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Why Quantitative Comparison Is the Highest-ROI Question Type on the GRE
Across the two Quantitative Reasoning sections on the shorter GRE, roughly 9 to 11 of your 27 questions are Quantitative Comparison (QC) items. While standard Problem Solving questions require you to compute an exact numerical value, QC questions only ask you to determine the invariant relationship between Quantity A and Quantity B.
Students who treat QC like regular algebra spend 2.5 minutes per question solving for exact values, starving themselves of time for Section 2 word problems. By contrast, 168+ scorers average under 65 seconds per QC question by combining algebraic matching with structured boundary-value testing.
Rule 1: Treat the Space Between Quantity A and Quantity B as an Inequality Sign
Whenever Quantity A and Quantity B are algebraic expressions or large arithmetic products, never evaluate each column in isolation. Instead, place a placeholder comparison symbol [ ? ] between them and perform identical valid operations on both sides:
- Add or subtract ANY real number or variable expression from both Quantity A and Quantity B without changing their relative order.
- Multiply or divide both quantities by a strictly positive quantity to clear denominators or large common factors.
- Never multiply or divide across the barrier by an expression that could be negative or zero (such as
xora - b) unless the centered givens explicitly guarantee it is positive.
Worked Example: Matching Exponents Instead of Computing
Suppose Quantity A is 4^16 - 4^14 and Quantity B is 15 × 4^14. A hesitant test-taker panics at the large exponents. An elite scorer factors 4^14 out of Quantity A immediately:
Quantity A = 4^14 (4^2 - 1) = 4^14 (16 - 1) = 15 × 4^14. Within 15 seconds, without touching the calculator, you prove that both quantities are identically equal (Choice C).
Rule 2: Decoding the 4 Classic ETS Quantitative Comparison Traps
ETS item writers construct Quantitative Comparison distractors around four recurring cognitive biases. Recognizing the trap archetype lets you spot the answer in seconds:
| Trap Archetype | What the Question Looks Like | Why Test-Takers Miss It | 330+ Elimination Rule |
|---|---|---|---|
| The Unstated Integer Trap | Centered info says x > 1; compares x^2 and 2x. |
Students plug in x = 2, 3, 4 and ignore x = 1.5. |
If the word "integer" is absent, immediately test a decimal/fraction just above the lower bound. |
| The Even-Exponent Sign Mask | Centered info gives a^2 = 36 or x^4 > y^4. |
Students take only the positive square root (a = 6) and forget a = -6. |
Write both positive and negative roots on your scratch pad before reading Quantity A. |
| The Equal-Looking Geometry Trap | A chord or inscribed triangle looks symmetrical in the diagram. | Visual inspection suggests two angles or segments are equal (Choice C). | Keep all stated lengths/angles fixed and mentally stretch one vertex to see if the figure can deform. |
| The Fake Choice D (Algebraic Identity) | Two complex expressions contain unconstrained variables x and y. |
Students assume unconstrained variables automatically mean Choice D. | Expand and subtract Quantity B from Quantity A first; sometimes variables cancel out completely! |
“Never pick Choice D just because a problem has two variables and no equations. Always simplify Quantity A minus Quantity B first—if the variables cancel or leave a squared term like (x - y)^2 + 3, the relationship is locked!”
Rule 3: The Equal/Not-Equal Two-Pass Method
When algebraic simplification isn't convenient, use the Equal / Not-Equal Two-Pass Method:
- Pass 1 (Seek Equality): Ask yourself, "Can I legally pick values that make Quantity A equal Quantity B?" If yes, eliminate Choices A and B immediately—the answer must be C or D.
- Pass 2 (Break Equality): Perturb one variable slightly (e.g., change
x = 1tox = 2orx = 1/2). If the quantities are no longer equal, pick Choice D immediately.
