GRE® Quantitative Comparison

The first time you see a Quantitative Comparison question on the GRE, you might find yourself doing a double take. You’re given two quantities, and instead of solving for a value, you have to decide which quantity is bigger. Even if you’ve prepared for other standardized exams, you probably haven’t seen anything quite like it.

The good news is, the format is actually quite learnable. If you’re able to think logically and apply a consistent process, you should be in great shape. Here’s how to do just that.  

What a Quantitative Comparison Question Looks Like

Every QC question shows you Quantity A and Quantity B. In some cases, additional information is included above them. Your job is to compare the two quantities, then pick one of the following four answer choices:

1. Quantity A is greater.
2. Quantity B is greater.
3. The two quantities are equal.
4. The relationship cannot be determined from the information given.

Get familiar with these answer options, because they never change. Luckily, once you’ve drilled enough QC questions, they should become second nature.

The Mental Shift: You’re Comparing, Not Solving

One of the keys to success on QC is to shift your mindset. On problem solving questions, you’ll often find yourself asking “what is this quantity equal to?” On QC, however, you’ll want to ask yourself a slightly different question – namely, “which of these quantities is bigger?”

That distinction is crucial for several reasons. 

First of all, you frequently won’t be able to pin down a specific value for the quantities. Yet despite that, you may still be able to figure out how they relate to each other. 

Second of all, you sometimes won’t be given enough information to compare the quantities at all, in which case the answer would be D (the relationship cannot be determined from the information given). In either case, trying to pin down the quantities to one specific value will only waste your time. Rather, you want to compare the values they could have under varying circumstances. 

A Method That Works

Here’s a simple process you can use for QC questions.

1. Simplify both quantities first. In some cases, the given quantities may look complicated, even intimidating. In those situations, the way they’re written could make them hard to compare. If that’s the case, try simplifying. Use all the methods from your algebra toolkit to clean them up. Sometimes, a few rounds of simplification will work wonders, making the quantities much easier to compare.
2. Don’t forget about the restrictions. At the top of a QC question, you’ll often see crucial information that’s easy to skip over or forget. The value of x may be limited to positive numbers, or negative numbers, or even integers, or odds. While these restrictions are almost always essential, they’re easy to overlook in the heat of the moment. In fact, they’re one of the most common causes of errors on QC.
3. Avoid random number-picking. In many cases, a mixture of logic, algebra, and other tools will be enough to pick an answer. If those methods fail, however, you may find yourself thinking about concrete scenarios to help you compare the two quantities. For instance, what if x were equal to a positive integer? Which quantity would be bigger in that case? What if x were negative? Would that change things at all?

Going down this road is sometimes useful, but it can also be a slippery slope. Here’s the issue in a nutshell – let’s say I pick a value for x, plug it in, and find that Quantity A is bigger. 

Does that mean that Quantity A is always bigger? Possibly not. But in that case, how many values of x should I plug in before I decide that A is bigger? Is two enough? Three? Why not four? And what kinds of numbers should I plug in? Integers? Fractions? Negatives? Really big numbers? 

You can imagine how time consuming this process could become. So how do you avoid it? Here’s the key: even if you think about concrete numbers sometimes, you want to be guided by logic above all. In other words, if you pick a certain number for x, don’t just do it randomly. Rather, pick a specific number for a specific reason, trying to induce a specific outcome. If you’ve found that Quantity A can be bigger, for instance, try really hard to break that result. Think, for example, about what values might make Quantity B bigger (or what might make Quantity B the same as Quantity A). If you succeed in breaking your first result, then the answer must be D. If you just can’t make B bigger than A (or the same as A), the answer must be A after all. Going down this path, you’ll hopefully start to grasp the underlying logic of the question, and avoid the trap of random number-picking.

Common Quantitative Comparison Pitfalls

Assuming variables are positive integers. When given a variable, most people tend to assume it’s a positive integer. Unfortunately, that assumption is one of the most common causes of errors on QC. Keep in mind, unless it’s specifically restricted, a variable could be positive, negative, zero, or even a fraction. And if it’s any of these, that could easily flip a comparison. Bottom line, always be aware of the restrictions placed on variables.

Multiplying or dividing both sides by something that might be negative. Remember that dividing or multiplying an inequality by a negative number flips the direction of that inequality. Forgetting this rule is another common cause of missed QC questions.

Trusting figures to be drawn accurately. Geometric figures on the GRE aren’t necessarily drawn to scale, so a shape that looks like a square might not actually be one. Work from the labels and the given information rather than from what the picture appears to show. Our geometry guide covers this in more detail.

Reaching for the calculator too early. The availability of a calculator can make the trap of random number picking especially tempting on QC. Watch out for that pitfall. Although the calculator can occasionally be your friend, it’s less useful than it may seem on Quantitative Comparison questions.

How to Practice Quantitative Comparison

Since QC doesn’t appear on other exams, official ETS material is the best source to practice this question type. Third-party questions often miss the nuanced nature of official QC questions, and should be used sparingly if at all.

Additionally, keep in mind that you don’t just want to be accurate on your QC homework – you also want to be efficient. If you get a question right after four minutes of trial and error, for instance, you probably missed a quicker, more logic-based solution path. Overall, Quantitative Comparison questions will often resolve through elegant insights rather than tedious grinding. 

Lastly, during your QC prep, make sure you pay special attention to the cause of your mistakes. As always, that’s where the learning and improvement on the GRE really happens.

For more information about the Quant section on the GRE, visit our full guide on the section.