numbers are divisible by 2 (last digit 0, 2, 4, 6, 8). Odd numbers are not (last digit 1, 3, 5, 7, 9). Sum of two evens is even; sum of two odds is even; sum of even and odd is odd.
- Prime numbers have exactly two factors: 1 and the number itself (2, 3, 5, 7, 11, 13, ...). Note: 1 is neither prime nor composite. 2 is the only even prime.
- Composite numbers have more than two factors (4, 6, 8, 9, 10, ...). Every composite number can be expressed as a product of primes (prime factorization).
Watch out for
- Confusing natural and whole numbers: Students forget that 0 is whole but not natural. Fix: Natural starts at 1; whole starts at 0.
- Wrong divisibility by 11: Applying the alternating sum rule incorrectly (forgetting which place is odd/even or miscalculating). Fix: Start from the rightmost digit as position 1 (odd), consistently alternate, and remember to check if difference is 0 or multiple of 11.
- Adding fractions without common denominator: Writing 2/3 + 1/4 = 3/7 (adding tops and bottoms separately). Fix: Always find LCM of denominators first, convert, then add only numerators.
Quick reference
- Divisibility shortcuts: 2 (last digit even), 3 (digit sum ÷ 3), 5 (last digit 0 or 5), 9 (digit sum ÷ 9), 10 (last digit 0), 11 (alternating digit sum difference ÷ 11).
- Rational = can write as fraction; irrational = cannot (like √2, π).
- Even ± even = even; odd ± odd = even; even ± odd = odd.
- Improper to mixed: divide numerator by denominator, quotient = whole, remainder/denominator = fraction.
- Fraction ops: add/subtract (common denominator), multiply (straight across), divide (multiply by reciprocal).
Check yourself: 3 questions
1. A number when divided by 5 leaves a remainder of 3. What will be the remainder when the same number is divided by 15?
2. The sum of three consecutive odd numbers is 63. What is the largest of these three numbers?
3. A number is divisible by both 5 and 12. By which of the following numbers will that number always be divisible?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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