What Are the Most Common GRE Quantitative Comparison Mistakes?
Four reasoning errors account for most wrong answers on GRE Quantitative Comparison (QC) questions: assuming an unconstrained variable behaves like a positive whole number, stopping after one convincing test case, assuming a fact about a figure that the question never actually stated, and losing track of the sign flip when multiplying or dividing an inequality by a negative number. None of these require difficult math to fix — each is a specific, checkable habit, worked through in full below.
A QC question gives you two values, Quantity A and Quantity B, and asks you to determine their relationship using the same four responses every time, in this exact order:
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Two format details matter more than they seem. First, a symbol that appears more than once in a question means the same thing every time it appears — the GRE will not quietly redefine a variable partway through a comparison. Second, a basic on-screen calculator is available for every Quantitative Reasoning question, QC included, so wrong answers on these questions are almost never arithmetic errors. They're reasoning errors, and the four specific ones above are demonstrated below with a fully worked example each.
Why Does Assuming a Variable Is a Positive Whole Number Lead You Astray?
Because the GRE deliberately tests whether you checked anything besides the first "obvious" number. ETS's own official strategy guidance for the Quantitative Reasoning measure instructs test-takers to plug in "zero, positive and negative numbers, small and large numbers, fractions and decimals" before answering — a direct signal that testing only positive integers is a known failure pattern, not a minor oversight.
Suppose Quantity A is and Quantity B is , with no constraint on given anywhere in the problem.
- Test : Quantity A , Quantity B . A is greater.
- Test : Quantity A , Quantity B . B is greater.
Two legitimate values of produce opposite relationships, so the correct answer is "cannot be determined" — choice 4. A test-taker who only tries whole numbers greater than 1 (2, 3, 4…) will see Quantity A win every time and confidently pick the wrong answer. Before you answer any QC question with an unconstrained variable, run it through zero, a negative number, and a fraction between 0 and 1. If any of those three flips the relationship, the answer is choice 4.
Why Isn't One Convincing Test Case Enough?
Because ETS's own problem-solving guidance states this explicitly: plugging numbers into an expression "may not be conclusive." A single value that produces a clean or symmetrical result can talk you into choice 3 ("the two quantities are equal") too early.
Take Quantity A as and Quantity B as , where is an integer.
- : Quantity A , Quantity B . Equal.
- : Quantity A , Quantity B . Equal.
- : Quantity A , Quantity B . B is greater.
- : Quantity A , Quantity B . A is greater.
A test-taker who tries , gets a clean tie, and stops has just picked the wrong answer — the relationship swings from equal, to B-greater, back to equal, to A-greater across four small integers, so the correct response is choice 4. The official guidance is precise about when testing values does settle the question: it's conclusive once you've found two values that produce different outcomes (that proves choice 4), or once you've exhausted every value the constraints allow. A single tidy result proves nothing on its own.
Why Can't You Assume Unstated Facts About a Shape?
Because QC geometry problems are built to punish exactly that assumption. ETS's official guidance states that geometric figures "are not necessarily drawn to scale" and recommends redrawing a figure while holding only the stated facts fixed, then varying everything the problem didn't pin down. The same discipline applies even when no image is shown and a shape is only described in words — any dimension or angle the question doesn't state is free to vary.
Consider a triangle with two sides fixed: . Quantity A is the length of the third side, . Quantity B is .
The only constraint the triangle inequality gives you is that must be strictly between and (the sum of the two known sides). Nothing pins to exactly — a narrow angle at makes small, a wide angle pushes it close to , and there's an angle in between that makes exactly . Since can land below, at, or above depending on an angle the problem never specified, the answer is choice 4. The actionable check: before comparing anything involving a figure, list only the facts explicitly given, and treat every other visual impression — a right angle that "looks" like 90°, a segment that "looks" equal to another — as unverified.
Why Does Dividing by a Negative Number Flip Your Answer?
Because inequality direction reverses when you multiply or divide both sides by a negative number, and ETS's own strategy guidance flags this directly as a reason to "consider the impact of each step carefully" when simplifying a comparison — along with the related warning that some simplification steps, like squaring both sides, aren't reversible at all and can silently invalidate a comparison.
Suppose you're given , and asked to compare Quantity A () with Quantity B ().
Dividing both sides by requires flipping the inequality: . Check it with a real value — satisfies the original condition since , and indeed , so Quantity B is greater. A test-taker who divides by without flipping the sign concludes and picks Quantity A — the opposite of the correct answer. Whenever a simplification step multiplies or divides by a variable or number that could be negative, confirm the sign before trusting the inequality's direction.
Quick Reference: Which Check Catches Which Mistake
| If the comparison involves… | Run this check | What it catches |
|---|---|---|
| An unconstrained variable | Test , a negative number, and a fraction | Assuming positive-integer behavior |
| An expression that looks symmetrical | Test at least two different values before concluding "equal" | Stopping at one convincing case |
| A described or drawn figure | List only the explicitly stated facts; vary everything else | Assuming unstated shape/angle facts |
| An inequality with a variable multiplier | Confirm the sign before multiplying or dividing | Missing an inequality-direction flip |
Run the matching check before you commit to an answer: all four traps above produce wrong answers on questions that involve no difficult math at all. TestPrepOS's GRE Quantitative Reasoning practice drills Quantitative Comparison sets specifically, with adaptive difficulty and explanations that identify which of these four checks a missed question actually needed.
Quantitative Comparison doesn't exist on the GMAT, but the underlying discipline — testing extreme values instead of defaulting to a single computation — is the same skill that separates strong and weak performers on GMAT Data Insights questions.