If you are new to the GRE, you may be surprised to learn that the GRE quantitative reasoning section consists of 4 different question types: multiple-choice questions, multiple answer questions, fill-in-the-blank questions (also referred to as numeric entry), and Quantitative Comparison (QC) questions. You may have never encountered QC questions, but the good news is that QC problems should not be an issue for you with the right approach and solid quant skills.

In this article, we will discuss what a QC question is and how to attack these questions, and walk through the solutions to some Quantitative Comparison examples. Additionally, you’ll get our top 3 tips for solving QC problems and the 5 keys to QC mastery.

First, let’s cover the basics of what Quantitative Comparison questions are and what they look like.


Developing an understanding of QC questions is essential, as roughly 15 out of the 40 quant questions on the GRE fall into this category. In a typical Quantitative Comparison GRE question, you are provided with some information, sometimes called the constraint, and two quantities: Quantity A and Quantity B. Your job is to decide the relationship between the two quantities, with the following standard answer choices, which you should memorize:

A. Quantity A is more significant than Quantity B.
B. Quantity B is greater than Quantity A.
C. Quantities A and B are equal.
D. The relationship between the two quantities cannot be determined.

Let’s look at an example to introduce you to the essence of a QC question.

Example
x > 0 and x^2 – x – 6 = 0
Quantity A: x
Quantity B: 2

Solution:
The constraint information tells us that variable x is greater than 0 and that x2 – x – 6 = 0. We need to compare quantity A, which is x, to quantity B, which is 2, and determine the relationship between them.

First, we will want to solve the equation x2 – x – 6 = 0, so that we know the possible value(s) of x:

x^2 – x – 6 = 0

(x – 3)(x + 2) = 0

x = 3 OR x = -2

We have two possible values of x, but since the constraint also specifies that x > 0, we see that x must be 3, not -2.

Thus, quantity A = 3 and quantity B = 2. Therefore, Quantity A is greater than Quantity B.

Answer: A

Now that you have a basic understanding of how QC questions work, the following three tips will be extremely useful for you in solving Quantitative Comparison questions.


While many QC questions can be answered by simplifying or solving algebraic expressions (as we did above) or using formulas, some cannot. In such cases, testing various possible values for variables may help determine which quantity is greater. When we plug in numbers, however, we do not do it blindly. We use the given information to guide us on which numbers to test, and then we can strategically consider testing the following types of numbers:

• Zero
• One
• Positive proper fraction
• Negative proper fraction
• Positive integer
• Negative integer

Memorize this list. Keep in mind that it is rare you will need to test all six types of numbers to arrive at a correct answer. In fact, the goal is to test the fewest numbers possible. Let’s practice this strategy with an example question:

Example 1
p is a positive number
Quantity A: p
Quantity B: p^2

Solution:
Suppose we were to look at these two quantities quickly. In that case, we might hastily (and incorrectly) conclude that quantity B must be greater than quantity A because a squared number is greater than the original number. However, as we will see, that reasoning is not always correct.

Since we know that p is positive, we choose only the following number types from the list provided above to test the quantities:

• One
• Positive proper fraction
• Positive integer

If p = 1:

Quantity A: 1

Quantity B: (1)^2 = 1

When p = 1, we see that the two quantities are equal, consistent with choice C.

If p = ½ (a positive proper fraction):

Quantity A: ½

Quantity B: (½)^2 = ¼

When p is ½, quantity A is greater than quantity B, consistent with choice A.

Already, we see that there is not a consistent relationship between quantity A and quantity B. So, we should choose answer choice D: the relationship cannot be determined from the information given.

We can stop at this point, but let’s also try out the number type, a positive integer.

If p = 2:

Quantity A: 2

Quantity B = 2^2 = 4

When p = 2, quantity A is less than quantity B, consistent with choice B.

Answer: D

The main takeaway here is that when you’re in doubt, test numbers, using the list as your guide for which numbers to choose. Let’s try one more example.

Example 2
Quantity A: x
Quantity B: 3x

Solution:
The goal is to determine the relationship between the two quantities, choosing from the standard answer choices. Your knee-jerk reaction may be to say, “Well, if I multiply a number by 3, the answer will be bigger, so quantity B is greater than quantity A, and so I choose answer choice B.” However, you would be incorrect in this case, having fallen for a trap that has tripped up many GRE students. Here’s why:

If you let x = 1 or 2 or 3.71, or any positive number, you are correct that 3x is greater than x. But what if x = 0? Plug in 0 for x, and you find that quantity A = 0 and quantity B = 0, too! So, in this case, the two quantities are equal, and answer choice C appears to apply. Or, if x were a negative number like -2, -3.5, or -100, then x would be greater than 3x, in which case the answer would seem to be A.

Now, take a careful look at the answer choices. Since answer choices A, B, and C are each sometimes true, but not always, we cannot choose them. Thus, our only recourse is to select answer D: the relationship between the two quantities cannot be determined.

Answer: D

Let’s now see why it’s important to know all those math formulas.


While this tip may seem obvious, it can’t go without saying: the better you know GRE quant formulas and rules, the more effectively you will answer QC questions. For example, if you do not know exponent rules, how can you expect to answer a QC question on exponents? If you do not know geometry formulas, how can you answer a QC geometry question correctly?