Key facts

  • BODMAS fixes the order of operations as brackets, orders, division, multiplication, addition and subtraction.
  • HCF is the largest common divisor of the given numbers, while LCM is the smallest positive common multiple.
  • Successive percentage change uses the revised base at each step, so increases and decreases are not added mechanically.
  • Profit and loss percentages are calculated on cost price, but discount percentage is calculated on marked price.
  • Simple interest grows linearly on the principal, while compound interest changes the base after every period.

Key Points at a Glance

  1. 1

    BODMAS fixes the order of operations as brackets, orders, division, multiplication, addition and subtraction.

  2. 2

    HCF is the largest common divisor of the given numbers, while LCM is the smallest positive common multiple.

  3. 3

    Successive percentage change uses the revised base at each step, so increases and decreases are not added mechanically.

  4. 4

    Profit and loss percentages are calculated on cost price, but discount percentage is calculated on marked price.

  5. 5

    Simple interest grows linearly on the principal, while compound interest changes the base after every period.

  6. 6

    In partnership questions, the profit share is proportional to capital multiplied by time.

  7. 7

    Time-and-work and pipes-and-cisterns questions are solved by rates, with productive rates added and opposing rates subtracted.

  8. 8

    Mensuration questions first require the candidate to identify whether the answer is length, area, surface area or volume.

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Arithmetic Basics and BODMAS

Numerical ability starts with place value, operation order and small-number fluency. In the decimal system, every integer is built from powers of 10. For example, 543.21 means 5 x 10^2 + 4 x 10^1 + 3 x 10^0 + 2 x 10^-1 + 1 x 10^-2. In objective questions, this matters because a misplaced zero or comma can change the option completely. Indian grouping such as 1,00,00,000 and international grouping such as 10,000,000 may show the same value, but the candidate must read the place values correctly before applying any formula.

BODMAS gives the fixed order for simplification: brackets, orders, division, multiplication, addition and subtraction. Division and multiplication are handled from left to right at the same priority, and addition and subtraction are also handled from left to right. In a nested expression such as 12 + [6 x {(8 - 3) + 4}] / 9, the inner bracket gives 5, then 9, then 54, then 6, and the final answer is 18. Common divisibility rules also save time: even last digit for 2, last digit 0 or 5 for 5, digit sum for 3 and 9, last two digits for 4, last three digits for 8, and alternating digit sum for 11.

Exam use: solve the bracket and divisibility layer first, because most arithmetic traps are created before the main calculation begins.

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