How to Review a GRE Quantitative Comparison Question
When you miss a GRE Quantitative Comparison problem, it’s easy to feel like you’ve been “tricked” by the test. You know the saying “fool me once, shame on me, fool me twice, shame on you?” On the GRE, it goes the other way. Getting tricked once is a learning opportunity. But if you’re getting tricked in the same way more than once, look at how you’re reviewing problems.
Ideally, you should review every Quantitative Comparison problem you do. However, if you’re short on time, these are the most important problems to review:
- Problems that you got right, but spent too much time on or had low confidence in.
- Problems that you missed, but basically understood—that is, problems that were just a little bit too hard.
- Problems that taught you something new and interesting.
Most importantly, don’t waste your time reviewing problems that you didn’t understand at all. Save those for later. Prioritize the ones that you could quickly get right next time with just a bit of work.
Getting Started Reviewing Quantitative Comparison
Here are the building blocks of review:
- A problem log. Here’s how to make one.
- A study calendar. Here’s an article on creating a study calendar for all of your GRE studying. However, we’re only talking about review in this article! For now, I’ll just ask you to block off a single one-to-two hour study session per week to focus solely on reviewing and redoing old problems.
- A good source of practice problems. The 5lb. Book of GRE Practice Problems is your best bet.
Reviewing a QC problem
The first step is to redo the problem. Do this on the same day that you did the original problem, or at least the next time you sit down to study. This time, don’t use a timer. Relax and allow yourself to try multiple approaches.
There’s only one thing you can’t do when you redo the problem:
DON’T READ THE EXPLANATION!
When you passively read an explanation, you’re practicing comprehension, or “getting it.” Unfortunately, “getting it” is a lot easier than what the GRE actually asks you to do. (Have you ever gotten totally turned around by a problem, then read the explanation and found that it seemed totally easy? That’s because you were at the “I get it” stage of learning.)
Don’t let yourself get away with “I get it.” Instead, figure out as much as you can on your own. If you have to test 10 different cases, go for it! If you have to look up a geometry rule in your book, feel free! Take all the time you need.
If you get stuck, you can use the explanation for hints only. Read a sentence or two at a time, and see if that gets you moving again. Only read the full explanation once you’ve gotten everything you can out of the problem on your own. Explanations are useful, after all: they’ll often show you faster or easier ways to solve a problem. Just don’t rely on them more than you need to.
Learning from a QC problem
After you’ve redone the problem, and you understand the right answer, it’s time to reflect and take notes. (And if you still feel like you don’t understand the answer, you’re allowed to set the problem aside for later. It may just be unrealistically hard, or you may not have learned the content you need yet.)
Let’s practice reflecting on a QC problem. Here’s a problem from the 5lb. Book of GRE Practice Problems. Try it out on your own first, then we’ll create a problem log entry together.
The first thing to reflect on is the given information. Not every QC problem gives you extra information, but many do. Here’s what you should ask yourself about the given info:
- Does anything stand out? What does it mean?
- Did you miss anything?
- Is there any math content you need to review?
These questions are general on purpose. There’s no better way to get bored with review than forcing yourself to rigidly answer a set of irrelevant questions. The goal here is to organize your thinking and make sure you’ll remember any lessons this problem could teach you.
Here are some examples of students’ notes about the given info.
Student A misunderstood the words “non-negative integers.” She assumed immediately that this meant “positive integers.” Here are her notes:
- Non-negative does NOT mean positive!
- Non-negative = 0 or positive (just not negative). Test 0!
Student B chose numbers for k, m, and n. However, the numbers she chose didn’t actually fit the equation she was given! Here are her notes:
- Info says k = 2m but I tested k = 3, m = 6. Be careful when you see “x = 3y” or something like that: plug the numbers back into the equation to make sure you didn’t get turned around. If you plug in k=3, m=6 you get 3 = 2(6) which isn’t true.
Student C got this one right. She caught the “non-negative” trick, but she jotted down some notes on it anyways because she knew she could have been fooled by it.
- Non-negative integer = 0, 1, 2, 3, 4, etc
The second part of a QC problem is the two quantities. These can look very different, depending on what the problem shows you. Here are some specific things to think about as you take notes.
- Was this a problem where you should test cases, or did you need to calculate? If you needed to test cases, what were the right cases to test?
- Was there a way to avoid doing math, by estimating or comparing the quantities instead of calculating?
- Could you simplify the quantities?
- Does anything else stand out that you want to remember?
Student A decided to test cases as she solved this problem. She tested two cases:
Based on this, she concluded that Quantity A was always greater. However, when she worked through the problem again, she realized that she’d made a few mistakes. Here are her notes.
- If it says not negative, don’t panic and test negatives! Check each case you test to make sure you aren’t breaking the rules!
- Always test 0 when it’s allowed by the rules.
- If everything is positive, you can divide both sides by the same variable. Divide both sides by k and just compare m versus n. (But doesn’t work if k = 0)
Student B also tested cases, but as described above, she didn’t test the right numbers. Instead of testing k = 6 and m = 3, she tested k = 3 and m = 6. This caused her to conclude that Quantity B was greater.
- Always test 0! Non-negative includes 0, positive doesn’t include 0
- Check the numbers you test by plugging them into the given info.
Student C didn’t test cases at all. She noticed that you can divide both quantities by k, letting you just compare m and n. However, she hesitated determining which value was greater, and she only noticed that they could equal zero at the very end.
- Always test 0!
- If 2m = 4n, then m = 2n. Be careful with this! Read it as “m is two times n,” which makes m bigger than n. If you aren’t sure, plug in numbers to double check.
By the way, the right answer to this problem is (D). If k, m, and n are positive integers, then m will be greater than n. But if they’re all equal to zero, the quantities will be equal.
The next step
Once you’ve taken notes on a problem, set it aside for a week or two. When your next review study session comes around, try the problem again. See if you get it right this time! If not, go back and reflect on it again, and consider doing some practice that targets the area you’re having trouble with.
You should also glance over your problem log once or twice during the week. There’s no need to redo the problems when you do this—just take fifteen minutes and reread your takeaways. This will remind you of what you’ve learned and keep everything fresh in your mind.
If Quantitative Comparison is a strong area for you, it’s fine to take minimal notes and just jot down any huge takeaways. However, if you’re performing better on other Quant problem types than you are on QC, intensify your review for a couple of weeks. Get organized and reflect deeply on every single problem. It’s not about how many problems you do! It’s about making (and understanding) your mistakes now so you don’t make them on test day.
[ Related: How to Review a GRE Vocabulary Question ]
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Chelsey Cooley
is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.