Math Question Realism

[Vince Kotchian GRE Prep]

hi guys,

I got a question from someone today about whether Magoosh or Manhattan Prep's GRE math practice questions were realistic. I'm posting my response because I want to see if anyone has thoughts on this topic, particularly people who have taken or studied for the GMAT (and also for the SAT). My response:

"All the third party questions I've ever seen tend to be less complex than real GRE questions. They will test the same concepts, but when companies like Manhattan try to make questions difficult, they tend to do things that make them difficult in markedly different ways than ETS questions will (for example, making problems very calculation-heavy). For instance, you might see a crazy problem with lots of third and fourth roots - something the GRE probably will never do.

 

Real GRE questions tend to have more of a logical component and tend to be more wordy, which is a different way of making things difficult. However, this way of making questions difficult is much harder to duplicate than just throwing in fourth roots, for example.

 

I know from experience writing test-prep books and making video courses for a few different companies that there is very little quality control or editorial pushback to make questions realistic. Quantity is much more important to companies (a reason Manhattan's 5-lb. book is so popular). Most buyers of test-prep books and products don't have enough experience to discern whether questions are realistic or not, so they often go for the biggest book or the product with the most videos, questions, or tests.

 

A good way to get used to real ETS questions, other than the ETS books, is to practice SAT or GMAT math questions written by the companies that publish those exams. Yep, SAT and GMAT. Since those companies write math questions that are wordy and involve logic, they're a good supplement to ETS GRE. ETS used to write the SAT but no longer does, so the old SAT Official Study Guide is a good source of practice (not the most current version).

 

With all that said, some companies (Manhattan GRE in particular) are good at making sure you know the concepts behind questions, but I wouldn't say it or any other test-prep company writes realistic GRE questions."

 

p.s. This advice probably only concerns people who need 70th percentile math or higher. 

 

[rageofanath]

Actually I got a few 3rd root questions on the GRE, and they were in different sections so they couldn't have all been "research" questions.

My last math class was high school precalc in 2006 so I went from diagnostic tests giving me 148 to getting a 160 (something like 76%?) a few weeks ago. I did a lot of prep -- basically nothing but math prep for about 3 months. I also couldn't afford more than one book so I had to deal with what the local library had. I spent $20 on test prep. As far as accuracy, it's hard to say which books were the most accurate. For me it was volume of math problems in general and learning "tricks" to shorthand some of the problem types, as well as saving all the quant comp and graph questions for last since they're easy to get into a calculating rut and waste time. (especially if the answer is D on a quant comp and you don't see it right away)

So I used:
Princeton: The math problems are SUPER easy compared to the ETS stuff but if you're not scoring high right now its a good first book. I used their "average pie" on the test multiple times and it's a really good trick to see the solution fast. I also used some of their estimating, if you're not writing and just thinking - move on, and "which answer should I plug in first" strategy suggestions among a few others. Their Math Workout was the only book I purchased, and I bought it on impulse the day I decided I'd take the test and didn't research it versus its competitors. I got the whole "general" book from the library and its a lot of the same ; a bit too easy but good intro material if you weren't a STEM major. 

Barrons: Not a huge fan but it was useful to just get the extra practice. It was harder than Princeton but easier than ETS + GRE in general.

Peterson: Did one problem set and returned it, happy I didn't pay for it. I don't know how accurate the questions are but they don't do a good job explaining how they got their solutions, especially for someone who was trying to relearn stuff like "dividing fractions."

Magoosh: Loved the few practice problems they let you do for free, seemed pretty accurate, but I couldn't afford the $100 season pass.

Khan Academy: The ETS site links Khan Academy with the "topics covered" page. I used it to practice my basic arithmetic / algebra, memorize geometry formulas, and practice combinations and permutations. It's not accurate at all to GRE questions since it doesn't even try to mimic them, but for brushing up on questions like "find the area and/or perimeter of this fairly straightforward geometric figure" its excellent. It was easier for me to practice this stuff outside of GRE context since Khan Academy doesn't try to trick you and hide that its actually a 45-45-90 triangle. So you can practice just the math. I started this after I finished all the problems in the Princeton book so I skipped any section that wasn't relevant or was going into more detail than necessary.

Kaplan: Signed up for their free practice test (ie sales pitch). Not accurate. There was a significantly higher percentage of the "hard / rare" problems like combinatorics. On the GRE I only saw a handful. I didn't do that well on their practice test but I had done enough prep by that time to see that the test they gave was not representative.

ETS: Everyone was saying "if you want to know what's on the test, go straight to the source", so I did, but not until the end. The ETS book is awful at explaining anything but accurate in terms of difficulty. I wouldn't recommend this book to learn from if you haven't had math in a while, but I would recommend it if you're scaling up the difficulty. There's a lot of stuff in there that I didn't see on the test, but its hard to say what they put in year after year. I also found the practice tests harder than the real test, I was scoring 155-158 usually... even got 152 on one of the powerprep practices. Despite that I got my highest score on test day. 
I borrowed this book from a friend who was going to take the GRE but decided against it, but it might have been worth paying for if I had to.

Manhattan: Couldn't afford it, library didn't have one. Can't comment on how good they are, but not a huge fan of the 6 volume, $20/each thing, though from what I've read they sound worth it... and fairly accurate...?

SAT/GMAT: I read this advice but didn't have a chance to try it out. I had more than enough GRE practice problems and general math. 

 

 

So yeah, I agree. No company really writes accurate questions. I think for me using a lot of companies helped because it meant that I wasn't stuck in one, inaccurate way of doing things. I also did a lot of basic math drilling that isn't strictly tied to GRE to try and decrease the amount of time per problem, since the goal is an average of 1.75 minutes / problem speed is #1. I actually aimed for 1.6 min/problem to give more wiggle room and allow plenty of time to click "review" and see what I had flagged.

I think it's a big mistake to simply pick up one GRE prep book and be done with it, unless you've got a math based undergrad and just want to figure out the problem format.

Edited March 31, 2016 by rageofanath