Arithmetic Operations
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Quantitative Aptitude - Arithmetic Operations
Fundamentals First
This topic forms the bedrock of quantitative aptitude. It involves being fast and accurate with the four basic operations and their applications on different types of numbers.
- The Four Operations: Addition (+), Subtraction (-), Multiplication (×), Division (÷).
- BODMAS Rule: Defines the correct order of operations: Brackets, Orders (powers, roots), Division, Multiplication, Addition, Subtraction.
- Number Types: Operations apply to Integers, Fractions, and Decimals.
Key Concepts
- Fractions:
- For addition/subtraction, find a common denominator.
- For multiplication, multiply the numerators and denominators straight across.
- For division, invert the second fraction and multiply.
- Decimals:
- For addition/subtraction, align the decimal points vertically.
- For multiplication, multiply the numbers as if they were whole numbers, then place the decimal point in the answer by summing the number of decimal places from the original numbers.
- Percentages: A percentage is a fraction out of 100. Knowing conversions between percentages, fractions, and decimals is crucial (e.g., 25% = 1/4 = 0.25).
⚡ Quick Solving Tips
- Estimation: Before calculating, round the numbers to get a rough answer. This helps you spot errors and eliminate options. E.g., \( 48.9 \times 10.2 \) is roughly \( 50 \times 10 = 500 \).
- Digital Sum Method: The sum of the digits of a number can be used to verify multiplication or complex calculations. The digital sum of the result should match the digital sum of the operation performed on the input numbers' digital sums.
- Percentage Trick: Remember that \( x\% \) of \( y \) is the same as \( y\% \) of \( x \). For example, calculating \( 75\% \) of \( 24 \) is easier when thought of as \( 24\% \) of \( 75 \) or simply \( \frac{3}{4} \) of 24, which is 18.
✍️ Suggestions for Examinations
- Speed and Accuracy are everything. Practice daily. Use apps or worksheets for timed drills on basic calculations.
- Learn your tables. Knowing multiplication tables up to 20, squares up to 30, and cubes up to 15 by heart is a significant advantage.
- Avoid the calculator for basic practice to build mental strength. In many exams, an on-screen calculator can be slower than mental tricks for simple operations.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
- Clocks
- Stocks & Shares
- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations
- Quadratic Equations
Other Subjects
- Quantitative Aptitude
- Reasoning
- English Language
- Current Affairs
- Constitutional Law
- Code of Civil Procedure
- Criminal Procedure (CrPC and BNSS)
- Criminal Law (IPC and BNS)
- Law of Evidence (IEA and BSA)
- Law of Contract
- Law of Torts and Consumer Protection
- Transfer of Property
- Family Law
- Specific Relief and Limitation
- Legal Language and Drafting
- General Awareness / General Knowledge (GK)