Video summary

Rajasthan Computer Anudeshak Bharti 2026 | Maths Class – संख्या पद्धति (Number System) Part 08

Main summary

Key takeaways

Educational

Main Ideas / Concepts Taught

  • Number system as the foundation of mathematics: The session emphasizes that a strong understanding of number-system concepts is essential, because later math topics build directly on them.

  • Rule of divisibility (main theme): Divisibility rules are repeatedly applied for multiple divisors such as 2, 3, 4, 6, 8, 11, 12, 13, 18, etc.

  • How to solve “which number is divisible by …” type questions:

    • Use divisor-specific conditions, e.g.:
      • Divisible by 2 → check the unit digit
      • Divisible by 3 → check the sum of digits
      • Divisible by 11 → use the alternating sum rule
    • Compare the given options and select the one(s) that satisfy the divisibility condition(s).

  • Counting/combinatorics in ranges (used with divisibility):

    • For questions like: “How many numbers from A to B are divisible by k?”
      • Count multiples up to the upper limit.
      • Subtract multiples up to just before the lower limit.
      • Pay close attention to whether the endpoints are inclusive (e.g., “from … to …” vs “between … and …”).

  • LCM usage:

    • When a number must be divisible by two or more divisors simultaneously, use the LCM of the divisors to combine conditions.

  • Exam strategy / error caution:

    • Don’t guess (“tukka”); computer-based checks won’t allow mistakes.
    • Common errors include misreading:
      • “between” vs “from”
      • “exactly divisible” vs “divisible”

Detailed Methods / Instruction-Like Content

A) Solving “which number is not divisible / is divisible by …” (conceptual steps)

Divisibility by 18

  • Since 18 = 2 × 9, check:
    • Divisible by 9 using the digit-sum rule
    • Divisible by 2 using the unit digit rule
  • If either condition fails → not divisible by 18.

Divisibility by 12

  • Since 12 = 3 × 4, check:
    • Divisible by 4 (typically last two digits form a number divisible by 4)
    • Divisible by 3 (digit sum divisible by 3)
  • Only the option satisfying both is divisible by 12.

Divisibility by 11

  • Apply the alternating sum rule:
    • Compute the alternating sum (difference between sums of digits in alternating positions).
    • If the result is divisible by 11 (commonly 0, 11, 22, …) → divisible by 11.
  • This rule is also used to find unknown digits (e.g., variables like x, y).

Divisibility by 6

  • Since 6 = 2 × 3, check:
    • divisible by 3 (digit sum divisible by 3)
    • divisible by 2 (unit digit even)

Finding smallest number with repeated digit/product exam pattern

  • For exam-style problems like: “When a number is multiplied by 7, all digits of the product are 3”

    • Determine how many times the digit 3 must appear based on digit-length and the divisibility logic mentioned in the explanation.
    • Compute using multiplication/division, then match with the option.

    • Similarly for: “multiplied by 13, all digits are 9”

    • Determine how many 9s must appear.

    • Then compute using 13 × (multiplier) to match the option.

B) Counting divisible numbers in a range ([A, B]) (or “between A and B”)

Core approach taught repeatedly

  • Count multiples up to a limit: The number of integers ≤ N divisible by k is: [ \left\lfloor \frac{N}{k} \right\rfloor ]

  • If endpoints are inclusive (from A to B): [ \left\lfloor \frac{B}{k} \right\rfloor - \left\lfloor \frac{A-1}{k} \right\rfloor ]

“Between” vs “from” language matters

  • The speaker warns that “between 1 and 100” can mean excluding endpoints (effectively 2 to 99), unlike “from 1 to 100”.
  • This changes counts when endpoints are divisible.

Conceptual examples used

  • “How many numbers between 1 and 100 exactly divisible by 7?”
    • The endpoints interpretation affects the count; the session highlights why “between” can differ from “from”.
    • The illustration notes that 100/7 and 99/7 both relate to 14, to demonstrate endpoint sensitivity.

  • Intervals like “50 to 100”:

    • Use: [ \frac{100}{k} - \frac{49}{k} ]

    • (Interpreted using floor values in actual calculation.)

OR / AND logic in divisibility

  • Divisible by “either a or b” (OR): Use inclusion-exclusion style reasoning (carefully handling overlap via LCM/comparisons).

  • Divisible by “both a and b” (AND): Use LCM(a, b) and count multiples of the LCM.

C) Using LCM for simultaneous divisibility

  • Numbers divisible by 2 and 3 (both):

    • [ \text{LCM}(2,3)=6 ]

    • Count multiples of 6 in the required range.

  • Numbers divisible by 2, 3, and 4:

    • [ \text{LCM}(2,3,4)=12 ]

    • Count multiples of 12.

  • For “either 2 or 3”:

    • Use LCM-related overlap handling so overlapping multiples are not double-counted.

D) “Set value of n” technique for conditional divisibility problems

For problems like:

  • “n is an even number. Then n, n+1, n+2 will always be divisible by ____.”

Method taught:

  • Since n has only limited constraints (e.g., even/odd/positive integer), pick the smallest possible value of n that satisfies the condition.
  • Substitute that value into the expressions to determine which divisor is guaranteed by the given condition.
  • Using the smallest valid n simplifies checking and helps confirm the guaranteed divisibility pattern.

Speakers / Sources Featured (as mentioned in subtitles)

Main instructor

  • Chaudhary Saheb (also referred to as “Sir”)

Other participants/commendations named on-screen/in chat style

  • Rihanna ji / Rihanna
  • Dhurandar ji (weak student)
  • Neelam ji
  • Anjali ji / Anjali Choudhary
  • Ayush Sharma ji / Ayush Sharma
  • Prakash ji / Prakash Meghwal ji
  • Piyush ji
  • Mayank Sharma ji
  • G (weak student)
  • Try Master (recurring “answer giver”)
  • Kabra G (mentioned once)
  • Vicky Mehcha ji

YouTube channel context only (no separate source named)

  • Video subject/context: Rajasthan Computer Anudeshak Bharti 2026 (used as exam-oriented practice context)

Original video