# GMAT: Math 39 | Problem solving | GMAT | Khan Academy | Summary and Q&A

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December 17, 2008
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GMAT: Math 39 | Problem solving | GMAT | Khan Academy

## TL;DR

This video explains how to find the minimum path between two points on a grid and solve ratios in problem-solving scenarios.

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### Q: How can you determine the minimum path between two points on a grid?

By analyzing the grid and counting the number of ways to reach each point, taking into account the different possible routes at each intersection.

### Q: How do you calculate the number of possible routes between two points on a grid?

You can sum the number of ways to reach a point from different paths. For example, in the provided grid, the number of routes to a specific point is the sum of the number of routes from the adjacent points.

### Q: How can you solve a ratio problem involving an altered ratio?

Start by determining the new ratio by doubling or halving the original ratio, as specified. Then, rewrite the ratios to compare the desired variables, and solve for the unknown using cross-multiplication.

### Q: How can you calculate the percentage of people who answered two questions correctly?

Analyze the information given and set up variables for the percentage of people who answered each question correctly. Use the given information to set up an equation and solve to find the desired percentage.

## Summary & Key Takeaways

• The video introduces a problem where Pat needs to find the minimum path between two points on a grid, using horizontal and vertical streets.

• By analyzing the different paths and applying logic, the video demonstrates how to calculate the number of possible routes between the two points.

• The video then presents another problem involving ratios, where the goal is to find the amount of water in a solution based on an altered soap-alcohol ratio.