GMAT: Math 11 | Problem solving | GMAT | Khan Academy

TL;DR

This video provides solutions to various math problems, including ratios, percentages, and probability.

Transcript

We're on problem 61. If 1 kilometer is approximately 0.6 miles, which of the following best approximates the number of kilometers in 2 miles? So we want to know 2 miles. So we could set up a ratio. We could say, 0.6 miles are to 2 miles as 1 kilometer is to x kilometers. And you could cross multiply. You could say 0.6 is equal to 2. And that x is e... Read More

Key Insights

• 😀 Ratios can be used to approximate quantities, such as kilometers in miles.
• 💱 Percentage changes can be applied sequentially to calculate the value of an investment account.
• 🥳 Ratios can help determine the expected number of defective items in a larger shipment.

Questions & Answers

Q: How can we approximate the number of kilometers in 2 miles?

By setting up a ratio with 0.6 miles to 2 miles and solving for x, which gives us approximately 3 1/3 kilometers.

Q: What is the value of an investment account after three years with percentage changes?

The account starts with $10,000 and grows by 10% (to $11,000), then grows by 5% (to $11,550), and finally decreases by 10% (to $10,350).

Q: How can we calculate the expected number of defective chips in a shipment?

We calculate the ratio of defective chips to total chips for different shipments, combine them, and then use the ratio to determine that 1 chip in every 3,000 will be defective in a shipment of 60,000 chips.

Q: How do we find the probability of the sum of two integers being 9?

We analyze the combinations that equal 9 from two different sets and determine that there is a 1 in 5 chance of the sum being 9, giving a probability of 0.2.

Summary & Key Takeaways

• Problem 61: Approximating the number of kilometers in 2 miles using a ratio.

• Problem 62: Calculating the value of an investment account after three years with different percentage changes.

• Problem 63: Finding the expected number of defective chips in a shipment based on ratios.

• Problem 64: Determining the probability of the sum of two integers being 9 from different sets.