GRE QC Practice Questions by Type: Algebra, Geometry & More
The fastest way to get better at GRE Quantitative Comparison is to practice by question type — not by grinding through random problems, but by recognizing the specific patterns that show up in algebra, geometry, fractions, and more. This guide walks through each major QC category with example questions and explanations so you know exactly what to look for.
If you’re just starting your GRE journey, it can help to first see where Quantitative Comparison fits into the bigger picture of the GRE Quantitative Reasoning section. From there, you can decide whether you want to self-study QC using guides like this one, work one-on-one with a GRE prep tutoring instructor, or contact us for more information.
Why Practice by Question Type?
Random practice builds general familiarity, but type-based practice builds pattern recognition. When you repeatedly work through algebra QC problems, for example, you start to automatically notice when a variable is unconstrained or when an inequality might flip. That instinct is what separates students who consistently score well on QC from those who feel like every question is a coin flip.
The GRE Quant section draws QC questions from a handful of recurring math domains. Getting comfortable with each one individually is the most efficient path to a higher score.
Algebra QC Practice Questions
Algebra is the most common QC category. Most algebra QC problems involve variables, expressions, or equations — and the central challenge almost always comes down to whether you can assume the sign or range of a variable.
Practice Question 1
Given: x > 0
Quantity A: x² + 2x + 1
Quantity B: (x + 1)²
Answer: (C) The two quantities are equal.
Explanation: Quantity A factors directly into (x + 1)², which is identical to Quantity B. The constraint x > 0 is a red herring — the equality holds for all real values of x.
Practice Question 2
No additional information given.
Quantity A: x²
Quantity B: x³
Answer: (D) The relationship cannot be determined.
Explanation: Try x = 2: A = 4, B = 8, so B > A. Try x = -2: A = 4, B = -8, so A > B. Try x = 1: both equal 1. Because different values produce different outcomes, the answer is (D). This is a classic unconstrained variable trap — the same type covered in our post on the most common GRE QC traps.
What to Watch for in Algebra QC
- Variables with no stated constraints — always test negative, fraction, and zero
- Expressions that look different but factor into the same form
- Inequalities that flip when you multiply or divide by a negative
Geometry QC Practice Questions
Geometry QC problems test triangles, circles, angles, and area — but the real challenge is that figures are not drawn to scale. Never assume an angle is 90 degrees or two sides are equal just because the figure looks that way.
If geometry feels like a weak spot, our blog post Is Geometry Hard? breaks down why students struggle and how to approach it more strategically.
Practice Question 3
Given: Triangle ABC has sides of length 5, 7, and x.
Quantity A: x
Quantity B: 13
Answer: (B) Quantity B is greater.
Explanation: By the Triangle Inequality, the sum of any two sides must exceed the third. The maximum value of x is any number less than 5 + 7 = 12. So x < 12 always, which means x is always less than 13. Quantity B is greater in every valid case.
Practice Question 4
Given: A circle has radius r. A square has side length r.
Quantity A: Area of the circle
Quantity B: 4 × Area of the square
Answer: (B) Quantity B is greater.
Explanation: Area of the circle = πr² ≈ 3.14r². Four times the area of the square = 4r². Since 4 > π, Quantity B is always greater regardless of r.
What to Watch for in Geometry QC
- The Triangle Inequality — the sum of any two sides must exceed the third
- Circle formulas: area = πr², circumference = 2πr
- Figures that look constrained but are not — no stated right angles, no equal-length marks
Fractions and Decimals QC Practice Questions
Fraction QC questions exploit a quirk most people forget: when a fraction is between 0 and 1, squaring it makes it smaller. Multiplying fractions does not always work the way intuition suggests.
Practice Question 5
Given: 0 < x < 1
Quantity A: x
Quantity B: x²
Answer: (A) Quantity A is greater.
Explanation: When x is between 0 and 1, squaring it produces a smaller number. For example, if x = 0.5, then x² = 0.25. Quantity A is always greater when 0 < x < 1. Without that constraint, the answer would be (D).
Practice Question 6
Given: a/b = 3/4 and a and b are positive integers.
Quantity A: a + b
Quantity B: 14
Answer: (D) The relationship cannot be determined.
Explanation: a/b = 3/4 means a = 3k and b = 4k for any positive integer k. So a + b = 7k. If k = 1, a + b = 7 < 14. If k = 2, a + b = 14 = Quantity B. If k = 3, a + b = 21 > 14. The relationship changes depending on k.
What to Watch for in Fractions and Decimals QC
- Fractions between 0 and 1 get smaller when squared — the opposite of integers
- Ratios do not fix actual values — always check whether the multiplier is constrained
- Cross-multiply to compare fractions rather than converting to decimals
Statistics and Data QC Practice Questions
Statistics QC problems typically involve averages, medians, ranges, or probability. These questions often look straightforward but contain a hidden constraint or an ambiguous data set that changes the answer entirely.
Practice Question 7
Given: A data set of five positive integers has a mean of 10.
Quantity A: The median of the data set
Quantity B: 10
Answer: (D) The relationship cannot be determined.
Explanation: Consider {2, 2, 2, 2, 42} — mean is 10, median is 2. Consider {10, 10, 10, 10, 10} — mean and median are both 10. The median can be less than, equal to, or greater than the mean.
Practice Question 8
Given: Set A = {3, 7, 9, 15}. Set B = {4, 5, 11, 12}.
Quantity A: The range of Set A
Quantity B: The range of Set B
Answer: (A) Quantity A is greater.
Explanation: Range of A = 15 – 3 = 12. Range of B = 12 – 4 = 8. Quantity A is greater. This is a good reminder to always calculate — range only depends on the max and min, not the middle values.
What to Watch for in Statistics QC
- Mean does not equal median unless the distribution is symmetric
- Range only cares about the maximum and minimum values
- Probability questions: check whether events are independent or mutually exclusive
Exponents and Roots QC Practice Questions
Exponent QC questions are particularly trap-rich. Negative bases, fractional exponents, and zero exponents all produce counterintuitive results that the GRE loves to use.
Practice Question 9
No additional information given.
Quantity A: (-2)⁴
Quantity B: -2⁴
Answer: (A) Quantity A is greater.
Explanation: (-2)⁴ = 16 because the negative sign is inside the parentheses and gets raised to the fourth power. -2⁴ = -16 because the exponent applies only to 2. Quantity A = 16, Quantity B = -16.
Practice Question 10
Given: x > 1
Quantity A: x^(1/2)
Quantity B: x^(1/3)
Answer: (A) Quantity A is greater.
Explanation: When x > 1, a larger exponent produces a larger result. Since 1/2 > 1/3, Quantity A is greater. Try x = 64: x^(1/2) = 8, x^(1/3) = 4.
What to Watch for in Exponents QC
- Parentheses matter: (-x)² is not the same as -x²
- Fractional exponents behave like roots — larger fraction means larger result when base > 1
- Zero and one as bases: 0^n = 0, 1^n = 1 always
How to Use These Practice Questions in Your Study Routine
Type-organized practice only works if you review your reasoning, not just your answers. After each question, ask yourself: Did I test enough value types? Did I use only the information explicitly given? Could I have solved this faster with a different approach?
For students who want structured guidance and a study plan tailored to their specific weaknesses, working with a GRE prep tutoring instructor makes a real difference. At Jantzi, we have helped hundreds of students move from inconsistent QC performance to reliable, confident scores.
It also helps to know how to pace yourself — our post on last-minute GRE tips is a great resource for building smart habits under timed conditions.
Frequently Asked Questions
Most students find algebra and exponent QC questions the most difficult because of the variable trap — the instinct to assume positive integers. Geometry QC is also challenging for students who rely on how figures look rather than what is explicitly stated.
Quality beats quantity. Doing 10 to 15 questions with careful review of your reasoning is more effective than rushing through 50. Focus on understanding why an answer is correct, not just what it is.
No — QC questions are mixed by type throughout the Quant section. That is exactly why practicing by type during prep is valuable. You build the pattern recognition needed to quickly identify what kind of problem you are facing before you start solving.
Yes, strategically. If you can rule out (A) and (B) with test values, you have narrowed it to (C) or (D). If you find two inputs that produce different outcomes, you can immediately select (D) without checking further.
It depends on your learning style and timeline. Self-study works well for disciplined, self-directed learners. A tutor or structured course is better if you need accountability, have a tight deadline, or keep hitting the same walls despite independent practice.
