GRE Quantitative Comparison Questions
The GRE consists of two Quantitative Reasoning sections, and according to the test developer and administrator, Educational Testing Service (ETS), the purpose of these sections is to assess:
- Basic mathematical skills
- Understanding of elementary mathematical concepts
- The ability to reason quantitatively
- The ability to model and solve problems using quantitative methods.
Quantitative Reasoning sections can be broken down as follows:
| Quantitative Reasoning Section | Number of Questions | Time Given |
| #1 | 12 | 21 minutes |
| #2 | 15 | 26 minutes |
Test-takers must answer a total of 27 Quantitative Reasoning questions. These questions may be posed in “real-life” settings, in purely mathematical settings, or as “word problems” that require a test-taker to translate and model them mathematically. An on-screen calculator is provided for use during Quantitative Reasoning sections.
Quantitative Reasoning sections assess knowledge of four content areas: 1) Arithmetic; 2) Algebra; 3) Geometry; and 4) Data Analysis. The ability to construct proofs is not tested, nor is trigonometry, calculus, inferential statistics, or advanced-level mathematics. The content of the Quantitative Reasoning sections is generally taught to students in high school algebra or introductory statistics courses. Test-takers do not need to have obtained an undergraduate degree in mathematics or a field of science in order to perform well on these sections, although they may find Quantitative Reasoning questions easier or more familiar than students who majored in the arts, humanities, or social sciences.
There are many different types of questions that make up the Quantitative Reasoning sections:
- Discrete questions
- Data Interpretation Set questions
- Quantitative Comparison questions
- Multiple-choice questions (one correct answer)
- Multiple-choice questions (one or more correct answers)
- Numeric Entry questions
Below we will examine Quantitative Comparison questions in detail so that you can easily recognize and solve them on the day of your exam.
Quantitative Comparison questions ask students to compare two quantities, Quantity A and Quantity B. There are four possible answers:
- Quantity A is bigger
- Quantity B is bigger
- The quantities are equal
- The relationship of the quantities cannot be determined from the provided information.
Every Quantitative Comparison question will always contain the same four answer choices. It is imperative that you be familiar with these choices to save time and think efficiently on test day, especially for questions that have insufficient information to determine the relationship of the quantities. There is no need to waste time attempting to solve a problem that cannot be answered, which is why being able to recognize Quantitative Comparison questions and select the right answer is key to managing your time and achieving your best GRE score.
Problem Solving
When it comes to solving Quantitative Comparison problems, start by simplifying the comparison if possible. Avoid unnecessary computations, but never select “impossible to determine” if it is possible to compute the value of each quantity. Plug in test numbers of various sorts to evaluate algebraic expressions, and be sure to consider all kinds of appropriate numbers before you select a final answer (zero, positive and negative numbers, large and small numbers, fractions and decimals).
If you see that Quantity A is bigger for some test numbers and Quantity B is bigger for other test numbers, than the answer is that their relationship cannot be determined. If you establish that one quantity is larger than the other quantity, be careful to ensure that you enter the correct answer and do not mix up your choices, as it is easy to become confused when you are attempting to work under strict time pressure.
Also, remember that geometric figures are not necessarily drawn to scale, so it may be helpful to redraw the figure while keeping constant only the variables that have been established by the information provided in the problem. According to ETS, when it comes to questions involving geometric figures, answers should be based on geometric reasoning rather than estimating or comparing quantities by sight or measurement.
Sample Problem
Quantity A
Number of four digit numbers less than 2000 that can be formed using the digits ‘0’, ‘1’, and ‘2’ with repetition of digits allowed.
Quantity B
Number of three digit even numbers that can be formed using the digits ‘1’, ‘2,’ ‘3,’ ‘4,’ and ‘5’ with no repetition of digits allowed.
Answer choices:
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be given from the information given.
Solution:
Because this question asks for calculating the number of numbers formed using digits, we will use “permutation” tactics: many numbers can be formed by changing the positions of the digits. For Quantity A, we need to fill up four positions. The first position must be a 1, because the number must be less than 2000. The second, third, and fourth positions can be filled in three ways, since each of the remaining numbers can be used multiple times. Thus the total number of combinations is (1) * (3) * (3) * (3) = 27.
For Quantity B, we need to fill up three blank positions. The third or last position can only be filled with a 2 or a 4, since the final number must be even. The first position can be filled in four ways, since ‘2’ or ‘4’ must be used in the third position. The middle position can only be used in three ways, since we cannot reuse the digits used in the first and third positions. Therefore the total possibilities are (4) * (3) * (2) = 24. Since Quantity A = 27 and Quantity B = 24, the correct answer is A.
GRE vs. GMAT
Generally, the Quantitative Reasoning sections of the GRE are considered less difficult than the analogous sections of the GMAT, although this will vary among individual test-takers depending on their academic backgrounds and exposure to mathematics courses.
The Quantitative Comparison questions from the GRE are similar to a type of problem called “Data Sufficiency” on the GMAT. Whereas Quantitative Comparisons require students to compare two quantities, including an evaluation of whether they can be compared quantitatively at all, Data Sufficiency problems give students discrete sets of information and ask them to assess which sets of information are sufficient to solve the problem. Quantitative Comparisons can be solved through a combination of test-taking techniques, problem-solving strategies, and active application of mathematical methods; Data Sufficiency questions require a more comprehensive understanding of mathematical theory.
Conclusion
Quantitative Comparison questions are one type of question you will find on the Quantitative Reasoning sections of the GRE. While these questions may initially appear daunting, they can be understood and mastered through focused and consistent test preparation.
In order to become comfortable with Quantitative Comparison questions, it is best to take several practice GRE exams as part of your overall study program. Since test-takers are given very little time on each Quantitative Reasoning section, it is important to develop time management skills, and one of the best ways to save time is to quickly recognize the type of question you are being asked. When you know what you are being asked to do, you can apply the most efficient problem-solving strategy to arrive at the correct answer, ensuring you are both fast and accurate when taking the GRE.