Master elimination and smart number strategies for math problems
Amy Seeley is the founder of Seeley Test Pros, a Cleveland-based test preparation company that has helped more than 10,000 students improve their standardized test scores. She also serves as president and owner of the Learning Enrichment and Assistance Program (LEAP), which supports students on their path to college and advanced education. A licensed and certified secondary education teacher, Amy began her career in test preparation in 1994 with The Princeton Review. She is the founder and co-host of the Test and the Rest: College Admissions Industry podcast and a co-founder and board member of the National Test Preparation Association.
Table of contents
- A four-step strategy for conquering GRE quantitative comparison questions
- Core insights
- What quantitative comparison questions test
- Step 1: Eliminate answers and choose numbers with intention
- Use elimination actively
- Choose test numbers that reveal traps
- Step 2: Draw helpful diagrams and double-check constraints
- Redraw when you feel uncertain
- Check constraints before you compute
- Step 3: Simplify quantities to make comparisons easier
- Simplify first, compare second
- Avoid overusing “cannot be determined”
- Step 4: Practice purposefully and learn from your mistakes
- Keep an error log that tells you what went wrong
- Use strategic guessing to protect time
- Reinforce fundamentals
- Success comes from strategy and flexibility
A four-step strategy for conquering GRE quantitative comparison questions
Quantitative Comparison (QC) questions on the GRE aren’t just about knowing math: they’re about making fast, reliable decisions under pressure. The format is simple (compare Quantity A vs. Quantity B), but the traps are not: hidden restrictions, misleading diagrams, and “nice” numbers that mask what’s really going on.
The best way to improve is to use a repeatable four-step process that helps you avoid common pitfalls, simplify quickly, and learn from mistakes so your score rises over time.
Core insights
- Using a step-by-step elimination process and trying less obvious numbers leads to both higher accuracy and faster test-taking.
- Drawing your own diagrams and checking problem constraints helps build stronger problem-solving skills and prevent mistakes.
- Simplifying complex math is the most effective way to compare quantities.
- Reviewing mistakes thoughtfully turns them into valuable learning opportunities and boosts long-term improvement.
What quantitative comparison questions test
QC questions on the GRE ask you to compare two quantities and choose one of four answer options:
- (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
The goal is not to compute everything. The goal is to compare efficiently, often using logic, estimation, testing values, or simplification.
Why students struggle: QC rewards precision. A single overlooked constraint (like “x is a positive integer”) can flip the answer. And “cannot be determined” is correct less often than many test-takers think: ETS expects you to try a strategy first.
Step 1: Eliminate answers and choose numbers with intention
Two habits immediately improve QC accuracy: elimination and smart test numbers.
Use elimination actively
Write the four answer choices down (or keep them in view) and cross off options as you rule them out. This reduces second-guessing and keeps you from cycling through the same ideas under stress.
Choose test numbers that reveal traps
When variables are involved, don’t default to “easy” values like 1, 2, or 10. Those often hide the very differences the question is testing.
Use a mix that exposes edge cases:
- a negative (e.g., –2)
- zero (if allowed)
- a fraction (e.g., 1/2)
- a larger number (e.g., 20)
Why it works: QC traps often live in sign changes, denominators, squares/roots, and inequality rules. Testing only friendly integers can make two expressions look equal when they aren’t.
Quick checklist before testing numbers
- Are there restrictions like “positive,” “integer,” “nonzero,” or “x ≠ 1”?
- Could plugging in a number make a denominator 0 or violate a square root condition?
- Do I need multiple test values to prove the relationship is fixed?
Step 2: Draw helpful diagrams and double-check constraints
Diagrams can clarify QC problems, or mislead you if you trust them too much.
Redraw when you feel uncertain
If a figure is included, remember: it may not be drawn to scale. If the image doesn’t match the stated measurements, the text is always more trustworthy than the picture. A quick sketch based solely on the given information can help prevent common geometry mistakes.
Check constraints before you compute
Many QC errors come from forgetting the rules of the problem:
- “x is an integer” eliminates fractions
- “x > 0” eliminates negatives and zero
- “x is a real number” allows negatives (even if a diagram suggests otherwise)
Constraints are not decoration: they’re the logic gate that determines which strategies are valid.
Best practice: Make it a habit to outline constraints before taking any action. It’s one of the simplest ways to raise accuracy.
Step 3: Simplify quantities to make comparisons easier
QC questions often appear challenging because the quantities appear messy. The fix is usually simplification, not more computation.
Simplify first, compare second
Look for fast moves like:
- reducing fractions
- factoring and canceling
- combining like terms
- using common denominators
- rewriting expressions in comparable forms
- estimating (when exact calculation is unnecessary)
Example idea (not a full problem):
Comparing 3/9 and 2/10 becomes trivial once reduced to 1/3 and 1/5.
Avoid overusing “cannot be determined”
Many test-takers choose (D) too quickly. While (D) is sometimes correct, ETS often builds QC questions so that one or two smart simplifications reveal a clear relationship.
Good rule: If you haven’t simplified or tested at least two valid values (when variables are present), it’s usually too early to pick (D).
Step 4: Practice purposefully and learn from your mistakes
Getting better at QC is less about volume and more about feedback.
Keep an error log that tells you what went wrong
After practice sets, write down:
- The problem type (algebra, geometry, inequalities, exponents, etc.)
- Your wrong answer and the correct one
- The reason you missed it (misread constraint, careless arithmetic, wrong assumption, rushed simplification)
Then look for patterns. If half your misses come from constraints, that’s your highest-return fix.
Use strategic guessing to protect time
If you’re stuck:
- Eliminate any impossible answers
- Test one smart number (if allowed)
- Guess and move on
Smart guessing is part of strong pacing, not a sign of failure.
Reinforce fundamentals
A QC strategy works best on top of solid basics, including arithmetic, algebra manipulation, inequality rules, and fluency with fractions and percentages. Short, focused drills (and reviewing errors) are more effective than endless random problem sets.
Success comes from strategy and flexibility
The strongest GRE test-takers don’t rely on one trick. They use a process:
- Eliminate answer choices and test meaningful numbers
- Redraw diagrams and obey constraints
- Simplify aggressively to make comparisons obvious
- Review mistakes to prevent repeated errors
Build these habits into your practice, and you’ll notice something important: speed improves because your approach becomes automatic, and accuracy improves because you stop falling into predictable traps.
Every QC question is another rep of this process. Over time, those reps compound into a higher score and stronger problem-solving skills, which extend well beyond the GRE.
