GMAT: Math 24 | Problem solving | GMAT | Khan Academy

TL;DR

Solving various math problems involving fractions, rates, and compound interest.

Transcript

And problem 124. According to a car dealer sales report, 1/3 of the cars sold during a certain period were sedans, and 1/5 of the other cars sold were station wagons. So 1/3 of the cars sold, so the total, were equal to sedans. And 1/5 of the other cars sold were station wagons, so 1/5 of the remainder of this. So that's 1/5 of the 2/3 cars that we... Read More

Key Insights

• 😒 Problem 124 demonstrates the use of equations and fractions to determine the number of sedans and station wagons sold.
• ❓ Problem 125 highlights the relationship between positive integers and the inequality they create.
• ☠️ Problem 126 illustrates the concept of combined rates and how they affect the time it takes to complete a task.
• 📦 Problem 127 showcases the cost comparison between separate and combined packages, emphasizing the importance of understanding given variables.

Questions & Answers

Q: How is Problem 124 solved?

Problem 124 is solved by setting up equations based on the given fractions and variables for the number of sedans and station wagons. By substituting variables and simplifying, the solution is found.

Q: How is Problem 125 approached?

Problem 125 involves determining which expression must be greater than 1. By understanding that p/q is less than 1 implies p is less than q, the solution is found by algebraically manipulating the inequality and identifying the correct expression.

Q: How is Problem 126 solved?

Problem 126 requires calculating the time it takes for two machines to complete an order when working together. By combining their rates and determining the time based on the combined rate, the solution is found.

Q: How is Problem 127 analyzed?

Problem 127 compares the cost of mailing separate packages versus combining them. By setting up cost expressions for each scenario and subtracting them, it is determined that combining the packages is cheaper.

Summary & Key Takeaways

• Problem 124 deals with determining the number of sedans and station wagons sold based on given fractions. The solution involves solving equations and substituting variables.

• Problem 125 examines the relationship between two positive integers and determines which expression must be greater than 1. By multiplying both sides by the positive integers, the solution is found.

• Problem 126 involves calculating the time it takes for two machines to complete a production order. By combining the rates of the two machines, the total time is determined.

• Problem 127 analyzes the cost of mailing separate packages versus combining them. By comparing the cost expressions, it is determined that combining the packages is cheaper.

• Problem 128 tackles compound interest by using the formula to determine the approximate time it takes for an investment to double. The total amount of the investment after 18 years is calculated using the rate and approximate doubling time.