GMAT: Math 49 | Problem solving | GMAT | Khan Academy | Summary and Q&A

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December 18, 2008
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Khan Academy
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GMAT: Math 49 | Problem solving | GMAT | Khan Academy

TL;DR

This video discusses solving GMAT math problems on topics such as coordinate geometry, reverse digits of a number, circle tangents, and parallel resistances, as well as probability calculations.

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Questions & Answers

Q: How do you find the equation of a line in a coordinate system?

To find the equation of a line, you need to determine the slope using the change in y over the change in x, and the y-intercept using a point on the line. The equation is typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Q: How do you find the radius of a circle tangent to both axes?

Drawing a line from the center of the circle to the x-axis creates a right triangle. The distance from the center to the x-axis is equal to the radius. Using the Pythagorean theorem, you can find the radius in terms of the distance from the origin to the center of the circle.

Q: What is the formula for calculating combined resistance in parallel resistances?

The formula for calculating combined resistance in parallel resistances is 1/r = 1/x + 1/y, where r is the combined resistance and x and y are the individual resistances.

Q: How do you calculate the probability of a specific event occurring?

To calculate the probability of a specific event occurring, you multiply the probabilities of each independent event together. If there are events that should not occur, you subtract the probability of those events from 1 to find the probability of the desired event.

Summary & Key Takeaways

  • The video begins with a discussion of how to find the equation of a line in a coordinate system using slope and the y-intercept.

  • It then moves on to solving a problem involving reversing the digits of a two-digit number and finding the difference between the original and reversed numbers.

  • The next problem involves finding the radius of a circle tangent to both axes, using the Pythagorean theorem and the distance from the origin to the center of the circle.

  • The video then covers the concept of parallel resistances in an electric circuit and how to calculate the combined resistance.

  • Finally, it concludes by solving a probability problem involving three individuals attempting to solve a problem, and finding the probability that two individuals solve it while the third does not.

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