Mastering Advanced GRE Quantitative Techniques
While basic math knowledge is essential for the GRE Quantitative section, advanced techniques can help you solve problems more efficiently and tackle the most challenging questions. Here are five powerful strategies that can elevate your performance.
1. Backsolving: Working Backwards from Answer Choices
Backsolving is particularly effective for complex algebra problems or when setting up equations seems cumbersome. Instead of solving the problem directly, you test the answer choices by plugging them back into the problem.
When to use it: Problems involving variables where solving directly would require complex algebraic manipulations.
Example approach:
- Start with answer choice C (the middle option)
- Substitute this value into the original problem
- If the result is too large, try a smaller value (B or A); if too small, try a larger value (D or E)
This approach can save significant time on problems that would otherwise require setting up and solving complex equations.
2. Number Properties for Quick Calculations
Understanding number properties allows you to make rapid deductions about possible answers without lengthy calculations.
Key properties to know:
- Even and odd number interactions: odd × odd = odd; even × anything = even
- Divisibility rules: quick ways to determine if a number is divisible by 2, 3, 4, 5, 9, etc.
- Prime factorization for finding GCD and LCM quickly
- Properties of perfect squares and their relationships
These properties can help you eliminate impossible answer choices and quickly identify the correct solution.
3. Strategic Estimation
Not every GRE question requires an exact calculation. Sometimes, strategic estimation can lead you to the correct answer more efficiently.
How to implement:
- Round numbers to make calculations easier (e.g., 19.8 to 20)
- Use benchmark fractions to compare values (e.g., knowing that 5/11 is slightly less than 1/2)
- Estimate the magnitude of an answer when exact calculation would be time-consuming
This technique is particularly useful for data interpretation questions and problems involving complex calculations.
4. Visualizing Geometric Relationships
Many GRE geometry problems can be solved quickly by visualizing relationships rather than using formulas.
Key visualization techniques:
- Drawing in auxiliary lines to create triangles or identify relationships
- Using symmetry to deduce angles or distances
- Visualizing 3D objects from different perspectives
- Recognizing similar and congruent triangles
These approaches can transform complex geometry problems into simple applications of basic principles.
5. Picking Smart Numbers for Variables
When a problem involves variables or algebraic expressions, substituting smart numbers can simplify the process.
Guidelines for smart number selection:
- Choose numbers that are easy to work with (10, 100, 2, 5)
- For problems with multiple variables, use distinct numbers (e.g., 2 and 5) to avoid confusion
- For problems involving fractions, choose numbers that make the fractions easy to work with
- For problems involving percentages, consider using 100 as your base value
This technique transforms abstract algebraic problems into concrete numerical ones, often revealing patterns or relationships more clearly.
Applying These Techniques in Your GRE Preparation
The key to mastering these advanced techniques is consistent practice. Incorporate these strategies into your regular study routine:
- Identify problems where these techniques might apply
- Practice applying each technique to different problem types
- Compare the efficiency of using advanced techniques versus standard approaches
- Note patterns in the types of problems where each technique is most effective
With practice, you'll develop the intuition to select the most efficient approach for each problem, saving valuable time during the test and improving your overall performance.
Remember, the GRE Quantitative section tests not just your mathematical knowledge, but also your problem-solving skills. These advanced techniques will help you demonstrate both, maximizing your score potential.