Key facts

  • BODMAS fixes calculation order as brackets, orders, then division/multiplication from left to right, then addition/subtraction from left to right.
  • The Euclidean algorithm finds the HCF of two numbers by repeated division until the final non-zero remainder appears.
  • The LCM of given numbers uses the highest power of every prime factor that appears in any one of them.
  • Successive percentage change uses the revised base at each step, so a 20 percent rise followed by a 20 percent fall gives a 4 percent net fall.
  • 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 calculation order as brackets, orders, then division/multiplication from left to right, then addition/subtraction from left to right.

  2. 2

    The Euclidean algorithm finds the HCF of two numbers by repeated division until the final non-zero remainder appears.

  3. 3

    The LCM of given numbers uses the highest power of every prime factor that appears in any one of them.

  4. 4

    Successive percentage change uses the revised base at each step, so a 20 percent rise followed by a 20 percent fall gives a 4 percent net fall.

  5. 5

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

  6. 6

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

  7. 7

    Average equals total divided by count; in replacement questions, the average changes by the net change divided by the count.

  8. 8

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

  9. 9

    Mean, median, and mode answer different central-tendency questions; always read the dataset order and frequency before choosing the measure.

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Number System, Divisibility and BODMAS

The decimal system writes every number through place value. For example, 543.21 means 5 x 100 + 4 x 10 + 3 x 1 + 2 x 0.1 + 1 x 0.01. This is why a misplaced zero changes the value sharply. Indian grouping writes 1,00,00,000 for one crore, while international grouping writes the same value as 10,000,000. In CET questions, first read the place value correctly, then choose the operation. Rajasthan's 2011 Census population is 6,85,48,437 and the State's area is 3,42,239 sq km; such official figures are useful for practising Indian-number grouping without inventing data.

Divisibility rules save time. A number is divisible by 2 if the last digit is even, by 5 if the last digit is 0 or 5, and by 10 if the last digit is 0. For 4, check the last two digits; for 8, check the last three digits. For 3 and 9, use the digit sum. A number divisible by both 2 and 3 is divisible by 6. For 11, subtract and add alternate digit sums; a difference that is 0 or divisible by 11 confirms divisibility. Prime factorisation rests on the fact that every integer greater than 1 has a unique product of prime factors, apart from their order.

BODMAS gives the operation sequence: brackets, orders, division, multiplication, addition, and subtraction. Division and multiplication are handled from left to right when they appear at the same level; addition and subtraction are also handled from left to right. In 12 + [6 x {(8 - 3) + 4}] / 9, evaluate the inner bracket first: 8 - 3 = 5, then 5 + 4 = 9, then 6 x 9 = 54, then 54 / 9 = 6, so the final value is 18. Exam cue: if two answer options differ only by a power of ten or by a bracket placement, recheck place value and BODMAS before marking.

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