How to Solve GMAT Math Problems with Fractions and Coordinates

TL;DR

To solve GMAT math problems involving fractions, find a common denominator to simplify equations. For coordinate problems, use properties of perpendicular bisectors to determine unknown points. Additionally, apply algebraic manipulation to solve for unknowns like prices or sums in various scenarios.

Transcript

We're on problem 198. If 1/2 plus 1/3, plus 1/4 is equal to 13/x, which of the following must be an integer? Fascinating. So let's see what they're saying. I don't know. I'm tempted to just work through this. So if I get a common denominator here, the common denominator is going to be 12. 1/2 is 6/12 plus 4/12, plus 3/12. 6 plus 4, plus 3, is 13. S... Read More

Key Insights

• 🆘 Common denominators and algebraic manipulation can help solve fraction problems.
• 🫥 Perpendicular bisectors can be used to find coordinates and determine relationships between lines.
• 💱 Algebraic equations and manipulation can solve problems involving price changes and quantities.

Questions & Answers

Q: How can the value of x be determined in problem 198?

By finding the common denominator and adding the fractions, the equation can be solved to find that x is equal to 12.

Q: How can the coordinates of point C be found in problem 199?

By using the properties of perpendicular bisectors, we can determine that point B is at 3, 2 and that point C is at 3, -2.

Q: What is the approach to solving problem 200?

By setting up equations based on the current price of each towel and the new price, and using algebraic manipulation, the current price can be found to be $3.

Q: What property of consecutive integers determines the answer in problem 201?

The sum of consecutive integers is always even, so the statement that n must be an even number is true.

Summary & Key Takeaways

• Problem 198 involves adding fractions and determining the value of x in the equation 1/2 + 1/3 + 1/4 = 13/x.

• Problem 199 deals with a coordinate system and finding the coordinates of point C when given the coordinates of point A, where y = x is the perpendicular bisector of segment AB.

• Problem 200 focuses on solving for the current price of a towel given information about the number of towels that could be bought at different prices.

• Problem 201 explores the properties of consecutive integers and their sums.