Hardest GRE math questions in 2022 | Full Solution

Hardest GRE math questions in 2022 | Full Solution

Are you having trouble with the hardest GRE math questions? If yes, then worry no more because I’ve got the answer for you. These are the toughest GRE math problems that you’ll ever face.

The Graduate Record Examination (GRE) is a standardized test required by many graduate schools across the United States. This exam tests your ability to solve basic algebraic equations and other mathematical concepts.

To get through these tough GRE math problems, you should always start by breaking down each problem into smaller parts. Then, try to simplify them using simple techniques such as adding or subtracting numbers from both sides of the equation.

GRE test takers always ask the hardest GRE math questions, but first, they need to understand that you don’t need to answer such questions correctly to get a good GRE score.  This is a test that favors accuracy and consistency in mid-level issues rather than the ability to get very difficult. 

You can get a grade of 90 percentile or higher without solving any of the most difficult GRE math problems.  If you’re wondering, here’s what GRE’s most challenging math problems look like.  Less than 20 percent of GRE test participants answered each of these questions correctly.

How to solve the hardest GRE math questions?

After you read the new question, give yourself about 10 seconds to just think about it.  Take your time.  This will provide a valuable opportunity to notice the overall picture/logic of the question, which can greatly facilitate the question.  Practice this to get into the habit and do it on a real test!

The GRE quantitative section examines four areas of mathematics before college: arithmetic, algebra, geometry, and data analysis.  Not all four are tested the same.  Some of these concepts occur more often, and some are usually more complex.

What to know about GRE math questions?

As you prepare for the GRE Quantitative, keep in mind this frequency and complexity.  Enjoy easy arithmetic questions, but also pay attention to how you handle more complex ones.  Algebra tasks should be at the top of your list of preparatory priorities, given their tendency to confuse many respondents. 

The same goes for data analysis, especially those that check statistics and probability.  Make the weaknesses of most test takers your strengths and you will increase your chances of getting the highest score.

What do GRE math questions consist of?

  • Arithmetic topics include properties and types of integers, such as divisibility, factorization, prime numbers, residuals, and odd and even numbers; arithmetic operations, indicators, and roots; and concepts such as estimate, percentage, coefficient, norm, absolute value, numerical line, decimal representation, and sequence of numbers.
  • Algebra includes operations with indicators;  decomposition and simplification of algebraic expressions;  relations, functions, equations, and inequalities;  solving linear and quadratic equations and inequalities;  solving simultaneous equations and inequalities;  compiling equations for solving text problems;  and coordinate geometry, including graphs of functions, equations, and inequalities, intersections, and slopes of lines.
  • Geometry includes parallel and perpendicular lines, circles, triangles, isosceles, equilateral and 30 ° -60 ° -90 ° triangles, quadrilaterals, other polygons, congruent and similar figures, three-dimensional figures, area, perimeter, volume, and measuring the angle in degrees.  The ability to build evidence is not tested.
  • Data analysis includes basic descriptive statistics, such as mean, median, mode, range, standard deviation, interquartile range, quartiles, and percentiles;  interpretation of data in tables and graphs, such as line graphs, bar charts, pie charts, block diagrams, scatter plots and frequency distributions;  elementary probability, such as the probability of complex events and independent events;  conditional probability;  random variables and probability distributions, including normal distributions;  and counting methods such as combinations, permutations, and Venn diagrams. 

These topics are usually taught in algebra courses in high school or in introductory courses in statistics.  The conclusion of the statistics is not verified.

Is GRE math hard?

Although the differences in the new quantitative section of the GRE are less significant than the changes made to the verbal section of the GRE, they are still worthy of attention and consideration in preparation.  The main differences are problems that have several correct answers, so be sure to read all the answers, even after you have identified the correct answer.

Also new to the revised test are the problems when you enter the actual number, unlike the previous quantitative GRE format, which consisted entirely of quantitative selection and quantitative comparison questions. 

In general, the revised quantitative section focuses more on the use of mathematics in different situations, ie data analysis, rather than just manipulating numbers, which was the focus of the old version.

Checkout: What is the average GPA for vet school in 2022

Additional Resources And Books to Use During Test Prep

Free practice tests

Let’s not forget that you can find many freely available resources online. Take at least one practice test prior to your exam day.

Official exam guidelines

The ETS also provides an overview of what to prepare for on the test, including content, structure, and so on.

Get a test prep book

Books that contain a lot of hard questions and problems from previous GRE tests will be good for practice. We like these three options:

The Official Guide to GRE General Test.

This book comes directly from the ETS. You’ll also receive four “real” practice exams when you purchase them. If you want to get the best GRE scores, there’s no better way to prepare for the test than by buying a book written by the official exam-makers themselves.

Barron’s GRE prep book

Barron GRE prep book makes solving your math problem easier and also help you understand how to approach the entire test. 

Manhattan Prep GRE Set of 8 Strategy Guides

When I found this set, I was instantly excited. It covers everything you’ll need to know about the test, from verbal questions to math problems. Even if math was never your strong point during high school, this set will help you get a good score on the GRE.

Read also: 15 Best SAT vocabulary books in 2022 | Best reviews

Types of GRE Math Questions

The Quantitative section contains five types of questions:

Quantitative comparison



Data interpretation

Numeric entry

Hardest GRE math questions in 2022

  1. Each employee in a company is in Division X or Division Y, and Department X has twice as many employees as Division Y. The average (arithmetic mean) salary is $ 25,000 for Department X employees and $ 35,000 for Department Y employees.  Which of the following amounts can be the average salary for all employees of the company?

  Enter all such amounts.

  A. $ 26,000

  B. $ 28,000

  C. $ 29,000

  D. $ 30,000

  E. $ 31,000

  F. $ 32,000

  G. $ 34,000

  • In the workforce, the ratio of the number of union members to the number of non-members is the same for both the sales sector and the protective service area.  Which of the following is closest to non-members in the sales sector?

  A. 2.9 million

  B. 3.6 million

  C. 10.4 million

  G. 11.1 million

  E. 14.0 million

  • In the chicken population, the mean (arithmetic mean) weight is 6.3 pounds and the standard deviation is 1.2 pounds.  Which of the following weights (in pounds) is within 1.5 standard deviations of the mean? 

Indicate all weights.










In conclusion, the hardest part about studying for the GRE Math Subject Test is actually finding the time to study. While cramming for exams is certainly helpful, it won’t help you prepare for the real test. Instead, you should focus on building a solid foundation of knowledge first.

This means spending plenty of time working through problems and reviewing concepts, rather than trying to memorize formulas and equations.

The key to success is to keep yourself motivated throughout the process. Don’t let yourself become overwhelmed by the amount of material you have to cover.

Instead, break the test down into manageable chunks and use the strategies outlined above to ensure that you’re prepared for each section. Then, spend a few minutes after each problem solving it, and review your answers later. This will help you avoid wasting precious time on a question that you already know the answer to.


What is GRE Math Practice Questions?

GRE math questions cover many topics, including arithmetic, algebraic concepts, geometry, and data interpretations.

What are the benefits of math?

They force students to think. Doing so, the student builds mathematical ability.

What should I do?

If you’re having trouble with something, don’t look up the answer or the explanation to the problem until you’ve tried your best at solving it.

What is the best way to practice math concepts?

It’s important to remember that although I like the Manhattan Prep 5 lb GRE Practice Book for repetition with math concepts (and I actually own one), it’s much more important for you to gain enough experience as you can while solving ETS-written GRE math questions, because ETS writes the GRE, and not because other companies’ questions mimic ETS’s logical reasoning and shortcuts to math questions.

What are the math questions in these books?

Some of the math questions in these textbooks aren’t difficult, but becoming a better test taker means getting lots of experience answering easy ETS questions.


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