Part 6 - Important Practice Questions

Duration: 9 min

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Inside: a video lesson and guided study material.

Module outline

  1. Mathematics: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics
  2. General Intelligence & Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, Clerical Aptitude, Verbal Classification
  3. General Awareness: Polity, Evolution of Indian Banking (Banking & Financial Awareness), Physics, Biology, Chemistry, History, Geography, Indian Economy, Static General Knowledge, GK- Current Affairs, NEP 2020, Environment
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This video is a tutorial on Data Sufficiency, a common format in competitive exams like the GMAT or GRE. The instructor, Yash Jain Sir, begins by introducing the topic and the importance of practice. The core of the video is a detailed walkthrough of a specific Data Sufficiency problem. The question asks whether 3^x is less than 500, given that x is an integer. Two statements are provided: Statement 1 is the inequality 4^(x-1) < 4^x - 120, and Statement 2 is the equation x^2 = 36. The instructor systematically analyzes each statement. For Statement 1, he simplifies the inequality to 4^x > 160, which leads to x > 3. For Statement 2, he solves for x, finding x = 6 or x = -6. He then evaluates the sufficiency of each statement individually and together, concluding that Statement 1 alone is sufficient to answer the question, while Statement 2 is not. The video uses a digital whiteboard for all calculations and explanations.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for 'DATA SUFFICIENCY' and a 'Questions' slide emphasizing the importance of practice. The instructor, Yash Jain Sir, introduces the topic. The main problem is presented on a digital whiteboard: 'Que: If x is an integer, is 3^x less than 500?'. Two statements are listed: 'Statement 1: 4^(x-1) < 4^x - 120' and 'Statement 2: x^2 = 36'. The five multiple-choice options for the Data Sufficiency format are displayed below.

  2. 2:00 – 5:00 02:00-05:00

    The instructor begins analyzing the problem. He first focuses on the main question, writing '3^x < 500' on the board. He then evaluates Statement 1: '4^(x-1) < 4^x - 120'. He simplifies this by subtracting 4^(x-1) from both sides, resulting in '4^x - 4^(x-1) > 120'. He factors out 4^(x-1), leading to '4^(x-1) * (4 - 1) > 120', which simplifies to '4^(x-1) * 3 > 120'. Dividing by 3 gives '4^(x-1) > 40'. He then calculates 4^3 = 64, which is greater than 40, so x-1 > 3, meaning x > 4. He then evaluates Statement 2: 'x^2 = 36', which gives x = 6 or x = -6.

  3. 5:00 – 9:26 05:00-09:26

    The instructor now evaluates the sufficiency of the statements. For Statement 1, he concludes x > 4. He then checks if this is sufficient for the main question. He calculates 3^4 = 81, 3^5 = 243, and 3^6 = 729. Since 3^6 = 729 is greater than 500, he determines that x must be less than 6. Therefore, x can be 5, 4, 3, etc. For x=5, 3^5=243<500, which is 'Yes'. For x=6, 3^6=729>500, which is 'No'. Since the answer is not unique, he concludes Statement 1 is not sufficient. For Statement 2, x=6 or x=-6. For x=6, 3^6=729>500, so 'No'. For x=-6, 3^(-6) is a fraction less than 1, so 'Yes'. Since the answer is not unique, Statement 2 is not sufficient. He then considers both statements together, but since Statement 1 is not sufficient, the combination cannot be sufficient. He concludes that the answer is (e) Both statements put together are not sufficient.

The video provides a comprehensive, step-by-step analysis of a Data Sufficiency problem. It demonstrates the core methodology: first, understand the question and the information required. Then, evaluate each statement independently to determine if it provides a unique answer. The instructor correctly identifies that Statement 1 leads to a range of values for x (x > 4) that result in both 'Yes' and 'No' answers to the main question, making it insufficient. Similarly, Statement 2 yields two different values for x, leading to different answers, making it insufficient. The video effectively teaches the process of testing sufficiency by finding counterexamples, which is a key skill for this type of question.

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