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GRE Math Practice Questions

Since readers are always asking for more GRE math practice, I’ve rounded up some of my favorite questions from Magoosh’s premium GRE prep to make them available to you for free. The truth is, when it comes to studying for GRE quant, you can never get your hands on enough practice questions.

I’ve broken down the questions below by difficulty, starting with the easiest. You can check your answer by clicking either the question or the link below that says “See answer”. It will take you to a new tab (and your timer will start!). There you can watch a video explanation or read the text explanation to help you understand the problem better.

Easy Level Math Practice Question

easy gre math practice question
[See Answer]

The question above is a question that you should have absolutely no trouble answering. If you do, then I’ll be honest and say you’ve got a long road ahead of you. That’s okay though. These kinds of questions are really straightforward. They’re just testing to see if you grasp the basic concept. This one’s a multiple answer question, so more than one answer could be right.

Medium Level Math Practice Question

medium gre math practice question
[See Answer]

This problem is a noticeably more difficult question to answer. You’ll see that not only are expected to know the straightforward math principle (as above), but you’ll have to wade through a word problem to even begin setting it up. That’s a common set up for a GRE math problem and you should get used to it.

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Hard Level Math Practice Question

hard gre math practice question
[See Answer]

Now you’re staring at a pretty tough problem. Any problem at this level will require multiple levels of work to arrive at the solution. Be careful with these kinds of problems, as often you’ll think you’ve finished and found the answer (which will be listed), but there’s actually another step or two until you’re actually done with it.

Very Hard Level Math Practice Question

very hard gre math practice question
[See Answer]

Now the problem above should have you shaking in your boots. And if it doesn’t, then you are either headed for a top score, or you’re delusional. Either way, come test day you’ll be face to face with a few questions of this caliber, or even slightly more difficult. The thing about these kinds of questions is that you’ll think you’ve got the answer right, but you probably don’t. That’s what makes them so hard. It’s best to get used to them now, but remember that on the GRE each question is worth the same to your score, so there’s no sense in dwelling over questions like this and when you could be getting to easier questions down the line. You can always come back if there’s time.

Top 3 GRE Math Study Tips


More GRE Math Practice

Here’s a link to more blog posts with lots of practice questions for you to sink your teeth into: Magoosh GRE Math Practice Blogs

There you’ll find plenty of questions, explanations and strategies to help you practice your GRE math.

Other GRE Math Resources

If you’re just starting out on your study journey, then I recommend checking out our complete GRE guide so you can get a good handle on what you’ll be expected to know on test day. Also important for more general GRE math practice is our GRE math formulas ebook.


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41 Responses to GRE Math Practice Questions

  1. Jamiul Islam May 30, 2018 at 12:13 pm #

    Dear Chris,

    I could solve the easy, medium and hard problems, but failed to crack the very hard one.

    Do u think i will be able to score around 164 to 165 in quant section of real GRE?

    My timing was good enough.

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert June 1, 2018 at 10:35 am #

      Hi Jamiul,

      It’s difficult to extrapolate a score from just one set of questions; the answer to this question really depends on the type of questions you get on the test and how confident you feel with them. I highly recommend that you take a few practice tests under test-like conditions to see how you perform. The GRE is a complex test, and your score depends on a lot of different factors, so taking practice tests consistently allows you to track your progress over time and understand your personal strengths and weaknesses.

  2. Brano October 3, 2017 at 6:43 am #

    Hi, actually the last one “Very Hard Level Math Practice Question” has a very simple solution.

    Let those sides be of a length 6, 8 and let the angle between them be theta. Then the area of the triangle formed by those two sides (and the third of an unknown length) is (1/2)*6*8*abs(sin(theta)) (standard high school formula, but if that’s not familiar, check cross product on wiki). Let’s assume that 0 < theta < pi, so the abs. value is not needed. That gives area = 24*sin(theta). Now we know that theta can be anywhere between 0 and pi, so area = anything between 0 (excluding) and 24 (including).

    Boom, that's our answer, without even using a calculator and trying a bunch of numbers.

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert October 3, 2017 at 12:02 pm #

      Hi Brano,

      Awesome! Sometimes the content of a question is not hard, though the question still earns that label because of how many people miss it. Nice job here! 🙂

  3. Haritha August 15, 2017 at 11:12 pm #

    Hi Chris,

    I had given my GRE in July, and scored 308, while all my practice tests scores were around 315. I find the major reason for this being Quants questions – Most of the material I referred to, (princeton & ETS) had quants questions which were much much simpler and mediocre when compared to the actual toughness level of the questions in the test. I am looking to re appear for the test by end of september, and would appreciate it if you could direct me to some kick ass quants material. I am ready to put in 3 hours of study everyday even if it requires me breaking my head. I just need to get that damn score straight.


  4. Dhiraj September 3, 2016 at 9:17 pm #

    Hi, I gave the GRE recently. The quant section was very difficult. The questions were lengthy. The powerpreps were way too simple. I did manhattan, and even it was not a match. The first section was easy. But then, next what I saw, was unexpected. The questions were very difficult. So, which book should be preferred for math section? Which book has questions with high difficulty level?

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert September 9, 2016 at 2:47 pm #

      Hi Dhiraj,

      I’m sorry to hear that you found the test questions so difficult! Many students say that both Magoosh and Manhattan questions are generally harder than those seen on the GRE test. We have heard from many students that they think the actual GRE is more difficult than the Powerprep test. I can’t be sure exactly what happened in your case, but it’s possible that the questions were particularly hard on that test, or that the questions that happened to come up were especially difficult for you for more personal reasons. I recommend that you check out Magoosh–our advantage is that we have video explanations for every question, which means that you won’t only do difficult questions, but you will also learn the most efficient methods for solving them. This can help you to learn how to simplify those complex problems to find more ‘elegant’ solutions.

      Another option would be to study from GMAT prep books. The math questions on the GMAT are very similar to those on the GRE in terms of concepts and strategies, but the GMAT questions are generally more difficult. You can check out our GMAT blog for some practice, or try a free trial of our GMAT product.

  5. Aashima July 13, 2016 at 10:18 am #

    I need GRE Online Practice Test series. How will i get that?

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert July 13, 2016 at 12:30 pm #

      As Rita mentioned earlier in the comments, you can get some mock GRE online practice tests with a $20 purchase from Manhattan Prep. Be careful though. the Manhattan-sponsored online GRE tests are great practice for Math, but the Verbal portions are not as authentic to the real GRE test. If you want online practice tests that are truly accurate to real test content in both Quants and Verbal, you’ll need to go the source and take the official GRE online practice tests created by ETS. You can get free practice GREs from ETS through their online PowerPrep service. You can also find other practice questions and exams (some free, some costing money) on the official GRE prep web page.

  6. Nene October 13, 2015 at 7:24 pm #

    I am taking the test on the 4th of november( in about 18 days) and I am doing poorly on the Quant section from my Magoosh practice.
    I started prepping a month and half ago. I am not that good at Maths so I went back to the basics using Princeton’s Cracking the GRE. I feel like that gave me a better understanding of the concepts. However now I started practicing using the Magoosh practice questions, I am not doing well. So. I started using the one month study schedule to give me some structure but I am getting overwhelmed with the amount of stuff I need to do and I do not feel like I am improving. I would really like your advice on how to move forward and at least start getting a better score. Yours desperately ):

    • Matt August 18, 2017 at 4:59 pm #

      I would suggest creating a set of flashcards for each testable concept in the quant section. In making the cards you will not only learn the material and be able to access it faster, but you will also learn the material in better depth as you are actually generating your card set. Works great! Give it a try. It only takes about 8 hours to generate a good set of flashcards.

  7. Cool Math Games October 11, 2015 at 12:32 am #

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  8. Vinod June 8, 2015 at 10:22 pm #

    Dear Chris,

    I’m going to take gre within two months.Can you please help me with suitable books as am targeting a score of around 310 plus. i dont have enough time, so can you also help me with study plan for this 2 months to achieve targeted score .

  9. usre June 1, 2015 at 5:02 am #

    Hi for this amazing site,
    what are the best and adequate and even summerized references for gre math part?
    i have a good background in math i just want to be familiar with ets even hardest math questions and get the complete score.
    i want to prepare myself in about less than 4 weeks.
    Thanks in advance

    • Rita Neumann
      Rita Kreig June 2, 2015 at 2:36 pm #

      Hi Usre!

      I’m so glad you’re enjoying our blog! 🙂

      We offer a free eBook about GRE Math, which summarizes the topics that you’ll find on the exam: GRE Math Formula eBook. I’d also recommend using Magoosh GRE Premium prep and one of our accompanying study schedules. That way you can study the concepts and then do practice problems to make sure that you’re really prepared on test day.

      Best of luck with your prep! Let me know if you have any other questions. 🙂


  10. Rhea June 21, 2014 at 4:42 am #

    Hello. I’ve subscribed to the Premium plan (the questions are phenomenal and have helped me a great deal in overcoming my fears of a few math topics. Probability YIKES!). However I think I’ve eaten up all the 500 so questions in math and now with 2 weeks to test day I was wondering if there was any way I could get my hand on a fresh set of questions?

    • Rita Neumann
      Rita Kreig June 23, 2014 at 5:16 pm #

      Hi Rhea,

      I’m so glad that Magoosh has helped you so much! I feel your pain when it comes to probability … but I’m glad you’re overcoming your fear! Congrats, by the way, on completing all the math questions. That’s quite an achievement.

      You’ve seen all the GRE questions that we have available, but if you’d like to try some GMAT-type quant questions, I’d recommend taking a look at the Quant section of the Magoosh GMAT Blog. You can also look through the Complete Guide to the GRE eBook, which has some math practice problems you can try. And definitely go back to problems that you had trouble with at the beginning of your prep – this is a great way to a) revisit tricky concepts and b) see how far you’ve come.

      I hope that helps! Good luck with your test in 2 weeks. 🙂

  11. Duke March 19, 2014 at 8:22 am #

    Hi. I’m on the premium plan and I gotta say I’m having a great time studying 🙂

    Also, there’s a little concern. I’m not having too much trouble with the Hard and Very Hard practice questions on the Quant section, so at the moment they just keep coming when I set my practice difficulty to Adaptive. I’m afraid, however, that I’m going through them at a rate that there won’t be any Hard/Very Hard questions left for me to do a couple of weeks before my actual exam. Since I want to keep myself sharp and ready comes exam time, I wouldn’t want that to happen! At the same time, I don’t want to cut down the maths on my daily practice for similar reasons.

    So, the question is, if there are only Easy and Medium questions left a couple of weeks before the exam, would they suffice to preserve my acuity, so to speak? I mean, would the lack of challenge in a few weeks negatively affect my score?

    Thanks a bunch! You guys are great.

    • Rita Neumann
      Rita Kreig March 19, 2014 at 2:54 pm #

      Hi Duke!

      I’m glad you’re having fun while studying! 🙂 That’s music to our Magoosh ears!

      I have some suggestions for you. First, make sure you also do all the easy and medium questions, as you will definitely see those topics on test day. You don’t want to rush through them and make careless mistakes, so practicing lower level quant is still really important.

      For more challenging quant questions, you have a couple options:

      1. There are lots of practice questions in our blogs that are not on the site (both on the GRE and GMAT blogs).

      2. Manhattan GRE has a pool of great questions in its practice test. For the $20 purchase of one of their books, you get all six online tests.

      I hope that helps! Good luck studying and I hope you do great on the GRE.


  12. Naomi November 18, 2013 at 8:26 am #

    Hello Chris-

    I have been studying with Magoosh for about 5 weeks and after the first couple of weeks my quant score had substantially declined. On Friday, I took the GRE and did OK on the Verbal, but only 153 on Quant. I’m planning on retaking the test in 3-4 weeks – what is the best way to better prepare for the next round?

    Thank you.

    • Chris Swimmer
      Chris Swimmer November 22, 2013 at 1:26 pm #

      Hey Naomi! At this point, I’d recommend reevaluating your study strategy. If you’re following a tight plan, it might not be giving you enough leeway to focus more on your trouble spots, if you’re not following any real plan at all, then it’s time to make one. A lot of students make the mistake of thinking they can just try a bunch of questions and that’s good enough. You have to really reflect on what your weaknesses are and then attack them as much as possible. Of course since you’re a premium student, you can always reach out to us through the Help tab on the Magoosh Dashboard for study advice. There, we can give you a bit more pointed advice based on your study history. 🙂

      Good luck!
      Chris S

  13. Grant November 6, 2013 at 8:28 pm #

    Hello. Isn’t the very hard question above with the triangles limited by the third side rule? If you have one side that is six and the other eight, doesn’t the other side have to be between two and fourteen? Wouldn’t that limit how the triangle also appears? Just wondering.

    • Chris Lele
      Chris Lele November 7, 2013 at 10:52 am #

      Hi Grant,

      Your reasoning is indeed correct. However, the question is asking for area. Therefore, all three are possibilities.

      Hope that helps!

      • Ronak September 7, 2014 at 12:00 pm #

        I believe his point is that there could be no triangle with an area of 2 because no such triangle can exist under the Triangle Inequality Theroem. Otherwise, under your approach, the triangle could have any area in the world, and I would also imagine that the GRE presumes that the shape can in fact exist

        • Chris Lele
          Chris Lele September 8, 2014 at 12:09 pm #

          Yes, my interpretation/GRE interpretation is that any area greater than zero and equal to the max area of the triangle is possible. Even if we obey the Triangle Inequality Theorem, we could have a triangle with some infinitesimally small area, say if the sides were 8, 6, 2.01. In other words the Triangle Inequality Theorem is about the length of the sides not the area.

          Hopefully that clears things up 🙂

  14. Akshay October 16, 2013 at 1:48 am #


    The universities I plan to apply to require 90+ percentile in Quant and 75 percentile in Verbal section. I took the Barron’s GRE diagnostic test and scored 94 percentile in Quant.
    ( Is Barron’s level the actual GRE difficulty level ?).
    Then I reviewed all the Maths fundamentals from Barrons too. I have 1 and half month left for the test. I solved all the above questions too. Please suggest me some more practice material for maths as well as verbal section. My focus is though more on the Maths section.

    Does Magoosh have a collection of practice questions for Maths and Verbal based of GRE difficulty level ?

    Also, as far as vocabulary is concerned, I plan to only complete the 1000 words in Magoosh’s flashcards and some other frequently occurring 250 words from your other pdf. Please let me know if that much vocab is enough.

    Thank you,

    • Chris Swimmer
      Chris Swimmer October 18, 2013 at 3:44 pm #

      Hey Akshay!

      Looks like you’re off to a great start! Magoosh does indeed have a question bank (500+ math questions), along with 150 math lessons to help you really learn the quant content. You can sort your practice by difficulty and challenge yourself just like in the real test. I’d recommend that over any book. But if a book is your thing, then the Manhattan series is quite nice. 🙂

      As for the vocabulary, when I personally took the GRE I only used Magoosh’s 1000 flashcards and was only stumped by a couple words. But honestly, unless you learn the dictionary or are Chris Lele, there’s no guarantee you’ll know all of the words.

      Good luck!
      Chris S

      • Akshay November 4, 2013 at 11:36 pm #

        Thanks for the response to my previous comment Chris.

        I just finished the Manhattan series’ all Math problems. I scored almost 90% on the Medium as well as Hard level difficulty problems. Is this enough for scoring more than 90 percentile on GRE math. I am planning to take the Powerprep tests in a couple days. I wanted to know how realistic are the Powerprep tests as compared to the actual GRE test.

        Also please suggest me more GRE material for honing my Maths as well as Verbal skills for the GRE

        Thanks again,

        • Chris Swimmer
          Chris Swimmer November 8, 2013 at 4:21 pm #

          Hey Akshay! I’d say the Powerprep is fairly accurate, though a bit too easy, depending on what your test day is like. I’d say at around the 90% mark, Magoosh, Manhattan, and the OG should be good companions, but it will be tough to move the needle too much.

          Chris S

  15. Pinky September 27, 2013 at 10:49 am #

    I’m going to take gre within two months.For math I have completed nova’s math bible,but i am not so good at hard problems. Should i start another book?i personally think too more books make me confused,and i dont have enough time.As your math related posts are so good,wil it be ok to follow your posts and revise nova?

    • Chris Swimmer
      Chris Swimmer September 27, 2013 at 3:32 pm #

      Hey Pinky! Great question. A lot of people have different study strategies. Two books isn’t so confusing since it’s covering generally the same material. I’d check out our GRE Study Plans and GRE Book Reviews to help you make a decision. 🙂

      • Pinky September 27, 2013 at 10:35 pm #

        Thanks a lot for your quick responce.As two books cover almost same materials,so is it neceaasry to go through multiple books?And yes it will be great if you help me make decision.

        • Chris Swimmer
          Chris Swimmer October 4, 2013 at 3:03 pm #

          Hey Pinky! Check out the book reviews I linked to above to figure out which one fits your weaknesses and goals the most. 🙂

          Chris S

  16. abhaykadam September 2, 2013 at 12:58 am #

    i have my gre on 22 oct 13,i m targeting a perfect quant score and have completed nova.,i want to practice a lot as i dont want to get even 169,can u suggest me some books to practice.i m targeting around 310-320.
    i have a BS in civil engineering and is applying to masters in architecture ,gre is just a formality and entire decision is based on portfolio .so is 310-320 a decent score?
    thanking you

    • Chris Swimmer
      Chris Swimmer September 6, 2013 at 6:05 pm #

      Hey Abhaykadam! If you’re aiming for a perfect score in quant simply out of pride, you’re headed down a dangerous path. Many tutors who live and breathe GRE quant don’t get perfect scores. Missing a couple questions often doesn’t mean you don’t know the material but rather that you made some oversight. It happens to the best and doesn’t doesn’t have any bearing on your own real world intelligence. 🙂

      Chris S

  17. Dream Chaser August 15, 2013 at 10:23 am #

    I just retook my GRE with just a couple of days preparation. Unfortunately, my schedule went crazy and I couldn’t afford to do better. Anyway, I did very poorly on the quant, 156. Do you think it is possible to make it 166 if I retake in January, possibly 1st week? I am a graduate student and my course load / research/ presentation at one conference will not give me plenty of time to prepare.

    • Chris Swimmer
      Chris Swimmer August 16, 2013 at 11:23 am #

      Hey Dream Chaser! Essentially what you’re asking is if you can increase your score by 10 points without putting much effort into it? Unfortunately that answer has to be “no”. Jumping from 156 to 166 will not be easy. If you’re serious about increasing to that level, you’ll need to make time for it. Since you have a few months, find an extra hour each day to study. Check out these study plans to find one that will fit you best:

      GRE Study Plans

      Chris S

  18. Nerwen Aldarion August 8, 2013 at 8:59 am #

    I want to know if I should actually retake the GRE, I’m not so good with standardized test and had a panic attack before taking the GRE for the second time.

    I got a 150 Quantitative which is the bare minimum of what I needed to be looked at by the Grad Schools of my choice. Should I considered going through the stress all over again or can I mitigate my average score with my admittedly stellar GPA?

    • Chris Swimmer
      Chris Swimmer August 9, 2013 at 4:57 pm #

      Hey! There’s so much to consider when you’re applying to graduate school and I don’t really know enough about your goal programs to comment specifically. I’d say reach out to someone at the universities and see if they can offer some guidance. 🙂

      Chris S

  19. raj June 23, 2013 at 2:22 am #

    in which books can i find such very hard math problems

    • Chris Lele
      Chris Lele June 24, 2013 at 1:18 pm #

      Hi Raj,

      Nova’s and the GMAT Official Guide (problem solving section) have some tough problems that should prepare you for the tough questions on the GRE quant.

      Hope that helps!

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