GMAT: Math 23 | Problem solving | GMAT | Khan Academy

TL;DR

This video explains the solution to three math problems involving algebraic expressions and mathematical operations.

Transcript

We're on problem 120. David has d books, which is 3 times as many as Jeff, and 1/2 as many as Paula. So d is equal to 1/2 the number of books Paula has. How many books do the three of them have together in terms of d? So they want to know how much d plus j plus p is, in terms of d. So what's j in terms of d? j is equal to-- divide both sides by 3--... Read More

Key Insights

• 🎮 The video covers three math problems, each requiring different mathematical concepts and approaches.
• 😑 Algebraic expressions and equations are used to solve the problems.
• ❓ Understanding the problem statement and identifying relevant variables is crucial in finding the correct solution.
• 🎮 The video demonstrates the importance of careful calculation and attention to detail in solving math problems accurately and efficiently.
• ✖️ These problems involve different mathematical operations such as multiplication, division, addition, and subtraction.
• 😤 In problem 121, the concept of a grid is introduced to visualize the relationships between teams playing each other.
• ❓ Problem 122 highlights the importance of defining the domain of an operation and considering the restrictions on the variables involved.

Questions & Answers

Q: How many books does David have if Paula has d number of books?

David has 3 times as many books as Jeff, and half as many books as Paula. Therefore, David has 3/2(d) number of books.

Q: What is the total number of games played in the league with 8 teams?

Since each team plays each other exactly once and a game involves 2 teams, the total number of games played is 28.

Q: How can we express the operation theta in terms of a and c?

The operation theta is defined as (a minus c) divided by (a plus c). If a theta c is equal to zero, then a must be equal to c.

Q: How do we calculate the average price per person excluding gratuity?

First, we find the price before gratuity by dividing the total price (including gratuity) by 1.15. Then, we divide the price before gratuity by the number of people to find the average price per person.

Summary & Key Takeaways

• Problem 120: Three individuals, David, Jeff, and Paula, have a certain number of books. David has 3 times as many books as Jeff, and half as many books as Paula. The total number of books they have together is 10/3 times the number of books David has.

• Problem 121: In a league with 8 teams, each team plays each other exactly once. Since one team cannot play itself and each game involves 2 teams, the total number of games played is 28.

• Problem 122: An operation theta is defined as the quotient of (a minus b) divided by (a plus b), excluding the case where a is equal to minus b. If a theta c is equal to zero, it implies that c is equal to a.