GRE Quantitative Comparison
Last updated: May 2, 2026
Quantitative Comparison questions are one of the highest-leverage areas to study for the GRE. This guide breaks down the rule, the elements you need to recognize, the named traps that catch most students, and a memory aid that scales to test day. Read it once, then practice the same sub-topic adaptively in the app.
The rule
Quantitative Comparison (QC) asks you to decide whether Quantity A is bigger, Quantity B is bigger, the two are equal, or the relationship can't be determined from the information given. The right answer must hold under every legal value of every variable — so your job isn't to find one outcome, it's to test whether the relationship is forced. Most wrong answers come from students who plug in one nice number, see a clear inequality, and lock in (A) or (B) before checking negatives, fractions, or zero.
Elements breakdown
The Four Choices
Every QC question uses the same fixed answer set, so memorize it and never re-read it.
- (A): Quantity A is always greater
- (B): Quantity B is always greater
- (C): The two quantities are always equal
- (D): Relationship cannot be determined
- (D) wins if even one case flips the result
The Plug-In Protocol
When variables are present, run a deliberate sequence of test values designed to break any tentative answer.
- Try a small positive integer first
- Try $0$ if it's legal
- Try a negative number
- Try a fraction between $0$ and $1$
- Try a number that satisfies edge constraints
- Stop only after two cases agree or one case flips
Common examples:
- $x = 2$ as your default starter
- $x = -1$ to test sign behavior
- $x = \frac{1}{2}$ to test fraction behavior
Algebraic Simplification First
Before computing, transform both quantities into comparable forms — often the comparison collapses.
- Subtract the same value from both sides
- Multiply both sides by a known positive
- Square both sides only if both are non-negative
- Cancel matching factors that are clearly positive
- Convert percents and ratios to common form
When (D) Is Impossible
If both quantities are fully specified numbers with no variables, (D) cannot be the answer — compute and pick A, B, or C.
- No variables anywhere $\Rightarrow$ (D) is out
- Geometry figures with all measurements given $\Rightarrow$ (D) is out
- Pure arithmetic comparisons $\Rightarrow$ (D) is out
Common patterns and traps
The Plug-In Protocol
When variables appear, systematically substitute test values rather than reasoning abstractly. Start with a small positive integer to get a baseline, then deliberately try the values designed to misbehave: zero, a negative number, and a fraction strictly between $0$ and $1$. The goal is not to confirm your hunch but to break it. If two well-chosen cases give the same comparison, you can usually trust (A), (B), or (C); if any case disagrees, it's (D).
Any QC with an unconstrained variable like $x$, $n$, or $a$ — especially involving exponents, reciprocals, or absolute values — is begging for plug-ins.
The Simplify-Both-Sides Heuristic
Before computing, treat the two quantities as the two sides of an inequality you're trying to resolve. You're allowed to add, subtract, or multiply by clearly positive quantities on both sides without changing the comparison. Doing this often turns an ugly comparison into a trivial one (e.g., comparing $3^{40}$ vs. $2^{60}$ becomes comparing $3^2$ vs. $2^3$ after taking a 20th root). The trap is multiplying by something whose sign you don't know — never multiply both sides by a variable unless you know it's positive.
Comparisons of large powers, fractions with shared denominators, or expressions where the same term appears on both sides.
The Hidden-Negative Trap
GRE writers love variables that look like they should be positive but aren't constrained to be. If the problem says $x \ne 0$ but doesn't say $x > 0$, negatives are fair game — and squaring, cubing, or taking reciprocals all behave very differently with negatives. A wrong answer here usually comes from the student silently assuming the variable is a "normal" positive number.
An answer choice that's defensible if you only test $x = 3$ and $x = 5$, but breaks instantly under $x = -2$.
The Fraction Flip
For $x$ between $0$ and $1$, intuition built on integers fails: $x^2 < x$, $\frac{1}{x} > x$, and $\sqrt{x} > x$. The GRE constantly exploits the fact that students forget this regime. Whenever a problem involves powers, roots, or reciprocals of an unconstrained variable, fractions belong in your test set.
Quantities like $x$ vs. $x^2$, $\sqrt{x}$ vs. $x$, or $\frac{1}{x}$ vs. $x$ where $x$ could legally be $\frac{1}{2}$.
The Phantom-(D) Trap
Students who've been burned by (D) sometimes pick it defensively on any question that looks complicated. But if every quantity is a fixed number — no variables, no "figure not drawn to scale" geometry ambiguity — the relationship is determined, even if computing it is annoying. (D) is never correct on a pure arithmetic comparison.
A comparison like $\frac{17}{23}$ vs. $\frac{19}{26}$ — ugly, but fully determined. (D) is wrong by construction.
How it works
Suppose Quantity A is $x^2$ and Quantity B is $x$, with no constraint on $x$. A student trying $x = 3$ sees $9 > 3$ and picks (A). But try $x = \frac{1}{2}$: now $x^2 = \frac{1}{4}$, which is less than $\frac{1}{2}$. One case said A wins, another said B wins, so the relationship isn't forced — the answer is (D). That's the QC mindset in miniature: a single confirming case proves nothing, but a single contradicting case proves (D). Always ask, "Can I find a legal value that flips this?" before locking in. The Plug-In Protocol exists precisely so you don't forget the troublemaker numbers — $0$, negatives, and fractions — that GRE writers built the question around.
Worked examples
$x$ is a nonzero real number.
Compare Quantity A and Quantity B.
- A Quantity A is greater.
- B Quantity B is greater.
- C The two quantities are equal.
- D The relationship cannot be determined from the information given. ✓ Correct
Why D is correct: Run the Plug-In Protocol. Try $x = 2$: $x^3 = 8$, $x^2 = 4$, so A is greater. Try $x = \frac{1}{2}$: $x^3 = \frac{1}{8}$, $x^2 = \frac{1}{4}$, so B is greater. Two legal values give opposite comparisons, so the relationship isn't forced. The answer is (D).
Why each wrong choice fails:
- A: True for $x > 1$ and for negative $x$ where $|x|$ is large, but false for $0 < x < 1$, where $x^3 < x^2$. One counterexample kills (A). (The Fraction Flip)
- B: True for $0 < x < 1$ and for negative $x$, but at $x = 5$, $x^3 = 125 > 25 = x^2$. The integer case kills (B). (The Plug-In Protocol)
- C: $x^3 = x^2$ only when $x = 0$ or $x = 1$. Since $x = 0$ is excluded and most legal values give unequal results, (C) fails.
No additional information.
Compare Quantity A and Quantity B.
- A Quantity A is greater.
- B Quantity B is greater. ✓ Correct
- C The two quantities are equal.
- D The relationship cannot be determined from the information given.
Why B is correct: Use Simplify-Both-Sides. Rewrite $6^{24} = (2 \cdot 3)^{24} = 2^{24} \cdot 3^{24}$. Now both quantities have the form $2^a \cdot 3^b$. Quantity A is $2^{30} \cdot 3^{20}$; Quantity B is $2^{24} \cdot 3^{24}$. Divide both by $2^{24} \cdot 3^{20}$ (a positive number, so the comparison is preserved): Quantity A becomes $2^{6} = 64$, Quantity B becomes $3^{4} = 81$. Since $81 > 64$, Quantity B is greater.
Why each wrong choice fails:
- A: Tempting because Quantity A's $2^{30}$ has a bigger exponent than anything visible in Quantity B, but after factoring $6^{24}$ into $2^{24} \cdot 3^{24}$, the extra $3^{4}$ in Quantity B outweighs the extra $2^{6}$ in Quantity A. (The Simplify-Both-Sides Heuristic)
- C: Equality would require $2^{6} = 3^{4}$, i.e., $64 = 81$, which is false.
- D: Both quantities are fixed numbers with no variables, so the relationship is fully determined. (D) is impossible here by construction. (The Phantom-(D) Trap)
$a$ and $b$ are integers with $a < b < 0$.
Compare Quantity A and Quantity B.
- A Quantity A is greater. ✓ Correct
- B Quantity B is greater.
- C The two quantities are equal.
- D The relationship cannot be determined from the information given.
Why A is correct: Both $a$ and $b$ are negative, with $a$ further from zero (more negative) than $b$. Test concrete values: let $a = -4$ and $b = -2$. Then $\frac{1}{a} = -\frac{1}{4}$ and $\frac{1}{b} = -\frac{1}{2}$. Since $-\frac{1}{4} > -\frac{1}{2}$, Quantity A is greater. Try another pair to confirm: $a = -10$, $b = -1$ gives $-0.1 > -1$. The constraint $a < b < 0$ forces this every time, because taking reciprocals of negative numbers reverses their order and brings them closer to zero.
Why each wrong choice fails:
- B: Students assume "$a < b$ implies $\frac{1}{a} < \frac{1}{b}$," which is true for positives but reverses for negatives. The Hidden-Negative Trap in action. (The Hidden-Negative Trap)
- C: $\frac{1}{a} = \frac{1}{b}$ only when $a = b$, but the constraint $a < b$ rules that out.
- D: The constraint $a < b < 0$ pins the sign of both variables and forces the reciprocal ordering. Every legal pair gives the same comparison, so the relationship is determined. (The Phantom-(D) Trap)
Memory aid
Run the FROZEN check before locking an answer: Fractions, Reciprocals, One, Zero, Extremes, Negatives. If any FROZEN value flips the comparison, the answer is (D).
Key distinction
The difference between (A)/(B)/(C) and (D) is universality. (A), (B), and (C) each claim the relationship holds for every legal value. (D) only needs two legal values that disagree. So one good counterexample beats a hundred confirming examples.
Summary
On QC, you're not solving for an answer — you're stress-testing a relationship, and (D) wins the moment any legal value breaks it.
Practice quantitative comparison adaptively
Reading the rule is the start. Working GRE-format questions on this sub-topic with adaptive selection, watching your mastery score climb in real time, and seeing the items you missed return on a spaced-repetition schedule — that's where score lift actually happens. Free for seven days. No credit card required.
Start your free 7-day trialFrequently asked questions
What is quantitative comparison on the GRE?
Quantitative Comparison (QC) asks you to decide whether Quantity A is bigger, Quantity B is bigger, the two are equal, or the relationship can't be determined from the information given. The right answer must hold under every legal value of every variable — so your job isn't to find one outcome, it's to test whether the relationship is forced. Most wrong answers come from students who plug in one nice number, see a clear inequality, and lock in (A) or (B) before checking negatives, fractions, or zero.
How do I practice quantitative comparison questions?
The fastest way to improve on quantitative comparison is targeted, adaptive practice — working questions that focus on your specific weak spots within this sub-topic, getting immediate feedback, and revisiting items you missed on a spaced-repetition schedule. Neureto's adaptive engine does this automatically across the GRE; start a free 7-day trial to see your sub-topic mastery climb in real time.
What's the most important distinction to remember for quantitative comparison?
The difference between (A)/(B)/(C) and (D) is universality. (A), (B), and (C) each claim the relationship holds for every legal value. (D) only needs two legal values that disagree. So one good counterexample beats a hundred confirming examples.
Is there a memory aid for quantitative comparison questions?
Run the FROZEN check before locking an answer: Fractions, Reciprocals, One, Zero, Extremes, Negatives. If any FROZEN value flips the comparison, the answer is (D).
What is "The one-nice-number trap" in quantitative comparison questions?
testing $x=2$ and stopping.
What is "The hidden-(D) trap" in quantitative comparison questions?
forgetting that fractions or negatives flip inequalities.
Ready to drill these patterns?
Take a free GRE assessment — about 20 minutes and Neureto will route more quantitative comparison questions your way until your sub-topic mastery score reflects real improvement, not luck. Free for seven days. No credit card required.
Start your free 7-day trial