Simple Equations 2 | CAT Preparation 2024 | Algebra | Quantitative Aptitude

Summary

This video discusses a mathematical problem involving two arithmetic sequences: one that decreases by 7 and starts at -1, and another that increases by 7 and starts at 6. The goal is to find how many terms from each series lie within the range of -200 to 200. The process involves determining the range of values for each series and counting the number of terms that satisfy the condition. The final solution combines the results of both series, yielding a total of 57 solutions. The video also promises to discuss shortcuts for solving similar linear equations in future segments.

Takeaways

• 😀 The video explains how to solve a problem involving arithmetic sequences with both negative and positive series.
• 😀 The first series starts at -1 and decreases in steps of 7, while the second series starts at 6 and increases in steps of 7.
• 😀 The goal is to find the total number of terms in each sequence within specified bounds (-200 for the negative series and 200 for the positive series).
• 😀 The negative series decreases by 7, and the maximum value for the sequence is determined by K=28 (which gives a value of -187).
• 😀 The positive series increases by 7, and the maximum value for the sequence is determined by K=27 (which gives a value of 196).
• 😀 The total number of terms in the positive series is 28 (from K=0 to K=27).
• 😀 The total number of terms in the negative series is 29 (from K=0 to K=28).
• 😀 The total number of solutions in the combined series is 57 (28 positive terms and 29 negative terms).
• 😀 The problem is a variation of a common linear equation question often seen in competitive exams, like CAT.
• 😀 The instructor hints that the next video will cover shortcuts for solving similar types of linear equations.

Q & A

What is the main topic discussed in the video?

The main topic discussed in the video is solving a linear equation with series that involve both positive and negative terms, using steps of 7. The video demonstrates how to count the number of terms in both the positive and negative series, which are constrained between -200 and 200.

How is the first series defined in the video?

The first series starts at -1 and decreases by 7 for each subsequent term. It follows the formula: -1 - 7k, where k is a non-negative integer.

How is the second series defined in the video?

The second series starts at 6 and increases by 7 for each subsequent term. It follows the formula: 6 + 7k, where k is a non-negative integer.

What is the maximum value of k for the positive series?

For the positive series, the maximum value of k is 27, because at k = 28, the term exceeds 200. The last term is 6 + 27*7 = 201, which is just over 200.

What is the maximum value of k for the negative series?

For the negative series, the maximum value of k is 28. At k = 28, the term -1 - 28*7 = -197, which is within the -200 limit. If k were 29, the term would exceed -200.

How many terms are in the positive series?

The positive series has 28 terms, from k = 0 to k = 27.

How many terms are in the negative series?

The negative series has 29 terms, from k = 0 to k = 28.

What is the total number of terms in both the positive and negative series combined?

The total number of terms in both the positive and negative series combined is 28 (positive) + 29 (negative) = 57 terms.

What does the speaker plan to discuss in the next video?

In the next video, the speaker plans to discuss shortcuts related to solving linear equations like the ones in this video, specifically focusing on special cases.

What makes the problem discussed in the video similar to previous CAD exam questions?

The problem discussed is similar to CAD (Common Admission Test) questions because it involves understanding arithmetic sequences with specific constraints, such as finding the number of terms within a defined range.