Important Practice Questions on Divisibility Rules

Duration: 15 min

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Inside: a video lesson and guided study material.

Module outline

  1. Quantitative Aptitude: Number System, Percentage, Profit and Loss, Ratio and Proportion (Ratios), Average, Time and Work, Speed Time and Distance, Simple Interest and Compound Interest, Mixture and Alligation, Data Interpretation, Permutation and Combination, Probability, Logarithm, Powers and Exponents (Surds and Indices), Age Problems, Divisibility Rules, Partnership, HCF LCM, Algebra, Pipe and Cistern
  2. Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Analogy, Coding Decoding, Blood Relations, Directions (Direction Test), Syllogisms, Logical Sequence Of Words, Data Sufficiency, Seating Arrangements, Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Arrangement
  3. English Language: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Vocabulary, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Active Passive Voice (Voice), Direct and Indirect Speech, Cloze Test (Cloze Passage), Tenses, Subject Verb Agreement (Verb Noun Agreement), Preposition, Articles, Conjunction, Adverb
  4. Written English Test: English Writing Ability
  5. Coding: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  6. Communication Round: Communication Assessment
  7. DBMS (Technical Interview): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Big Data Systems, NoSQL, Data Warehousing & Mining
  8. SQL (Technical Interview): SQL
  9. Operating Systems (Technical Interview): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  10. Computer Networks (Technical Interview): Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  11. OOPs (Technical Interview): Object Oriented Programming (OOPS)
  12. HR Interview: MR & HR Interview Preparation
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a lecture on divisibility rules, presented by an instructor named Yash Jain Sir from Knowledge Gate Eduventures. The video begins with an introduction to the topic, using a colorful circular diagram that outlines the divisibility rules for numbers 2 through 10. The main content consists of a series of practice problems. The first problem asks to find the value of K in the number K35624 so that it is divisible by 11. The instructor applies the rule for 11, which involves the alternating sum of digits, and solves the resulting equation to find K=6. The second problem involves the number 42573K being divisible by 72. The instructor factors 72 into 8 and 9, then applies the divisibility rules for 8 (last three digits) and 9 (sum of digits) to determine that K=6. The final problem asks for the value of K in 97215K6 to make it divisible by 11, again using the alternating sum rule to find K=3. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide displaying 'DIVISIBILITY RULES' over a background of scattered numbers. This transitions to a colorful, hand-drawn circular diagram titled 'DIVISIBILITY RULES' which visually explains the rules for divisibility by 2, 3, 4, 5, 6, 8, 9, and 10. The instructor, Yash Jain Sir, is visible in a small window, introducing the topic. The next slide, with a space theme, is titled 'Questions on Divisibility' and sets the stage for the problem-solving session.

  2. 2:00 – 5:00 02:00-05:00

    The first problem is presented: 'Find the value of K if K35624 is divisible by 11?'. The instructor begins the solution by writing the number K35624 and applying the divisibility rule for 11, which states that the difference between the sum of the digits in odd positions and the sum of the digits in even positions must be a multiple of 11. He writes the equation: (K + 5 + 2) - (3 + 6 + 4) = 0 or 11. This simplifies to (K + 7) - 13 = 0 or 11, leading to K - 6 = 0 or 11. He concludes that K=6 is the only valid single-digit solution.

  3. 5:00 – 10:00 05:00-10:00

    The second problem is introduced: 'If 42573K is divisible by 72, then the value of K is:'. The instructor explains that 72 = 8 x 9, so the number must be divisible by both 8 and 9. For divisibility by 8, the last three digits, 73K, must be divisible by 8. He tests values and finds that 736 is divisible by 8, so K=6. For divisibility by 9, the sum of the digits (4+2+5+7+3+K) must be divisible by 9. The sum is 21+K, and for K=6, this is 27, which is divisible by 9. He confirms K=6 satisfies both conditions.

  4. 10:00 – 15:00 10:00-15:00

    The third problem is presented: 'Find the value of K if 97215K6 is divisible by 11?'. The instructor applies the alternating sum rule for 11. He writes the equation: (9 + 2 + 5 + 6) - (7 + 1 + K) = 0 or 11. This simplifies to 22 - (8 + K) = 0 or 11. He then solves the equation 22 - 8 - K = 0, which gives 14 - K = 0, so K=14. Since K must be a single digit, he considers the other possibility: 22 - 8 - K = 11, which gives 14 - K = 11, so K=3. He concludes K=3 is the correct answer.

  5. 15:00 – 15:05 15:00-15:05

    The video concludes with a final screen that displays the text 'THANKS FOR WATCHING' in white letters against a dark, gradient background. This is the end of the lecture.

The video provides a structured and practical lesson on divisibility rules. It begins with a conceptual overview using a visual aid, then progresses to a series of progressively challenging problems. The core teaching method is the application of specific rules: the alternating sum for 11, the last three digits for 8, and the sum of digits for 9. The instructor demonstrates a systematic approach to solving each problem, showing the step-by-step derivation of equations and the logical elimination of invalid solutions, particularly when dealing with the constraint that K must be a single digit. The progression from a single rule (11) to a composite rule (72) and back to a single rule (11) effectively reinforces the concepts and problem-solving strategies.

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