Key facts

  • This topic belongs to the CET Senior Secondary 2026 Logical Reasoning and Mathematics block, especially arithmetic, work-speed, mensuration, charts, c...
  • LCM uses all required prime factors with highest powers; HCF uses only common factors with lowest powers.
  • Percentage, profit-loss and interest questions depend on identifying the correct base quantity before calculating.
  • Simple interest keeps the principal fixed; compound interest changes the base after each completed compounding period.
  • Time-work and pipes should be solved through rates: work per unit time is added or subtracted.

Key Points at a Glance

  1. 1

    This topic belongs to the CET Senior Secondary 2026 Logical Reasoning and Mathematics block, especially arithmetic, work-speed, mensuration, charts, code-decode and sitting arrangement.

  2. 2

    LCM uses all required prime factors with highest powers; HCF uses only common factors with lowest powers.

  3. 3

    Percentage, profit-loss and interest questions depend on identifying the correct base quantity before calculating.

  4. 4

    Simple interest keeps the principal fixed; compound interest changes the base after each completed compounding period.

  5. 5

    Time-work and pipes should be solved through rates: work per unit time is added or subtracted.

  6. 6

    Time-speed-distance depends on consistent units and the identity distance = speed x time.

  7. 7

    Mensuration starts by separating perimeter, area, surface area and volume; the unit is the first answer check.

  8. 8

    Graphs, code-decode and sitting arrangement require reading the given scale, pattern or direction before calculation.

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Syllabus fit and arithmetic base

For CET Senior Secondary 2026, this topic sits inside the official Logical Reasoning and Mathematics block. The relevant syllabus bullets are: LCM and HCF; average; profit and loss; percentage; simple interest; compound interest; ratio and proportion; time, speed, distance, work and time; area of triangle, circle, ellipse, rectangle, sphere and cylinder; volume of sphere, cylinder, cube and cone; graphical representation of data; code and decode; sitting arrangement; mental ability and analytical ability. That means this lesson should not drift into graduation-only algebra or India-wide economy facts. It should stay with school arithmetic, movement, work, mensuration, data reading and basic reasoning.

LCM and HCF are factor-based tools. HCF is the greatest number that divides all given numbers exactly. LCM is the smallest number divisible by all the given numbers. For 12 and 18, HCF is 6 and LCM is 36. In prime factorization, common factors with the lowest powers give HCF; all required prime factors with the highest powers give LCM. In word problems, HCF is usually signalled by largest equal size, while LCM is signalled by repeated events meeting again.

Average means total divided by the number of observations. If marks are 60, 70, 75, 80 and 90, the average is 375/5 = 75. When a new observation is added, update the total and count first. Ratio compares quantities in the same unit. If boys:girls = 3:2 and total students are 50, the 5 equal parts represent 50 students, so one part is 10; the numbers are 30 and 20. Proportion means two ratios are equal; if a:b = c:d, then ad = bc.

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