GMAT: Math 20 | Problem solving | GMAT | Khan Academy | Summary and Q&A

TL;DR

Students use ratios and equations to solve math problems.

Key Insights

• 🥳 Ratios and equations can be used to solve problems involving student-to-teacher ratios and increasing enrollment.
• ⚾ When comparing exponents with different bases, it is helpful to rewrite them with the same base to solve inequalities.
• #️⃣ Adding two odd prime numbers always results in an even number, making it impossible for them to equal an odd number such as 91.

Transcript

We're on problem 106. The present ratio of students to teachers at a certain school is 30:1. So the ratio of students to teachers is equal to 30:1. If the student enrollment were to increase by 50 students, and the number of teachers were increased by 5, the ratio of students to teachers would then be 25:1. So if we increase the students by 50 stud... Read More

Questions & Answers

Q: What is the present number of teachers in the given problem?

To find the present number of teachers, we can set up an equation using the given ratios and solve for the variable. The solution is 15.

Q: How can we determine the smallest integer n for which 25ⁿ > 5¹²?

We can rewrite the equation using the same base, 5, and solve for the exponent. 2n > 12, so n must be greater than 6. The smallest integer greater than 6 is 7.

Q: Why is it impossible for x and y to be prime numbers that equal 91 when added together?

Prime numbers greater than 2 are always odd. When adding two odd numbers together, the result is an even number. Since 91 is an odd number, it cannot be formed by adding two prime numbers greater than 2.

Q: Why is the statement "x divided by y is not an integer" true?

If x divided by y were an integer, it would mean that y divides evenly into x, suggesting that x is not a prime number. However, the video states that x is a prime number, therefore making the statement true.

Summary & Key Takeaways

• The video discusses solving math problems involving ratios and equations.

• It provides step-by-step explanations for solving various problems.

• The examples in the video cover topics such as increasing student enrollment and determining the smallest integer.