GMAT: Math 31 | Problem solving | GMAT | Khan Academy

TL;DR

This content explains problem-solving techniques and demonstrates how to work with ratios in math problems.

Transcript

We're on problem 161. The positive integer n is divisible by 25. If the square root of n is greater than 25, which of the following could be the value of n divided by 25? So what could be a valid value for n divided by 25? So let's see if we can manipulate this a little bit. If we square both sides, we get n, right-- the square of the square root o... Read More

Key Insights

• ❎ Manipulating equations by squaring both sides and then dividing helps solve problems involving inequalities with square roots.
• 👻 Converting fractions to a common denominator allows for easier addition or comparison.
• 🥳 Assigning variables to ratio numbers and expressing weights in terms of these variables simplifies solving ratio problems.
• 🥳 Ratios can be used to find the relative quantities of different components in a mixture or combination.
• 🍳 Problem-solving often involves breaking down complex problems into simpler steps or equations.
• 🥳 Understanding basic concepts like fractions, ratios, and equations is crucial for solving mathematical problems.
• 👻 Substituting variables back into an equation allows for easier calculation and determination of unknown values.

Questions & Answers

Q: How can we determine a valid value for n/25 when the square root of n is greater than 25?

To find a valid value for n/25, we square both sides of the equation and then divide both sides by 25. The resulting value of n/25 must be greater than 25.

Q: How do we simplify the expression 1/(1 + 1/2 + 1/3)?

To simplify, we find a common denominator by converting 1/2 to 3/6 and 1/3 to 2/6. Then, adding these fractions yields 7/6. Taking the reciprocal gives us the simplified value of 7/10.

Q: How can we solve a ratio problem involving apples, peaches, and grapes?

By assigning a variable to the ratio number (x) and using it to express the weight of each fruit (6x, 5x, and 2x), we can set up an equation to solve for x and determine the weights of apples, peaches, and grapes.

Q: What is the difference in weight between apples and grapes in problem 163?

To find the difference, we solve the equation 6x + 5x + 2x = 39, where x represents the ratio number. Once we find the value of x, we can subtract the weight of grapes (2x) from the weight of apples (6x) to determine the difference.

Summary & Key Takeaways

• In problem 161, the video explains how to determine a valid value for n/25 when the square root of n is greater than 25.

• Problem 162 involves manipulating fractions to find the value of 1/(1 + 1/2 + 1/3), which simplifies to 7/10.

• Problem 163 demonstrates how to solve a ratio problem involving apples, peaches, and grapes and find the difference in weight between apples and grapes.