GRE · Guides · November 6, 2026 · 7 min read

GRE Quantitative Comparison: the four answers, picking numbers, D traps and worked examples

Quantitative Comparison (QC) is the question type that, among today’s admissions tests, only the GRE uses. You do not solve for an answer: you compare two quantities and decide which is greater, whether they are equal, or whether the information given is not enough to tell. Because the four answer choices never change, QC rewards a fixed routine more than any other Quant format. Most QC questions can be done faster than a standard multiple-choice problem, which buys time for Data Interpretation. This guide covers the routine, the number-picking method, the situations where D is right and where it is a trap, and six original examples.

The four answers

Every QC question has a centered piece of information (sometimes none), Quantity A, Quantity B, and the same four choices:

The key idea: A, B and C are claims about every possible case. Answer A means Quantity A is greater for every value allowed by the information. If one allowed value makes A greater and another makes them equal or B greater, the answer is D.

That gives you a quick rule. If both quantities are fixed numbers, with no variables or unknowns, the answer can never be D. A fixed number is either bigger than, smaller than or equal to another fixed number. You may still need to work it out, but D is off the table.

The routine

1. Read the centered information first. It sets the limits: “x is negative”, “0 < y < 1”, “n is an integer”. Every case you test has to obey it.
2. Simplify both sides the same way. You may add or subtract the same thing on both sides, and multiply or divide both sides by the same positive number, without changing which side is greater. Do not multiply or divide by a variable unless you know its sign. A negative number flips the comparison.
3. Compare, or test cases. If the simplified sides are easy to compare, you are done. If variables remain, pick numbers.
4. Try to break your first answer. After the first case, deliberately pick a different kind of number. If the result changes, answer D.

On the noteboard, write the comparison as “A ? B” and carry the question mark through each step. When you know the relationship, replace it with >, < or =.

Picking numbers: the cases to test

When a variable is not restricted, check these types of numbers, in roughly this order:

• A positive integer such as 2 or 3 (avoid 1, which hides patterns).
• Zero. Zero times anything is zero, and 0² = 0.
• A negative number. It flips inequalities and makes odd powers negative.
• A fraction between 0 and 1. Squaring makes it smaller: (1/2)² = 1/4.
• A negative fraction between −1 and 0. Here x³ is greater than x: (−1/2)³ = −1/8.
• 1 and −1. Equal cases often hide here.
• Large numbers, when one side grows faster than the other.

You rarely need all seven. Usually two or three well-chosen cases settle the question.

Six worked examples

All examples are original questions in the GRE style. Try each before reading the solution.

Example 1: fixed numbers

Quantity A: 15% of 80

Quantity B: 80% of 15

Both are fixed numbers, so the answer cannot be D. 15% of 80 = 0.15 × 80 = 12, and 80% of 15 = 0.8 × 15 = 12. Answer: C. The shortcut: a% of b always equals b% of a, because both are ab/100.

Example 2: the sign decides

x < 0

Quantity A: x²

Quantity B: x³

A negative number squared is positive, and cubed it is still negative. Every allowed x gives a positive A and a negative B. Answer: A. No case testing needed: the centered information settles the signs.

Example 3: the classic D

x ≠ 0

Quantity A: x

Quantity B: 1/x

Test cases. x = 2: A = 2, B = 1/2, so A is greater. x = 1/2: A = 1/2, B = 2, so B is greater. The result changed, so answer: D. If you had tried only whole numbers, you would have picked A. A fraction between 0 and 1 is the case that breaks it.

Example 4: geometry without a figure

A triangle has two sides of lengths 5 and 8.

Quantity A: The length of the third side

Quantity B: 13

The third side can take many values, which looks like D. But in any triangle each side is shorter than the sum of the other two, so the third side is less than 5 + 8 = 13. It is also greater than 8 − 5 = 3. Whatever its exact length, it is less than 13. Answer: B. This is a D trap: the quantity varies, but every possible value falls on the same side of B. Unknown does not automatically mean undeterminable.

Example 5: data analysis

The list 3, 7, 7, 11, x contains five numbers, and x > 11.

Quantity A: The mean of the five numbers

Quantity B: The median of the five numbers

Since x > 11, x is the largest number, so the ordered list is 3, 7, 7, 11, x and the median is 7 whatever x is. The mean is (28 + x)/5. With x just above 11, the mean is just above 39/5 = 7.8, and it only grows with x. So the mean is always greater than 7.8, which is greater than 7. Answer: A.

Example 6: harder algebra

x > y > 0

Quantity A: x/y

Quantity B: (x + 1)/(y + 1)

Try numbers first. x = 3, y = 2: A = 1.5, B = 4/3 ≈ 1.33, so A is greater. x = 10, y = 1: A = 10, B = 5.5, so A again. Now confirm algebraically, since two cases are not proof. Both denominators are positive, so you can multiply both sides by y(y + 1) without flipping anything. That compares x(y + 1) with y(x + 1), which is xy + x versus xy + y. Subtract xy: x versus y. The centered information says x > y. Answer: A.

Here number-picking gave the answer quickly and algebra confirmed it. When your test cases keep agreeing but you are not sure why, a 30-second algebra check like this protects you from a hidden D.

The D traps, in both directions

Choosing D too fast. A variable or a figure not drawn to scale looks uncertain, but constraints often pin the relationship down. Examples 4 and 5 both had a quantity that changed, and the answer was still A or B. Before choosing D, ask: is there a rule, such as a triangle inequality, the sign of a variable, or an ordering, that holds for every case?

Not choosing D when you should. The more common error is testing one or two similar numbers and stopping. If you tried x = 2 and x = 3, you have tested the same kind of number twice. Change the type: try a fraction, zero or a negative.

Trusting the figure. GRE geometry figures are not necessarily drawn to scale. An angle that looks like 90° or two segments that look equal prove nothing unless the information says so.

Dividing by a variable. Turning “xy ? x” into “y ? 1” by dividing by x is valid only if you know x is positive. If x could be negative or zero, test cases instead.

Timing

Quant gives you 47 minutes for 27 questions, about 1 minute 45 seconds each. QC questions should take less than that, often under a minute, because there is nothing to calculate to the last digit. If a QC question is taking more than two minutes, use Mark, make your best guess and move on. There is no stated penalty for wrong answers, so never leave one blank.

Practice

Nomto’s Quantitative Comparison practice gives you original QC questions at your level across arithmetic, algebra, geometry and data analysis. Every explanation names the case that decides the answer. If algebra is where you slip, go straight to algebra QC questions. The level shown in practice is Nomto’s estimate, not a GRE score; Nomto is not affiliated with ETS, and GRE is a registered trademark of ETS. To see how QC fits into the Quant sections, read the GRE format guide. For the graph and table questions that share the section, see the Data Interpretation guide.

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