GRE Quantitative Reasoning is not only given to examine test-takers’ quantitative skills. It is provided in the standardized tests so a graduate school can evaluate the problem-solving skills of aspiring students. Acquiring problem-solving skills improves the cognitive ability and managerial skills of an individual. It aims to develop their ability to be methodical and to be critical thinkers in their approach to solving problems. Problem solving in the GRE is generally done in three steps: understanding the problem, carrying out a strategy to solve the problem, and verifying the answer. Examinees are trained to devise a plan based on their understanding of the provided information. Their chosen course of action will determine the success of their resolution. Thus, strategies are employed to address particular issues methodically. Moreover, examinees also learn to justify their resolutions and to ensure the accuracy of their solutions.
Yes, there are problem-solving questions on the GRE. These questions are usually presented as standard multiple-choice questions. Answers may be provided through a numeric entry or by selecting choices that are applicable to the problem. Therefore, examinees must develop an excellent mathematical foundation to support the methodical approach that will be employed in the resolution of these types of questions.
A problem-solving question in the GRE is either a standard multiple-choice question or a data interpretation question. Problem-solving commonly appears in quantitative questions. In the first variant, options are provided for the examinees to select based on the results of the strategies they implemented to resolve the problem. Answers may also be entered in a box. In the second variant, information is provided through charts or graphs. Typically, 3 data interpretation questions appear in the test. (2)
Yes. As long as problems are solved in the test, problem-solving skills will remain crucial in achieving a high GRE score. When answering quantitative reasoning sections or analytical writing, problem-solving skills are very essential. Thus, examinees must strive to improve their performance in this particular aspect so they can use it in different areas of knowledge. Keep in mind that business school and other grad schools focus more on quantitative reasoning score reports.
Problem-solving skills not only improve the cognitive ability of the examinees but their managerial skills as well. It tests their ability to identify problems and motivates them to exercise their creativity in resolving such conflicts. Like any examination, test takers face problems with limited resources in a time-constrained setting. Hence, they need to employ comprehensive strategies to achieve desirable results. The ability to make a decision and justify it with reasonable justification boosts confidence in facing challenges. Having competent problem-solving skills is critical in achieving a high score in the quantitative reasoning aspect. (3)
Graduate schools value problem-solving skills because they train students to thrive in a challenging and competitive environment. Difficult higher education programs and career-related situations are common in graduate schools, law school, and business programs. The standardized admissions tests help them perceive whether the prospective graduate students can handle the responsibilities of grad school programs. Problem-solving skills improve the students’ self-efficacy as they become more confident in resolving issues and conflicts with their creativity and analytical skills. It allows them to become independent enough to motivate the growth they require in their studies, as they require little to no supervision. (4)
Problem-solving formats have specific directions to follow. Examinees may encounter the following types:
- Selection of the best answer. A problem is provided with five choices. The examinee can only choose one option, which is thought to be the most applicable to the problem.
- Selection of applicable answers. The examinee may select any correct answer from the options provided.
- Numeric Entry. A space is provided for the integer that answers the question.
- Selection of specific answers. The instruction may ask you to select a specific number of answers to solve the problem.
These formats require examinees to have a good mathematical foundation to acquire a high score. Invest in prep materials and take the time to answer. Use practice tests to develop your problem-solving skills and mathematical skills. (5)
The general problem-solving steps include three phases:
- Problem identification and comprehension. Examinees should carefully read the problem and understand its nature so appropriate strategies can be developed to address it. Knowing the problem and knowing how it can be solved is critical in laying the foundation for the plan that will be organized.
- Implementation of strategies. Steps are organized to gradually solve the problem in a traditional approach or in a creative way. Examinees must appropriately apply the mathematical fundamentals involved in the process and execute it accordingly.
- Verification of the Answer. The correctness of the computation is evaluated to justify the steps or to fix any errors that arise in the process. To check the answer, examinees may recall basic mathematical facts or perform mathematical operations to determine the consistency of the results.
In order to correctly solve a problem in GRE, the above-mentioned ways must be observed in the process. (6)
In solving quantitative reasoning problems, one may use the following strategies:
- Word-to-Algebraic expression. Textual information about a mathematical problem is translated into its arithmetic or algebraic equivalent to get a clearer understanding of what operations are involved in the process. This translation is successful when one is knowledgeable about different linguistic representations of equations.
- Simplification of equations. This converts seemingly complicated arithmetic or algebraic representations to their simplest form.
- Visual representation. Geometric figures can be added to the solution to have a clearer picture of the problem. It reduces the complexity of the information to a visual representation, which provides better guidance in the process.
- Pattern identification. Finding a pattern generates a hypothesis that will yield a point of direction to the appropriate solution for the problem. One may consider doing this first when facing a complex mathematical problem.
- Estimation. Using the theoretical knowledge that one possesses about a mathematical situation, an estimation can be used to provide the closest solution possible. It may not achieve the same accuracy as extensive calculations, but it can be sufficient on some occasions.
- Adaptation of Relative Solutions. Examinees may adapt a working solution used on related problems if problems only differ in surface features such as numbers, labels, or categories.If it’s a problem that has not been encountered before, adapting known solutions can also work to determine their compatibility with the problem.
- Consistency of conclusion with the provided information Justify the step-by-step process of the solution using the given knowledge of the problem and the mathematical fundamentals involved in the process. The consistency of the truth of the conclusion in all cases shows the validity of the solution.
These strategies are applicable to different mathematical situations. With this, one must determine their appropriateness in problem-solving to choose the correct answer choices.
Below are some examples of hard problem-solving questions that can be encountered on the test:
- Each of the 100 balls has an integer value from 1 to 8, inclusive, painted on the surface. The formula Nx = 18 (-4) defines the number Nx of balls representing the integer x.2. What is the interquartile range of the 100 integers?
- The two lines are tangent to the circle. If AC = 10 and AB = 103, what is the area of the circle?
- A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible unit digits of Sophie Germaine primes greater than 5 is
- In a certain game, a large bag is filled with blue, green, purple, and red chips worth 1, 5, and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
When examinees become more familiar with the process and practice it frequently, these mathematical problems become more manageable. (7)
Yes. Test makers are adapting to the work of the most highly regarded mathematician educator, George Polya. The process is somehow similar to the general problem solving steps in GRE.
Polya problem-solving strategies involve the following aspects:
- Problem identification. The examinee must pay attention to the details of the problem so they can understand its premises. Sufficient information must be gathered in preparation for the next step.
- Strategy formulation. When the problem is understood and the choices to consider are identified, examinees may use their gathered information to choose the best formula for the problem.
- Plan implementation. When the strategy is formulated, the examinee may begin the methodical process of solving the problem. In this phase, the problem is translated into an arithmetic or algebraic expression so necessary operations can be executed.
- Review of answers. As the examinee arrives at a conclusion, the verification of the answer can be done by checking the consistency of the response and the solution, identifying potential errors, and evaluating whether the necessary information has been practically used in the condition of the problem.
Compared to the general problem-solving steps, Polya strategies provide a more detailed explanation of what happens in the analytical process. Smart students commonly incorporate Polya strategies into their GRE answer techniques. (8)
Problem-solving skills in quantitative reasoning can be improved in four ways:
- Knowing the art of understanding a problem. Prior to the definition of the problem, an examinee must know the scope and limitations of the problem. One must narrow it to avoid irrelevant information from clouding the formulation of strategy so the process can focus on its goal. Rephrasing the question to gain a better understanding of the meaning of the statement is one way to do this.
- Recognizing resemblance in different situations. Solving math problems involves formulas and patterns that can be recognized in different statements. When one encounters a foreign problem, existing solutions can be utilized to test their appropriateness in the context. In this course of action, an examinee must have a sharpened reasoning skill to justify their choices.
- Practicing consistently. Complex math problems become easier when an examinee gains enough knowledge and skills to solve them. Unfamiliarity impedes the successful resolution of the problem; hence, one must develop good habits to motivate improvement in their performance. Video lessons and improving practice test scores in the math sections will help you reach your target score.
- Exercising mental ability. Strengthening the skill set that involves mental performance is one way to improve problem-solving skills. Understanding practice questions is very effective for developing your problem-solving capacity and getting a higher score range to successfully employ in graduate programs. One must engage in activities that require the use of logical reasoning and critical thinking skills to formulate the best solutions, not just to mathematical problems but also to real-life situations.
Although problem-solving skills are mainly improved through mental activities, it is worth noting that one must take care of their physical health too to mentally perform better.