GMAT: Math 30 | Problem solving | GMAT | Khan Academy

TL;DR

This video covers the solution to multiple math problems, including filling a pool, squaring roots, solving equations, calculating percentages, and finding areas.

Transcript

We're on problem 154. An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. So you could say you can fill 3/5 of a pool every 8 hours, which is just another way of saying that you can fill, let's see, 3/5 divided by 8 is 3 over-- what's 5 times 8? 3/40 pools per hour. I have a feeling that they're ju... Read More

Key Insights

• ☠️ It is essential to divide the remaining volume of a pool by the filling rate to determine the time needed to complete filling.
• ❎ Squaring both sides of an equation can help solve problems involving square roots.
• 🚱 Evaporating water from a solution does not affect the concentration of non-volatile substances.
• 🆘 Substituting values from one equation into another can help solve systems of equations.
• 🗂️ The probability of an event occurring can be calculated by dividing the desired outcomes by the total number of possible outcomes.
• ❓ Prime factorization is helpful for solving problems involving products of integers.
• 💠 The area of a path can be calculated by subtracting the area of the inner shape from the area of the outer shape.

Questions & Answers

Q: How do you calculate the remaining time needed to fill a pool based on its filling rate?

To calculate the remaining time, divide the remaining volume (2/5 of the capacity) by the filling rate (3/40 pools per hour). In this case, it takes 5 hours and 20 minutes to finish filling the pool.

Q: How do you solve an equation involving square roots and multiplication?

Start by squaring both sides of the equation, then simplify. Next, multiply both sides by the necessary factor to isolate the variable. In this example, dividing both sides by x yields x = 2/3.

Q: How do you calculate the percentage of sodium chloride in a solution after water evaporates?

Divide the initial amount of sodium chloride by the new total volume of the solution. In this case, the percentage of sodium chloride becomes 6.67% after losing 2,500 gallons of water from the original 10,000-gallon solution.

Q: How do you determine the value of y in an equation involving variables x and y?

Substitute the value of x given in the equation into the other equation and solve for y. In this example, y equals 8.

Summary & Key Takeaways

• The video explains how to calculate the remaining time needed to fill a pool, given that it takes 8 hours to fill 3/5 of its capacity.

• It provides a method for finding the value of x in an equation involving square roots and multiplication.

• The video demonstrates solving a problem involving the percentage of sodium chloride in a solution after a certain amount of water evaporates.

• It explains how to find the value of y in an equation involving variables x and y, given another equation involving the same variables.

• The video teaches how to calculate the probability of selecting a woman from a committee, after adding members to the committee.

• It covers finding the values of four integers, given their product, and determining the sum of two specific integers.