7 Tips for GRE Quantitative Comparison Questions

The GRE Quantitative Reasoning section can be tricky for even the best math students. It assesses your ability to think critically about math and use foundational mathematical principles in a variety of scenarios.
The Quantitative Reasoning section is made up of three question types: Quantitative Comparison, Problem Solving, and Data Interpretation. Each section type requires different strategies and approaches. In this article we’ll discuss some tips for Quantitative Comparison questions. 

Quantitative Comparison presents two quantities, and sometimes additional information centered above the quantities—often a graph, an equation, or a geometric shape.

The given information is x > 0. The problem then details the two quantities: A and B. Quantity A in this example is x^2, and Quantity B is x^3. The answers on the Quantitative Comparison question will always be the same, no matter what the quantities or given information. They are as follows:
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
The trick is to figure out which option is correct based on the information you are given. Quantitative Comparison questions require more than simple problem-solving; it’s important to bring skill and strategy to the section as well. Here are seven tips to help you nail the Quantitative Comparison section of the GRE.

1. Aim for efficiency, not thoroughness. You’ll have a little over an hour to complete the Quantitative Reasoning section, which will include Quantitative Comparison and other question types. Many test-takers get stuck trying to solve one problem meticulously. But unlike in some of your other math tests, nobody is checking your work; the point is that you find the right answer as quickly as possible. 
2. Compare the quantities. Because answer choices are identical on all Quantitative Comparison questions, you can focus completely on the given quantities and the given information above, if applicable. Understanding all the information you’re given is one way to improve your speed and efficiency, which is paramount on this section.
3. Pick numbers. Substituting convenient values can help reveal the relationship between the quantities. Every selected value must satisfy the problem’s restrictions. Testing only positive integers such as 2 and 3 can miss important cases, so consider fractions, zero, negative numbers, 1, and −1 when permitted. For example, if a problem states that x > 0, zero and negative values are excluded, but fractions between 0 and 1 remain possible. The goal is to test values that could produce different relationships between the quantities.
4. Start with D. Look for two valid cases that produce different relationships between the quantities. If Quantity A is greater in one case but Quantity B is greater in another, the answer is D. The same applies if the quantities are equal in one case but unequal in another. Once two valid cases establish different relationships, no further testing is needed. However, several examples with the same result do not prove that the relationship always holds. Choosing A, B, or C requires reasoning that covers every value allowed by the problem.
5. Avoid the calculator. Digital calculators are available on the GRE, and they will be tempting. But pulling up and using the calculator takes up time and often distracts you from efficiently solving the problem.
6. Do the math. Sometimes, simply solving is the best way to proceed. If you have exhausted all your tricks and other options, try to fully calculate the problem.
7. Skip it, and come back. This is the oft-overlooked virtue of the GRE: you can skip a question and return later. Timing is of critical importance on the Quantitative Comparison section. Don’t be afraid to mark questions you aren’t sure about on the computer, and return later. Once you’ve answered the other test questions in the section, you can easily return to the Quantitative Comparison questions before submitting your answers.

GRE Quantitative Comparison Example: Test Different Number Types

In the earlier example, x > 0, Quantity A is x², and Quantity B is x³. Testing different positive values shows why choosing only integers greater than 1 can be misleading.

Value of x	Quantity A: x²	Quantity B: x³	Relationship
2	4	8	Quantity B is greater.
1	1	1	The quantities are equal.
1/2	1/4	1/8	Quantity A is greater.

The correct answer is D: The relationship cannot be determined from the information given.

All three values satisfy x > 0, but the relationship changes. In fact, the first two rows already establish that D is correct. The fraction example illustrates another possibility: raising a positive number between 0 and 1 to a higher positive integer power makes it smaller.

Use FROZEN to Remember Useful Test Values

The mnemonic FROZEN can help students remember alternatives to positive integers when choosing numbers for GRE Quantitative Comparison questions:

• FR: Fractions, including positive and negative values between −1 and 1
• O: One and negative one
• ZE: Zero
• N: Negative numbers, including integers less than −1

Together with positive integers greater than 1, these categories provide a useful range of values to consider. Students do not need to test every category on every question. The problem’s restrictions and the operations involved should guide the choices.

Zero deserves particular attention: it is an even integer, but it is neither positive nor negative. Multiplying by zero gives zero, while dividing by zero is undefined. Similarly, 1 and −1 can behave differently from numbers with larger absolute values. For positive integer exponents, powers of 1 remain 1, while powers of −1 alternate between −1 and 1 depending on whether the exponent is odd or even.

If the problem specifies integers, fractions are excluded. If it specifies positive numbers, zero and negatives are excluded. Any additional restrictions, such as odd, even, or prime, must also be satisfied.