GMAT: Data sufficiency 34 | Data sufficiency | GMAT | Khan Academy

TL;DR

Problem solving involving inequalities and geometry circles; determining values of variables and calculating circumference.

Transcript

We're on problem 135. I just did some pilates, so I'm slightly out of breath. If x is less than 0, is y greater than 0? All right, statement number 1, x/y is less than 0. So this is actually pretty useful. They're telling us that x is a negative number. So we have a negative here, and we're dividing it by some other number. They're telling us that ... Read More

Key Insights

• ❎ Negative numbers divided by positive numbers yield negative results.
• 🙃 Comparing the lengths of the sides of a triangle can lead to solving for the radius of a circle.
• 🫠 Understanding the relationship between arcs and the circumference of a circle.
• 🙃 Utilizing Pythagorean theorem to find the lengths of sides in a triangle.
• 🆘 Linear equations can help solve for unknown variables.
• 🦻 Patterns and matching can aid in solving equations.
• 🟰 Isosceles triangles have equal side lengths.

Questions & Answers

Q: How does statement 1 in problem 135 help determine the value of y?

Statement 1 informs us that x/y is less than 0, implying that x is negative. Dividing a negative by any positive number results in another negative, so y must be positive.

Q: Why is statement 2 in problem 135 insufficient in determining the value of y?

Statement 2 states that y minus x is greater than 0, which does not provide enough information about the values of x and y. It is possible for y to be greater than 0 or not depending on different scenarios.

Q: What is the approach to solving problem 136 and determining the circumference of the circle?

By solving for x in statement 1 (perimeter of triangle OXZ), we find that x equals the radius of the circle. Using the formula for circumference (2 pi times the radius), we can calculate the circumference of the circle.

Q: How do both statements in problem 137 contribute to finding the value of a to the fourth power minus b to the fourth power?

Statement 1 establishes the equation a squared minus b squared equals 16, while statement 2 provides the equation a plus b equals 8. By combining these equations and solving for a and b, we can find the value of a to the fourth power minus b to the fourth power.

Summary & Key Takeaways

• Problem 135: Solving an inequality to determine the range of a variable, y, based on negative values.

• Problem 136: Finding the circumference of a circle by solving for the radius using the perimeter of a triangle.

• Problem 137: Simplifying and solving equations to find the value of a to the fourth power minus b to the fourth power.