Number System & Basics

C ClearYourExam 1 / 9 Maths · Quantitative Aptitude The Number System is the foundation of every objective and descriptive math paper. SSC, RRB Group D/NTPC, Banking and most state exams begin with 3–5 questions that directly test fractions, decimals, divisibility, LCM/HCF, BODMAS and roots…

Why it matters

C ClearYourExam 2 / 9 Expect 4–6 marks in SSC CGL/CHSL, 3–4 marks in RRB Group D, and 2–3 marks in IBPS Clerk. Divisibility shortcuts and BODMAS speed are the fastest scoring areas.

Number System (Fractions, Decimals, Integers, Divisibility)

C ClearYourExam 3 / 9 1 / 4 The number system classifies numbers into Natural (1, 2, 3…), Whole (0, 1, 2…), Integers (…-2, -1, 0, 1, 2…), Rational (p/q form), Irrational (√2, π) and Real numbers. Exam tip A number divisible by 12 must be divisible by both 3 and 4 (not 2 and 6). Always pick co-prime factors.

LCM and HCF (Least Common Multiple & Highest Common Factor)

C ClearYourExam 4 / 9 2 / 4 HCF is the largest number that divides two or more numbers exactly; LCM is the smallest number that is exactly divisible by them. Exam tip When a problem asks for the largest tile/measure that fits exactly, use HCF. When it asks for the smallest distance/time/quantity that contains all given quantities a whole number…

BODMAS / PEMDAS (Order of Operations)

C ClearYourExam 5 / 9 3 / 4 BODMAS is the rule for the order in which a mixed expression is simplified: Brackets → Of → Division → Multiplication → Addition → Subtraction. Exam tip A negative sign before a bracket flips every sign inside when the bracket is removed: −(a − b + c) = −a + b − c.

Square Roots & Cube Roots

C ClearYourExam 6 / 9 4 / 4 The square root (√n) of a number is the value which when multiplied by itself gives the original number. The cube root (∛n) is the value which when cubed gives the original number. Exam tip For perfect squares, the unit digit is always 0, 1, 4, 5, 6 or 9 — never 2, 3, 7 or 8. Use this to eliminate options instantly.

Short Tricks

C ClearYourExam 7 / 9 Divisibility by 7 (double-and-subtract) Double the last digit, subtract from the rest. Repeat. If the result is divisible by 7 (or is 0), the original number is too. Divisibility by 11 (alternate-digit-sum) Take the difference between the sum of digits in odd positions and the sum of digits in even positions. If it is 0 or a multiple of 11, the… Square of any number ending in 5 For a number ending in 5 (say n5): square = (n × (n+1)) followed by 25.

Quick Revision Facts

C ClearYourExam 8 / 9 Sum of first n natural numbers = n(n+1)/2. Sum of squares of first n naturals = n(n+1)(2n+1)/6. Sum of cubes of first n naturals = [n(n+1)/2]². 0 is even; 1 is neither prime nor composite; 2 is the only even prime.

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