While much of the subject matter on the Quant section of the GRE will be familiar to you, one common question type is likely to be unfamiliar: Quantitative Comparisons. QC questions are extremely important to focus on in your GRE prep, as they account for over a third of the entire Quantitative section of the test. However, it’s likely that you haven’t encountered this particular question structure before.
Luckily, just because the question structure is unique, that doesn’t mean you shouldn’t be able to solve them. It just means you should focus on learning how to work with QC questions as you proceed through your GRE prep. Here, we’ve collected 7 powerful tips for mastering GRE Quantitative Comparison questions. If you focus on these tips as you study for the GRE, you’ll be in a great position to maximize your GRE Quant score.
Familiarize Yourself with the Question Structure
GRE Quantitative Comparison questions aren’t necessarily harder than any of the other GRE Quant questions. In fact, QC questions test your knowledge of the same subject matter, which means arithmetic, algebra, geometry, and data analysis. The only thing that makes QC questions seem uniquely hard is the unfamiliar question structure. QC questions require you to apply the same quantitative knowledge in a slightly unfamiliar way.
The basic structure of every QC question is the same. Each QC question gives you two different quantities, as well as some additional information (sometimes called the “constraint”). It’s your job to determine whether one quantity is greater than the other, whether they’re equal, or whether their relationship can’t be determined from the given information.
This sounds simple, but the complication lays in the fact that the two quantities are not absolute. They’re typically written as algebraic expressions with variables, as unspecified geometric quantities (like polygon side lengths or angle measures), or as unspecified data analysis measures (like probabilities, means/averages, medians, etc.).
Developing familiarity with the QC question structure is the key to solving them accurately and efficiently, and the only way to develop this familiarity is through practice. Even if you’ve mastered arithmetic, algebra, geometry, and data analysis, if you took the GRE cold, you’d likely lose a lot of time just trying to understand how the QC questions work.
Memorize the Answer Choices
Another key to solving QC questions accurately and efficiently is to memorize the answer choices. Luckily, the answer choices for every QC question are exactly the same. This means you can save time by skipping the instructions and answer choices and diving straight into the content of each individual QC question.
The answer choices to every QC question are as follows:
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given
Memorize the Relevant GRE Rules and Formulas
At their core, QC questions are testing your knowledge of the fundamental rules and formulas of the mathematical subject matter covered by the entire GRE Quantitative section, which includes 12th-grade arithmetic, algebra, geometry, and data analysis.
Ideally, you should make a “cheat sheet” of all the necessary rules and formulas to aid in your prep. But don’t let yourself depend on always being able to consult this cheat sheet. You should do your best to memorize each of these formulas, since they won’t be given to you on the actual GRE.
In Arithmetic and Algebra, you should memorize the following:
- The laws of exponents
- The laws of square roots
- The laws of even and odd numbers
- The formulas for calculating percentages, including percent change
- The solutions to quadratic equations
- The formulas for calculating simple and compound interest
In Geometry, you should memorize the following:
- The formulas for calculating the area and perimeter of a triangle, rectangle, square, and trapezoid
- The formulas for calculating the area, circumference, and diameter of a circle, as well as the length of an arc and the area of a sector
- The formula for calculating the volume of a sphere, cylinder, cube, pyramid, and rectangular prism
- The formula for calculating the sum of the angle measures for polygons
- The Pythagorean theorem
- Common right triangle side-length ratios, including 3:4:5, 5:12:13, and 8:15:17
- The side-length ratios for special right triangles, such as 45-45-90 and 30-60-90 triangles
- The formula for calculating the slope and equation of a line in a coordinate plane
- The formula for calculating distance as a function of rate and time
- The relationships between opposite angles, adjacent angles, corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles
In Data Analysis, you should memorize the following:
- How to calculate the mean, median, and mode of a data set
- The formulas for calculating probabilities, combinations, and permutations
- The definitions and calculations of variance and standard deviations
Simplify, Then Solve
Many QC questions on the GRE are less complicated than they first appear. For algebra-centered QC questions in particular, the quantities are often written as algebraic expressions that seem to complex to compare. However, these expressions can almost always be simplified, which makes comparing them much easier.
For example, you might encounter the following QC problem.
y > 1
Quantity A |
Quantity B |
(y^{5})^{6} |
y^{3}(y^{4})^{2} |
These quantities may look very complicated to compare, but if you’ve memorized the laws of exponents, you can simplify them and make the question much easier.
Knowing that (y^{a})^{b }= y^{ab}, Quantity A can be simplified to y^{5}^{⋅6}, or y^{30}. Adding the law that y^{c} ⋅ y^{d} = y^{(c+d)}, Quantity B can be simplified first to y^{3} ⋅ y^{8}, then to y^{11}. And since this QC question adds the constraint that y > 1, Quantity A is greater than Quantity B.
When In Doubt, Test Different Numbers
For many QC questions, even after you’ve simplified the expressions involved, the greater quantity may still not be apparent. In your GRE prep, you should practice plugging in different numbers in order to test the two quantities.
You should also be smart about which numbers you choose to test. In general, you should consider the following numbers as a trustworth test bank for plugging into QC questions: -10, -2, -1, -1/2, 0, 1/2, 1, 2, and 10. There’s a logic behind this bank of test numbers, which has to do with the ways different kinds of numbers behave differently when subjected to different conditions and constraints. For example, negative numbers and fractions (especially fractions whose absolute value is between 0 and 1) behave differently with exponents than whole positive integers do. Similarly, larger numbers (like 10) sometimes behave differently than smaller numbers (like 1/2 or 1). And of course 0 often performs differently from other numbers.
Often, the given constraints will shrink the test bank so you don’t have to test every one of those numbers. And of course, as you practice your QC questions, you’ll develop a better sense for which numbers make sense to test with different problems. In the example above, because the constraint identifies the variable as greater than 1, the only numbers you might consider testing are 2 and 10. If you’ve familiarized yourself with the properties of exponents, then you’d know that both 2 and 10 will increase when raised to a positive exponent. Therefore, you only really have to test one of them.
Don’t Do More Work Than You Have To
When you’re plugging in different numbers to test, it can be easy to do more work than you really need to. But by thinking logically, you can make sure you don’t lose time to unnecessary calculations. For example, if your understanding of number properties tells you that -10, -2, and -1/2 will all behave similarly in a given expression, there’s no need to test all of them—you can just test one.
You should also think logically as you plug in numbers and calculate the results they yield for Quantities A and B. If you plug in one number and Quantity A is greater, then plug in another number that either makes Quantity B greater or makes Quantities A and B equal, you’ve already determined that the given information is not sufficient to determine which quantity is greater.
Work with a GRE Tutor
While all the tips listed here are helpful, they still won’t be anywhere near as helpful as working with a qualified GRE tutor. Working with a tutor remains the gold-standard for improving your mastery of the material and maximizing your GRE score. At MyGuru, our tutors all have several years’ worth of experience helping students meet and exceed their target scores. Our tutors can help you gauge your starting performance, set a target score, devise a study plan, and master the material.
Conclusion
The Quantitative Comparison questions on the GRE may seem intimidating when you first encounter them, but they don’t have to be. With a little practice, you can quickly develop familiarity with this unique question structure. Applying these tips will help you improve your accuracy and speed as you work through the QC questions on the GRE.