GMAT: Math 38 | Problem solving | GMAT | Khan Academy

TL;DR

The video discusses problem-solving techniques for solving math questions related to operations, dimensions, and the manipulation of equations.

Transcript

We're on problem 190. If the operation star with a circle around it is defined for all a and b by the equation, a star with a circle around it b is equal to a squared times b over 3, then what does 2 star with a circle around it 3 star with the circle around it minus 1 equal? So 3 star minus 1. That's equal to-- let's see, I'll do this in magenta--... Read More

Key Insights

• ❓ Problem-solving techniques involve understanding and applying defined operations.
• 🔇 Maximizing volume often requires analyzing dimensions and utilizing formulas.
• 😑 Properties like the difference of squares can simplify complex expressions.

Questions & Answers

Q: What is the result of the operation "star with a circle around it" for 2 and 3?

The operation is defined as a squared times b divided by 3. Therefore, applying the operation to 2 and 3 yields 2² * 3 / 3, which simplifies to 4.

Q: How can the maximum volume of a cylindrical canister be achieved in a rectangular box?

To maximize the volume, the radius of the cylindrical canister should be equal to half of the smaller side of the rectangular base. In this case, the radius would be 4 inches.

Q: What is the simplified result of √2 + 1 * √2 - 1 * √3 + 1 * √3 - 1?

By applying the difference of squares property, the expression simplifies to √2² - 1² * √3² - 1², which further simplifies to 2.

Q: How many students are in the calculus class?

By solving the given equations, we find that the number of math majors is 8 and the number of non-math majors is 20, resulting in a total of 28 students.

Summary & Key Takeaways

• The video begins by solving a problem involving a defined operation called "star with a circle around it" and its application to find the value of a mathematical expression.

• The second problem revolves around maximizing the volume of a cylindrical canister inside a rectangular box and determines the radius that yields the maximum volume.

• The third problem presents an equation involving square roots and utilizes the property of a difference of squares to simplify the expression.

• The final problem involves ratios in a calculus class and uses simultaneous equations to find the number of students in the class.