Part 7 - Important Practice Question

Duration: 8 min

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AI Summary

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This video is a lecture on data sufficiency, a common question type in standardized tests like the GATE. The instructor, Yash Jain Sir, introduces the concept using a problem where the goal is to find the value of X given that X and Y are distinct integers and their product is 30. The problem presents two statements: Statement 1 (X is odd) and Statement 2 (X > Y). The lecture systematically analyzes the sufficiency of each statement individually and then together, using a methodical approach of listing all possible integer pairs (x, y) that satisfy xy = 30. The instructor demonstrates that Statement 1 alone is not sufficient because it allows for multiple values of X (e.g., 1, 3, 5, 15, -1, -3, -5, -15). Statement 2 alone is also not sufficient as it allows for multiple values (e.g., 15, 10, 6, 5, 3, 2, -1, -2, -3, -5, -6, -10, -15). However, when both statements are considered together, the only pair that satisfies both conditions (X is odd and X > Y) is (15, 2), which uniquely determines X as 15. The video concludes that both statements together are sufficient to answer the question, which is the correct answer choice for this type of problem.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for a 'DATA SUFFICIENCY' lesson, featuring a futuristic cityscape. It then transitions to a second slide with the title 'Questions' and motivational text about practice. The main content begins with a problem statement on a whiteboard: 'Que: What is the value of X, if X and Y are two distinct integers and their product is 30?'. Below this, two statements are listed: 'Statement 1: X is odd' and 'Statement 2: X > Y'. The instructor, Yash Jain Sir, is visible in a small window. The multiple-choice options are presented: (a) Statement I alone is sufficient, (b) Statement II alone is sufficient, (c) Both statements put together are sufficient, (d) Either of the statements individually is sufficient, (e) Both statements put are not sufficient.

  2. 2:00 – 5:00 02:00-05:00

    The instructor begins to solve the problem by analyzing Statement 1: 'X is odd'. He writes the condition 'xy = 30' and starts listing the possible integer pairs (x, y) that satisfy this equation. He systematically lists the positive factor pairs: (1, 30), (2, 15), (3, 10), (5, 6), (6, 5), (10, 3), (15, 2), (30, 1). He then considers the negative pairs: (-1, -30), (-2, -15), (-3, -10), (-5, -6), (-6, -5), (-10, -3), (-15, -2), (-30, -1). He then applies the condition from Statement 1, 'X is odd', to filter the list. The possible values for X are {1, 3, 5, 15, -1, -3, -5, -15}. Since there are multiple possible values for X, he concludes that Statement 1 alone is not sufficient to determine a unique value for X.

  3. 5:00 – 7:37 05:00-07:37

    The instructor now analyzes Statement 2: 'X > Y'. He reviews the list of all possible integer pairs (x, y) where xy = 30. He applies the condition X > Y to each pair. For example, (15, 2) satisfies 15 > 2, but (2, 15) does not. He identifies all pairs where X > Y, which include (15, 2), (10, 3), (6, 5), (5, 6), (3, 10), (2, 15), (1, 30), (-1, -30), (-2, -15), (-3, -10), (-5, -6), (-6, -5), (-10, -3), (-15, -2), (-30, -1). The possible values for X are {15, 10, 6, 5, 3, 2, 1, -1, -2, -3, -5, -6, -10, -15, -30}. Since there are multiple possible values for X, he concludes that Statement 2 alone is not sufficient. Finally, he combines both statements. He takes the list of X values from Statement 1 ({1, 3, 5, 15, -1, -3, -5, -15}) and the list from Statement 2 ({15, 10, 6, 5, 3, 2, 1, -1, -2, -3, -5, -6, -10, -15, -30}) and finds their intersection. The common values are {1, 3, 5, 15, -1, -3, -5, -15}. He then checks which of these values satisfy X > Y. For X=15, Y=2, 15>2 is true. For X=5, Y=6, 5>6 is false. For X=3, Y=10, 3>10 is false. For X=1, Y=30, 1>30 is false. For negative values, X=-1, Y=-30, -1>-30 is true, but X=-3, Y=-10, -3>-10 is true, and so on. He realizes he needs to check the actual pairs. He identifies that the only pair that satisfies both conditions is (15, 2). Therefore, X=15 is the only possible value. He concludes that both statements together are sufficient to answer the question, and the correct answer is (c). The video ends with a 'THANKS FOR WATCHING' screen.

The video provides a clear, step-by-step demonstration of how to solve a data sufficiency problem. It emphasizes the importance of considering all possible cases, especially when dealing with integers and inequalities. The core method involves listing all potential solutions to the main condition (xy=30) and then applying the constraints from each statement to narrow down the possibilities. The key insight is that a statement is sufficient only if it leads to a unique answer. The instructor effectively shows that while neither statement alone is sufficient, their combination is, which is a common pattern in such questions. The visual aid of writing on the board helps to organize the thought process and makes the logic transparent for the student.