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AskSiaThe GRE Bible series

GRE · Quantitative Reasoning

The GRE Quantitative
Comparison Bible

Compare · Test Cases · Traps

The GRE-only format that rewards reasoning over computation: compare two quantities and pick one of four fixed choices. Master the case-testing method, the unconstrained-variable and not-to-scale traps, and the exact moment the answer is “cannot be determined.”

Built to mirror the official GRE specification. Pure-English edition.asksia.ai/explore

AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeAt a glance

How to use this bible

Read this first

What Quantitative Comparison is, and how to build the reflexes that beat it.

Quantitative Comparison (QC) is roughly a third of GRE Quant, and it is the format that punishes fast, careless computation. This bible teaches the method — simplify, then test cases — and the named traps that make a wrong choice feel right. Work the practice set at the end as a mini-diagnostic.

✓The one habit

When a variable is unconstrained, test positive, negative, zero, and a fraction. If any two cases disagree, the answer is (D) cannot be determined. Most QC errors are a missed case.

iHow it is built

Every rule is verified against the official GRE specification and paraphrased in plain English. Practice items are AskSia originals that mirror the exam; we never reproduce real test questions.

Quantitative Comparison at a glance

The format on one page

The four fixed choices, the scoring, and the rule that trips up most test-takers.

Fixed answer choices

130–170

Quant score scale

Penalty for guessing

Choice

Meaning

Quantity A is greater

Quantity B is greater

The two quantities are equal

The relationship cannot be determined from the information given

The four choices are the SAME on every QC question — memorize them.

★The not-to-scale rule

On the GRE, geometric figures are not necessarily drawn to scale — never solve a QC geometry question by measuring the picture. Coordinate systems and statistical graphs (bar, line, circle) are drawn to scale.

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeReasoning

Chapter 1 · Overview

What Quantitative Comparison is

The GRE-only format where you compare two quantities and pick one of four fixed choices.

A Quantitative Comparison (QC) question shows you two quantities — Quantity A and Quantity B — sometimes with shared information above them, and asks a single question: which quantity is greater, or can you even tell? QC lives inside the Quantitative Reasoning measure (scored 130–170) and is one of four Quant question types. What makes it unique is the answer set: it never changes.

THE 4 FIXED CHOICESThe four answer choices are FIXED — same wording, same order, every single time:

(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

A.What is on the screen

Optional shared information (an equation, a figure, a constraint) that governs both quantities.
Quantity A and Quantity B side by side.
The same four labelled choices (A / B / C / D) — you never read new options.

B.What makes QC different

You are not asked to solve for a value — only to compare.
Because the choices are fixed, every wrong answer is a reasoning error, not a mis-calculation.
Choice (D) exists only here — a whole answer that means "it depends."

iWhere QC sits in the test

Quantitative Reasoning is 2 sections, 27 scored questions, scored 130–170 in 1-point steps with no penalty for wrong answers. A basic on-screen calculator (add, subtract, multiply, divide, square root — no graphing) is available. Master QC and you gain points on a large, recurring share of every Quant section.

Chapter 1 · Overview

Why it rewards reasoning, not computation

The fastest QC solvers compare structure — they rarely finish the arithmetic.

Because you only need the relationship between A and B, you can almost always skip full computation. Cancel what both sides share, estimate, or test a value — then read off the label. Grinding out both quantities in full is the classic time sink QC is designed to punish.

answer choices, always the same

of them (D) means “cannot be determined”

130–170

Quantitative Reasoning score scale

EX 1Compare, don't computeRelative reasoning

Shared info: $x > 0$ . Quantity A: $\;x + 5\;$ Quantity B: $\;x + 3$

Subtract the common $x$ from both sides — a legal move that never changes which is larger. You are left comparing $5$ against $3$ . Quantity A is greater for every allowed $x$ , so the answer is (A). No value of $x$ was ever needed.

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeChoice D

✓The QC habit: reduce before you resolve

Before touching the calculator, ask: can I cancel a common term, factor, or estimate? QC gives points for knowing the direction of a comparison, not its exact size. If you find yourself computing two full messy values, you have probably missed a shortcut.

Chapter 1 · Overview

When (D) is right — and when it is a trap

“Cannot be determined” is a precise claim, not a shrug.

Choice (D) is correct only when the relationship genuinely changes depending on the allowed values. The test rule is exact: if you can find one case where A is greater and another case where B is greater or equal, a single counter-case forces (D). But if the values are pinned down — or a figure looks like it settles things — (D) becomes a trap that punishes lazy or over-cautious guessing.

Situation

Correct call

Why

An unconstrained variable could be negative,

0

, or a fraction, and the comparison flips

(D) is right

You found two cases that disagree — the relationship truly is undetermined.

Shared info fully pins both quantities to numbers

(D) is a trap

One definite relationship exists; “it depends” is false.

A geometry figure looks like a right angle or a square, but nothing is stated

Usually (D)

Figures are not to scale — the drawing can hide a second case.

Only one test value was tried and it “worked”

Do not stop

“Consistent so far” is not “always”; seek a second, different case.

!The #1 QC error: assuming a variable is “nice”

Compare Quantity A: $x^2$ with Quantity B: $x$ . If you assume

x

is a positive whole number,

x^2 \ge x

looks like (A). But run the full battery — try

x = \tfrac{1}{2}

: then

x^2 = \tfrac{1}{4} < \tfrac{1}{2}

, so B is greater. Two cases disagree, so the answer is (D). Whenever a variable is unconstrained, test

0

1

, a negative, and a fraction before you commit.

Read the shared info first. Every stated constraint ( $x>0$ , “integer,” a marked angle) shrinks the cases you must check.
Simplify by comparison. Cancel common terms; do not compute both sides in full.
Stress-test with the value battery. $0$ , $1$ , a negative, a fraction — if the comparison flips, choose (D).
Trust marks, not looks. On geometry, use only what is stated or marked; figures are not drawn to scale.

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeCase-testing

Chapter 3 · The Method

Compare, don't compute

Quantitative Comparison rewards relative reasoning. Your job is to decide how two quantities relate — not to finish the arithmetic on either one.

Choice

What it claims

(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

iThe four choices never change

Every QC question offers exactly these four choices, always in this order. The wording and order are fixed, so a wrong answer is never a mis-typed number — it is a reasoning error. Choice (D) is a real, frequent answer, not a throwaway: it is correct whenever the comparison can come out differently under different allowed values.

Simplify both sides in parallel. Cancel or add the same amount to each quantity, reduce fractions, factor — anything that makes the two easier to line up. If both quantities share a term, drop it from both; the comparison is unchanged.
Compare structure, not final values. Often you can see which side is larger without computing either — e.g. a positive times a bigger positive is larger. Stop the moment the direction is clear.
If a variable is unconstrained, test cases. Run the sign/zero/fraction battery (next page). This is the single decisive habit in QC.
If any two cases disagree, choose (D). One case where A wins and another where B wins (or they tie) is a proof that the relationship is not fixed — the answer is (D).

!The over-calculation trap

QC is a relative question, so grinding out the full value of each quantity wastes the time the timed section is built to pressure. Before you reach for the basic on-screen calculator, cancel common terms and estimate. If you find yourself computing a long product or a messy square root on both sides, you have probably missed a cancellation.

✓The decisive habit: the sign/zero/fraction battery

When a variable has no stated restriction, it can be positive, negative, zero, or a fraction between 0 and 1 — and those regions behave differently under squaring, cubing, and multiplication. Test one value from each region. The instant two cases point to different answers, you are done: the answer is (D).

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeFigures · percents

Test value

Why it can break a comparison

A positive (e.g. 2)

The “obvious” case; growing an exponent grows the value.

Zero (0)

0 is neither positive nor negative; it zeroes out products and powers.

A negative (e.g. −2)

Odd powers stay negative; even powers turn positive — signs flip.

A fraction (e.g. 1/2)

Between 0 and 1, higher powers shrink:

x^3 &lt; x^2 &lt; x

WEX 1An unconstrained variable → (D)unconstrained-sign

Quantity A: $x^2$ Quantity B: $x$ (no restriction on $x$ )

Test $x = 2$ : $A = 4$ , $B = 2$ → A is greater.

Test $x = \tfrac{1}{2}$ : $A = \tfrac{1}{4}$ , $B = \tfrac{1}{2}$ → B is greater.

Two allowed values give opposite outcomes, so the relationship is not fixed. Answer: (D). Choosing (A) here is the classic mistake — assuming an unnamed variable must be a whole number greater than 1.

WEX 2A constraint that pins the answer → (A)constraint-decides

Quantity A: $x^2$ Quantity B: $x^3$ given $x < 0$

Now the sign is fixed. For any negative $x$ : $x^2 > 0$ while $x^3 < 0$ , so Quantity A is positive and Quantity B is negative.

Test $x = -2$ : $A = 4$ , $B = -8$ . Test $x = -\tfrac{1}{2}$ : $A = \tfrac{1}{4}$ , $B = -\tfrac{1}{8}$ . Every case agrees. Answer: (A).

Same-looking problem as WEX 1, opposite verdict: the constraint $x < 0$ removes the cases that would have flipped it. Read the given information before you case-test.

!Never measure a not-to-scale figure

On the GRE, geometric figures are not necessarily drawn to scale — you may not assume that lengths, angles, or areas are what they look like. Base every geometry answer on geometric reasoning, not on eyeballing the picture. You may assume that lines shown straight are straight, that curves are not straight, and that points are in the order shown. Redraw a figure to an extreme to expose a hidden (D).

iTwo figure regimes to keep straight

The not-to-scale rule applies to plain geometric figures. It does not apply to coordinate systems (the

xy

-plane, number lines) or to statistical graphs (bar, circle, and line graphs) — those are drawn to scale, so you may read and compare values by sight. Watch only for a scale that does not start at 0.

WEX 3The percent-base-shift trap → (B)percent-base-shift

Setup: a price of 100 is increased by 20%, then the result is decreased by 20%.

Quantity A: the final price Quantity B: 100

Compute on the new base each step: $100 \to 100 \times 1.2 = 120 \to 120 \times 0.8 = 96$ . So Quantity A $= 96$ , which is less than 100.

Answer: (B). The trap is (C): a $+20\%$ then $-20\%$ feels like it cancels, but the second percent is taken on the larger base (120), so it removes more than the first added. Percentages do not cancel unless they act on the same base.

fixed answer choices, one order

disagreeing case forces (D)

130–170

Quant score scale

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeTrap 1

iAbout this guide

AskSia is independent and not affiliated with, endorsed by, or sponsored by ETS. GRE is a registered trademark of ETS.

Methodology & corrections: asksia.ai/about/methodology

Chapter 4 · The QC traps

Every wrong choice is a named trap

Quantitative Comparison has exactly four fixed labels, so a distractor can only be a reasoning error.

In a Quantitative Comparison item the four answer choices never change: (A) Quantity A is greater, (B) Quantity B is greater, (C) the two quantities are equal, and (D) the relationship cannot be determined from the information given. Because the labels are fixed, ETS cannot tempt you with a mis-typed number — it tempts you with a flawed line of reasoning. Learn the flaw and the choice loses its pull.

Fixed answer choices

One counter-case forces it

130–170

Quant score scale

iThe label-D meta-rule (memorize this)

Choice D means the comparison is not fixed by the information given — that is, Quantity A is greater in one legal case and Quantity B is greater (or equal) in another. So a single counter-case is enough to force D. Conversely, you may pick A, B, or C only when the relationship holds for every value allowed by the setup. This is why "it worked for one number" is never a proof.

!Trap 1 — unconstrained-sign (the #1 QC error)

Why it tempts: you silently assume an unconstrained variable is positive, an integer, or greater than 1 — so squaring "must" enlarge it and multiplying "must" preserve the inequality. How to detect it: when a variable is not pinned down, run the 0 / 1 / negative / fraction battery — test

x=0

x=1

, a negative like

x=-2

, and a proper fraction like x = 1/2. If the comparison flips across the battery, the answer is D. If it survives all four, only then trust A, B, or C.

Working the sign battery

EX 1Unconstrained-sign in actionBattery method

Suppose the only information is $x < 1$ . Compare Quantity A: $x^2$ with Quantity B: $x$ .

The tempting read: " $x<1$ , so $x$ is small, and squaring a small number makes it smaller — pick B." That silently assumes $x$ is a positive fraction.
Run the battery. Try x = 1/2: then x² = 1/4 < 1/2, so B is greater.
Now try $x=-2$ (still satisfies $x<1$ ): then $x^2=4 > -2$ , so A is greater. The comparison flipped.
One case gave B, another gave A — the relationship is not fixed. The answer is D.

The distractor B is not a wrong subtraction; it is the unconstrained-sign assumption dressed up as arithmetic.

✓Cancel before you compute

QC rewards relative reasoning, not full evaluation. If both quantities share a common positive factor or term, cancel it and compare what is left — but never cancel a factor that could be zero or negative, because that is exactly where the sign trap hides. Estimating the comparison beats grinding out both values.

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeTraps 4–5

The geometry and one-case traps

!Trap 2 — figure-not-to-scale

Why it tempts: the drawing looks like a right angle, a square, or an isosceles triangle, so you read the picture as the data. The rule: "Geometric figures are not necessarily drawn to scale — do not assume that lengths and angle measures are as they appear." You may assume lines shown straight are straight, that points fall in the order shown, and that objects sit in the relative positions shown — but never that a

90^\circ

-looking angle is

90^\circ

. How to detect it: use only marked or stated facts, then redraw the figure to an extreme (stretch one side, flatten one angle). If a legal redraw changes the comparison, the answer is D. Industry estimates put over 80% of GRE geometry errors on trusting the diagram.

iThe exception: coordinate systems and data graphs ARE to scale

The not-to-scale rule is for geometric figures only. In an xy-plane, number line, or statistical graph (bar, circle, or line graph) you may read, estimate, and compare by sight or measurement — tick marks are evenly spaced unless noted. Caution: a bar or line graph scale may not start at zero, so check the axis before comparing heights.

!Trap 3 — insufficient-cases

Why it tempts: you plug in one value, the comparison comes out clean, and you commit to A, B, or C. How to detect it: before you lock in, hunt for a second, deliberately dissimilar case — cross a sign, cross zero, or jump from integer to fraction. "Consistent so far" is not "always true." If a second legal case disagrees with the first, the answer is D; only if every dissimilar case you can construct agrees may you choose A, B, or C.

The arithmetic and statistics traps

!Trap 4 — percent-base-shift

Why it tempts: a 20% increase followed by a 20% decrease "obviously" cancels back to the start. It does not, because the second percent is taken on a new, larger base. How to detect it: recompute each step on the current value, never the original.

EX 2Why up-then-down does not cancelNew-base method

A price of $100$ rises 20%, then the new price falls 20%. Compare Quantity A: the final price with Quantity B: $100$ .

Step	Base used	Computation	Result
Start	—	—	$100$
Up 20%	$100$	$100 \times 1.20$	$120$
Down 20%	$120$	$120 \times 0.80$	$96$

The final price is $96$ , so Quantity B is greater — the answer is B, not C. The down-step was 20% of $120$ ( $=24$ ), a bigger cut than the $20$ the up-step added. Symbolically the net factor is $1.2 \times 0.8 = 0.96$ , a 4% loss regardless of the starting number.

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeTrap 6 & map

!Trap 5 — SD-vs-range confusion

Why it tempts: a wider range "must" mean a larger standard deviation. The distinction: range is just

\max - \min

, while standard deviation measures spread about the mean. A set can have a huge range yet a small SD if the bulk of its values cluster tightly near the mean with a lone far value. How to detect it: never infer one from the other — if only the range (or only the endpoints) is given, the SD is not determined, and the answer is often D.

Counting, and the full trap map

!Trap 6 — permutation-vs-combination

Why it tempts: you count arrangements (

_nP_r

) when the problem only asks for selections (

_nC_r

), inflating the count by an

r!

factor. How to detect it: ask "does reordering the same chosen elements make a new outcome?" If yes (a race finish, a password, a seating), it is a permutation; if no (a committee, a handful of toppings, a subset), it is a combination. Recall

_nC_r = \dfrac{_nP_r}{r!}

, so mistaking one for the other is never off by a little — it is off by

r!

Trap

The false assumption it rewards

Disconfirming check

Unconstrained-sign

A variable is positive / an integer; squaring always grows it.

Run the 0 / 1 / negative / fraction battery; if it flips → D.

Figure-not-to-scale

The drawing preserves angles and proportions.

Use only marked facts; redraw to an extreme.

Insufficient-cases

One test value settles the comparison.

Find a second, dissimilar case (flip a sign, cross zero).

Percent-base-shift

+20% then −20% returns to the start.

Recompute on the new base:

100 \to 120 \to 96

SD-vs-range

A larger range means a larger standard deviation.

SD measures spread about the mean, not the endpoint gap.

Perm-vs-comb

Selections are counted as ordered arrangements.

Does reordering make a new outcome? No → combination.

iAffiliation

AskSia is independent and not affiliated with, endorsed by, or sponsored by ETS. GRE is a registered trademark of ETS.

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeFAQ

Reference

GRE glossary

The exact terms used across the GRE Bible series — and on your score report.

Term

What it means

Quantitative Comparison QC

A GRE Quant question type that asks you to compare Quantity A and Quantity B and choose which is greater, whether they are equal, or whether the relationship cannot be determined.

Quantity

One of the two expressions being compared in a QC question, labeled Quantity A and Quantity B; each may be a number, an expression, or a value defined by a figure or condition.

Cannot be determined

Answer choice (D): the relationship between the two quantities changes depending on allowed values, so no single comparison holds. Valid only when at least two permitted cases give different comparisons.

Fixed answer choices

The four QC options — Quantity A greater, Quantity B greater, the two equal, or cannot be determined — which are identical and in the same order on every QC question.

Not necessarily to scale

The convention that geometric figures (lines, circles, triangles, quadrilaterals) may not reflect true lengths or angles; base answers on geometric reasoning, not on appearance.

Drawn to scale

The convention that coordinate systems (xy-planes, number lines) and statistical graphs (bar, circle, line graphs) do reflect true values, so you may read or estimate quantities by sight.

Term

What it means

Unconstrained variable

A variable with no stated restriction on its sign, integrality, or size; it may be negative, zero, or a fraction, which is the root of most QC traps.

Test cases

The technique of substituting specific allowed values — chosen to probe sign, zero, and fractions — to see whether the comparison stays fixed or changes.

On-screen calculator

The basic four-function-with-square-root calculator provided for the entire Quantitative Reasoning measure; it is not a graphing calculator and is best reserved for tedious computation.

Section-level adaptive

The GRE design in which the difficulty of a measure's second Quant section is selected from your performance on the first; adaptation is per section, not per question.

Scaled score

The reported Quantitative Reasoning score from 130 to 170 in 1-point increments, reflecting both correct answers and the difficulty of the sections received.

Geometric reasoning

Deriving lengths, angles, and areas from stated facts and theorems (e.g., the Pythagorean theorem) rather than from measuring or eyeballing a not-to-scale figure.

Reference

Frequently asked questions

Quick, source-verified answers to the questions students ask most.

What is a GRE Quantitative Comparison question?

A Quantitative Comparison (QC) question presents two quantities — Quantity A and Quantity B — and asks you to determine how they compare. Instead of computing an exact value, your job is to decide which quantity is greater, whether they are equal, or whether the relationship cannot be determined from the information given.

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeNext

How many answer choices does a Quantitative Comparison question have?

Exactly four, and they are always the same, in the same order: (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. Unlike other GRE Quant questions, QC never has five choices and never varies its options.

Are the figures in GRE Quantitative Comparison drawn to scale?

It depends on the figure. Geometric figures — bare lines, circles, triangles, and quadrilaterals — are NOT necessarily drawn to scale, so you must reason from the given facts, not from how they look. Coordinate systems (xy-planes and number lines) and statistical graphs (bar, circle, and line graphs) ARE drawn to scale, so you may read, estimate, or compare values by sight in those.

Can you use a calculator on GRE Quantitative Comparison?

Yes. A basic on-screen calculator (add, subtract, multiply, divide, square root) is provided for the entire Quantitative Reasoning measure, which includes QC. It is not a graphing calculator. ETS advises using it only for genuinely tedious computation, because most QC questions are decided by reasoning, not arithmetic.

How is GRE Quant scored?

The Quantitative Reasoning measure is scored on a scale of 130 to 170 in 1-point increments. Your score reflects both how many questions you answer correctly and the difficulty of the sections you receive, because Quant is section-level adaptive. There is no separate score for Quantitative Comparison on its own.

What is the single biggest mistake on Quantitative Comparison?

Assuming a variable is positive, an integer, or non-zero when nothing in the problem says so. An unconstrained variable can be negative, zero, or a fraction, and each of those can flip the comparison. The fix is to test cases across sign, zero, and fractions before you commit to an answer.

When is the answer 'cannot be determined'?

Choose (D) only when you can produce two allowed cases that give different comparisons — for example one case where Quantity A is greater and another where the quantities are equal. If every case you can construct yields the same relationship, the answer is not (D). Note that if both quantities are specific numbers with no variables, (D) can never be correct, because two fixed numbers always have a definite relationship.

Should I guess on Quantitative Comparison?

Yes — always answer. GRE Quant has no penalty for a wrong answer, so a guess can only help, and QC's four fixed choices make an educated guess especially efficient after you eliminate one or two options with a single test case.

Where to go from here

You know the format. Now build the reflexes.

You now understand Quantitative Comparison better than most GRE test-takers ever will — the four fixed choices, the case-testing method, and the traps that make a wrong choice feel right. The points come from reps.

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AskSia · The GRE Quantitative Comparison Bible · Method · Traps · PracticeNext

Do this next

Why

Take an official ETS POWERPREP practice test

Convert the QC method into reflexes under the real timer.

Drill Text Completion & Sentence Equivalence

The Verbal formats where vocabulary and traps decide the score.

Re-read the not-to-scale rule

Never solve a QC geometry question by measuring the picture.

Drill traps in the AskSia app

Per-distractor coaching on why you miss — bilingual, the part a guide can’t give.

★Study with Sia

The AskSia app turns this bible into a plan: a diagnostic sets your target, then daily practice adapts to your weak skills and coaches every wrong answer in your language. asksia.ai/explore

The GRE Quantitative Comparison Bible, from the AskSia GRE Bible series. Pure-English edition, built to mirror the official GRE specification. AskSia is independent and not affiliated with, endorsed by, or sponsored by ETS. GRE is a registered trademark of ETS.

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Gre · Prep Guide

The GRE QuantitativeComparison Bible

Read this first

The format on one page

What Quantitative Comparison is

A.What is on the screen

B.What makes QC different

Why it rewards reasoning, not computation

When (D) is right — and when it is a trap

Compare, don't compute

Every wrong choice is a named trap

Working the sign battery

The geometry and one-case traps

The arithmetic and statistics traps

Counting, and the full trap map

GRE glossary

Frequently asked questions

What is a GRE Quantitative Comparison question?

How many answer choices does a Quantitative Comparison question have?

Are the figures in GRE Quantitative Comparison drawn to scale?

Can you use a calculator on GRE Quantitative Comparison?

How is GRE Quant scored?

What is the single biggest mistake on Quantitative Comparison?

When is the answer 'cannot be determined'?

Should I guess on Quantitative Comparison?

Where to go from here

Let's Get in Touch

The GRE Quantitative
Comparison Bible