Good news: GRE Quantitative Comparisons aren’t like anything you had to do in math class. Mastering these tricky problems is a quick way to improve your GRE Quant score without a ton of computation. Get started with our 10 best GRE Quantitative Comparisons tips! Then, once you’re done reading, check out the GRE Math Strategy Guide for even more.
1. Memorize the answer choices on GRE Quantitative Comparisons.
The answer choices are always the same! If you save ten seconds on each Quantitative Comparisons problem by not rereading them, that’s more than a minute saved per Quant section.
2. (D) doesn’t stand for ‘don’t know.’
On GRE Quantitative Comparisons problems, answer choices (A),(B), and (C) are pretty straightforward. Then, choice (D) comes out of left field with this:
The relationship cannot be determined from the information given.
How are you supposed to prove that you can’t determine something? Here’s the secret: you aren’t. You can imagine that (D) says this, instead:
Quantity A is bigger sometimes, and Quantity B is bigger sometimes.
Thinking about it this way will keep things concrete and straightforward. Is Quantity A always bigger, no matter what you do? Then pick answer (A). Is Quantity B always bigger? Pick answer (B). But does it go one way in one situation and the opposite way in another? Pick answer (D). (By the way, you should also pick (D) if the quantities are sometimes equal and sometimes not equal!)
3. Make smart, fast guesses on GRE Quantitative Comparisons.
You’re going to guess on the GRE. The number-one trick for guessing on Quantitative Comparisons? Know which answers to eliminate before you guess.
On some GRE Quantitative Comparisons problems, the two quantities are definite values. They might be values that you and I can’t calculate, like in this problem:
Quantity A: 7943
Quantity B: 8031
Even though those are huge numbers, they’re both just numbers, not variables or expressions. If both quantities refer to specific numbers, choice (D) can’t be the right answer! Either one of the numbers is bigger than the other, or they’re both equal. Eliminate answer (D) and make a guess.
In some cases, you can also tell that the answer shouldn’t be choice (C). Maybe you have no idea whether 7943 is bigger or smaller than 8031. But with some logic, you can tell that they can’t be equal. After all, 8031 has to end in a 0, and 7943 definitely doesn’t. Eliminate choice (C) before guessing.
Finally, this might seem silly, but be careful not to guess any answer you’ve already eliminated. Suppose that you’re working on a tough Quantitative Comparisons problem, and you’ve figured out that Quantity A is sometimes bigger. Now you’re running out of time, and you can’t decide whether Quantity B is sometimes bigger, too. You need to make a guess, but don’t make a guess that contradicts what you already figured out. Since A is sometimes bigger, you can definitely eliminate answers (B) and (C) before guessing.
4. Simplify everything.
To start any GRE Quantitative Comparisons problem, breathe and simplify. That’s not a meditation mantra! It’s actually a problem-solving technique. A lot of Quantitative Comparisons problems are hard because the information is given to you in an overly-mathematical or complicated form. Simplify the given information and each quantity as much as possible. A good starting point is to try making the two quantities look as similar as possible. For instance, if one contains decimals and the other contains fractions, convert both to the same form before you keep working.
Once everything is simplified, the answer might jump out at you! But if it doesn’t, keep reading…
5. Try to prove (D).
If you’ve simplified as much as you can, and it isn’t clear which quantity is greater, the next step is to try proving answer (D). The method for doing that is called case testing. You do it by considering different situations and thinking about which quantity would be greater. Here’s an example:
3x² + 5y² > 200
x² + y² = 61
Quantity A: y
Quantity B: 3
Remember tip number 4 first: simplify! You can simplify the given information into a single inequality:
3x² + 5y² > 200
3(61-y²) + 5y² > 200
183 + 2y² > 200
2y² > 17
y² > 8.5
It looks a lot better, but the answer isn’t completely obvious. The next step is to look at different cases, and the goal when you do that is to prove answer (D). That means proving that Quantity A is bigger sometimes, and Quantity B is bigger other times (alternatively, that they’re sometimes equal, and sometimes different).
You already know that y² has to be bigger than 8.5. Start by showing that y can be bigger than 3, since that’s easier! y could definitely be 100, 1,000, or even 1,000,000. So, in some cases, y is bigger than 3.
The next step is to try to show that y could be smaller than, or equal to, 3. It turns out that y can equal 3, because 3² is greater than 8.5. At this point, you’ve successfully proven answer (D). y is sometimes equal to 3, and sometimes greater than 3, and since it can go either way, (D) is the right answer. Keep moving!
6. Get organized.
Case testing is sometimes a lot more complicated than that. Get organized about it by creating a chart on your scratch paper.
Keep everything neat and clear by creating a column on your paper for each value you might have to calculate, and a different row for each case you test. If you need to do additional math, do it off to one side, or above or below your chart.
7. Simple first, then weird.
Start by testing a simple scenario, whatever is easier to prove or makes the math more straightforward. We did that in the problem from tips 4 and 5, when we said that y could equal 100 or 1,000. Those are simple, round numbers, and since they’re very large, it’s easy to tell that y² is large as well. Don’t think that you need to come up with really exciting cases to test right away. Start with a simple case and just see what happens, then eliminate as many answers as possible on that basis.
8. Weird cases? Try ZONEF.
Not sure what values to test while solving a GRE Quantitative Comparisons problem? Here’s some help! ZONEF is a mnemonic that stands for “zero, one, negatives, extremes, fractions,” and it can help remind you which cases are most likely to help you prove answer (D).
9. Compare, don’t calculate.
You can solve some GRE Quantitative Comparisons problems with much less math than you’d expect. Here’s an example:
A certain class consists of 14 undergraduate students and 9 graduate students. The undergraduates earned an average grade of 70% on the final exam, and the graduates earned an average grade of 80%.
Quantity A: The average grade earned by the entire class on the final exam
Quantity B: 76%
You don’t need to know the exact average grade: you only need to know whether it’s higher or lower than 76%. Before you calculate, pause and reason about the problem. The average should be closer to 70% than to 80%, because there were more undergrads than grads. So it’ll definitely be lower than 76%, and the answer has to be (B).
In some GRE Quantitative Comparisons problems, you have no choice but to calculate! But in a lot of them, you can get away with just comparing the two values. It doesn’t matter what the exact values are if you can tell which one has to be bigger. Put that calculator away!
10. Pay attention to constraints…and non-straints.
A “constraint,” in a GRE Quantitative Comparisons problem, is any extra piece of info that you’re given about the values involved. For instance, “y is even” is a constraint. So are “x is a positive integer” and “k is less than 1.” There are even implied constraints: if somebody has b bananas or c children, you can safely assume that b and c are integers!
If a Quantitative Comparisons problem includes a constraint, always jot it down on your paper. Many of these problems are designed so that the answer comes out differently if you ignore the constraint! The test writers are hoping to trap people who don’t notice, or forget about, a constraint.
You should also train yourself to notice constraints that aren’t there. If a problem doesn’t tell you that x and y have to be positive, it’s possible that something interesting will happen when you make them negative! If a problem doesn’t say that all of the numbers are integers, check what happens when you use fractions! And if there isn’t a constraint, anything is fair game, and a great test taker knows when to get creative.
Bonus: Quantitative Comparisons are usually pretty short problems. That makes it tempting to dive into a problem without slowing down and thinking it through first. But, in our experience, slowing down at the beginning of a GRE Quantitative Comparisons problem pays off. Take the extra few seconds to tidy your scratch work and really read everything in the problem. It might make you a little slower on each problem, but it’ll pay off when you avoid getting confused and bogged down. 📝
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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.