GMAT: Data sufficiency 11 | Data sufficiency | GMAT | Khan Academy

TL;DR

The video analyzes three GMAT practice questions involving geometry, algebra, and problem-solving.

Transcript

Problem 51. Actually, let me scroll all the way up, problem 51. They drew a little triangle here, which I assume I need, so I'll draw it as well. That side is flat and that side goes down like that, and then they draw some angles. This is being angle x, this is angle y, this is angle z. And they say, what is the value of z in the triangle above? Fa... Read More

Key Insights

• 🔺 Understanding the properties of a triangle, particularly the sum of its angles, is essential for solving geometry problems.
• 🗂️ Dividing an equation and simplifying can help isolate variables and solve for unknowns.
• ❓ Combining multiple statements may be necessary to determine the complete solution to a problem.

Questions & Answers

Q: How is the value of angle z determined in Problem 51?

The value of z is determined by the equation x + y + z = 180. From statement 1, we know that x + y = 139, allowing us to solve for z.

Q: How do we solve the equation xz = 12 in Problem 52?

Statement 1 provides x^2 * yz = 12xy, which simplifies to xz = 12. Dividing both sides by x and y, we get xz = 12. Thus, statement 1 is sufficient to determine the value of xz.

Q: How do we determine the number of employees in Problem 53?

Statement 1 states that if 3 employees are hired, there will be at least 20 employees. Statement 2 indicates that if 3 employees resign, there will be fewer than 15 employees. Both statements are required to determine the exact number of employees.

Summary & Key Takeaways

• Problem 51: In a triangle, the value of angle z is determined by the equation x + y + z = 180. Statement 1 provides x + y = 139, which allows us to solve for z. Statement 2 (y + z = 108) is insufficient.

• Problem 52: The equation xz = 12 is given. Statement 1 provides x^2 * yz = 12xy, which simplifies to xz = 12. Statement 2 (z/4 = 3/x) can also be simplified to xz = 12. Each statement alone is sufficient to determine the value of xz.

• Problem 53: The number of employees at a company is in question. Statement 1 indicates that if 3 employees are hired, there will be at least 20 employees, while statement 2 states that if 3 employees resign, there will be fewer than 15 employees. Both statements are required to determine the exact number of employees.