Key facts

  • BODMAS fixes operation order as brackets, orders, division/multiplication left to right, and addition/subtraction left to right.
  • The Euclidean algorithm finds HCF by repeated remainders; the final non-zero remainder is the HCF.
  • LCM uses the highest power of every prime factor appearing in the given numbers.
  • Successive percentage change uses the revised base after each step, so percentage changes do not simply add.
  • Profit and loss percentages are measured on cost price, while discount percentage is measured on marked price.

Key Points at a Glance

  1. 1

    BODMAS fixes operation order as brackets, orders, division/multiplication left to right, and addition/subtraction left to right.

  2. 2

    The Euclidean algorithm finds HCF by repeated remainders; the final non-zero remainder is the HCF.

  3. 3

    LCM uses the highest power of every prime factor appearing in the given numbers.

  4. 4

    Successive percentage change uses the revised base after each step, so percentage changes do not simply add.

  5. 5

    Profit and loss percentages are measured on cost price, while discount percentage is measured on marked price.

  6. 6

    Partnership profit share is proportional to capital multiplied by time, not capital alone.

  7. 7

    Time-and-work and pipes-and-cisterns questions are solved by adding or subtracting rates.

  8. 8

    For equal distances at two speeds, average speed is 2uv/(u+v), not the arithmetic mean.

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Number System, Divisibility and BODMAS

Basic numeracy starts with place value. In the decimal system, each digit is read as a power of 10; for example, 543.21 equals 5 x 10^2 + 4 x 10^1 + 3 x 10^0 + 2 x 10^-1 + 1 x 10^-2. This matters in objective questions because one misplaced zero changes the option. Indian grouping and international grouping may show the same value differently, so read the number first and then calculate.

Divisibility rules reduce calculation time. A number is divisible by 2 if the last digit is even, by 5 if the last digit is 0 or 5, by 10 if the last digit is 0, by 4 if the last two digits are divisible by 4, by 8 if the last three digits are divisible by 8, by 3 or 9 if the digit sum is divisible by 3 or 9, by 6 if both 2 and 3 rules hold, and by 11 through the alternating digit-sum method. Prime factorisation is the base of many questions: the first primes up to 100 include 2, 3, 5, 7, 11, 13, 17, 19, 23 and continue to 97. Every integer greater than 1 has a unique prime-factor form, and if n = p^a x q^b x r^c, the number of factors is (a+1)(b+1)(c+1).

BODMAS gives the fixed order: brackets, orders, division/multiplication left to right, and addition/subtraction left to right. In 12 + [6 x {(8 - 3) + 4}] / 9, solve 8 - 3 = 5, then 5 + 4 = 9, then 6 x 9 = 54, then 54 / 9 = 6, and finally 12 + 6 = 18. The exam habit is simple: settle place value, test divisibility, then follow BODMAS without skipping brackets.

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