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GRE Quantitative Practice With Worked Reasoning
GRE Quantitative Reasoning rewards clear setup as much as fast calculation. This public teaching resource uses original examples to show how to translate wording into math, compare quantities, and check an answer’s units and size. The examples are separate from protected prediction reports and are not official test questions.
Use one skill at a time: read the setup, solve without rushing, then compare your reasoning with the worked feedback. ETS identifies arithmetic, algebra, geometry, and data analysis as the measure’s core content areas, alongside Quantitative Comparison, multiple-choice, multiple-select, and numeric-entry formats.
Practice the skill, then review the reasoning
Quantity A is 3/4 of 40. Quantity B is 28. Which relationship is correct?
A rectangular garden is 9 meters long and 5 meters wide. What is its area? Enter an integer.
The mean of three values is 16. Two values are 12 and 19. What is the third value? Enter an integer.
Set up ratios, rates, and percent change
For a ratio, label what each number of parts represents before scaling. If blue:white is 2:3 and white equals 18, one part is 6 and blue is 12. This prevents reversing a ratio or reporting the total when the question asks for one category.
For percent change, the denominator is the original amount. Compute new minus original, divide by original, then convert to a percent. With two consecutive percent changes, use a multiplier for each step because the second percentage has a new base.
Compare quantities through structure and cases
Quantitative Comparison asks for a relationship, not necessarily a fully computed value. Simplify only enough to decide. If a variable has restrictions, use them; for positive x, x divided by x plus 1 must be less than 1 because the denominator is larger and positive.
When a relationship may vary, try valid boundary-like cases and values with different signs or sizes if the conditions permit them. If one allowed case gives equality and another gives Quantity A greater, the relationship cannot be determined. Do not infer from a diagram unless the information determines the measurement.
Model equations and use geometric invariants
In a word problem, separate a fixed amount from a variable rate. A fee plus per-unit charge becomes a constant plus coefficient times a variable. Solve one operation at a time and substitute the result back into the original equation when the context is important.
Geometry is easier when you start with an invariant: triangle angles total 180 degrees, a rectangle’s area is length times width, and a right triangle follows a squared-length relationship. Label whether a question needs boundary length, interior area, surface area, or volume because their units and formulas differ.
Interpret center, spread, chance, and overlap
Mean is total divided by count; median is the middle ordered value. A large outlier can shift the mean while leaving the median’s position unchanged. For a missing value, convert the stated mean to a total first.
Probability starts with the sample space. Multiply independent probabilities for events linked by “and,” and update the remaining count after a draw without replacement. For two overlapping groups, add the group counts and subtract the overlap once to avoid double-counting.
Questions about this practice
Are these official GRE questions?
No. These are original public teaching exercises. ETS materials remain the source for official test content and format information.
Should I always use the on-screen calculator?
No. Use it when arithmetic is tedious, but set up the relationship first. A calculator cannot correct a reversed ratio, wrong percent base, or unsupported inference.
What does “cannot be determined” mean in a quantitative comparison?
It means the allowed information permits more than one relationship. Demonstrate that with valid cases or show why the information is insufficient; do not select it merely to avoid calculating.
How should I review a missed Quant question?
Name the skill and error type: setup, rule, arithmetic, units, or interpretation. Redo a fresh example of that skill after reviewing the method, rather than only memorizing the prior answer.
References
- ETS GRE Quantitative Reasoning Overview
- ETS GRE General Test Structure
- ETS Khan Academy GRE Quantitative Preparation Videos
Updated October 25, 2026 · PassPredictor