GRE Quantitative Reasoning Guide

• Score: 130–170 in 1-point steps.
• Adaptive by section: your performance on Section 1 decides how hard Section 2 is. Within a section, you can skip, mark and go back to any question.
• Calculator: a basic on-screen calculator. No formula sheet, so the formulas you need have to be in your head.
• Level: ETS describes the math as roughly no higher than a second course in algebra. No trigonometry, no calculus.

The math isn't the hard part. The hard part is reading precisely, spotting what a question really asks, and not burning three minutes on one problem.

ETS sorts Quant content into four areas. It doesn't publish a percentage split, so plan to be solid in all four.

• Arithmetic: integer properties (divisibility, factors, primes, remainders, odd/even), exponents and roots, fractions and decimals, percent, ratio and rate, absolute value, the number line, estimation, and sequences.
• Algebra: manipulating expressions and exponents, factoring, linear and quadratic equations and inequalities, systems of equations, functions, word problems, and coordinate geometry (slopes, intercepts, graphs of equations and inequalities).
• Geometry: lines and angles, triangles (including isosceles, equilateral, 30-60-90 and 45-45-90), quadrilaterals and other polygons, circles, similar and congruent figures, area, perimeter, volume and surface area, and the Pythagorean theorem.
• Data Analysis: mean, median, mode, range, standard deviation, quartiles and percentiles; reading tables and graphs (bar, line, circle, scatterplots, boxplots); basic probability; counting (permutations and combinations, Venn diagrams); and distributions, including the normal distribution.

1. Quantitative Comparison

You compare Quantity A with Quantity B and pick one of four fixed answers: A is greater, B is greater, they're equal, or the relationship can't be determined. They reward reasoning over calculating.

Example. n is an integer greater than 1. Quantity A: 3ⁿ. Quantity B: 4^{n − 1}.

Try n = 2: A = 9, B = 4, so A is greater. Try n = 5: A = 243, B = 256, so B is greater. Two different outcomes means the answer is cannot be determined. The lesson: one test value proves nothing. Keep testing until you've tried a small value and a large one.

2. Multiple choice, select one answer

Standard five-choice questions. The wrong answers are often exactly what you'd get from a predictable mistake: the wrong base for a percent, a missed negative, or an answer to a different question than the one asked.

3. Multiple choice, select one or more answers

Pick every answer that works. Some questions tell you how many to pick; others say “select all that apply.” No partial credit.

Example. n is a positive integer. Which of the following could be the units digit of 3ⁿ? Choices: 0, 1, 3, 5, 7, 9.

The units digits cycle: 3, 9, 27, 81, 243… gives 3, 9, 7, 1, then repeats. Answer: 1, 3, 7 and 9. Don't stop after finding one that works.

4. Numeric Entry

No choices. You type an integer or decimal into a box, or a numerator and denominator into two boxes for a fraction. Equivalent forms count, and fractions don't have to be reduced. Round only if the question tells you to.

Example. After a 20% discount, a shirt costs $40. What was the original price? The sale price is 80% of the original, so 0.8p = 40 and p = 50. Typing 48 (adding 20% of $40 back on) is the classic mistake.

Data Interpretation sets

Some questions share one table or graph. They use the same formats above but test reading data carefully: percent of a total, percent change, and comparing shares across years. Read titles, units and footnotes before you calculate anything.

• In Quantitative Comparison, do the same thing to both sides. Add, subtract, or multiply and divide by a positive number. Never multiply or divide both quantities by something that could be negative or zero.
• Test the weird numbers. When variables are involved, check 0, 1, a negative, a fraction between 0 and 1, and a big number. Most QC traps hide in one of those.
• Know when “cannot be determined” is impossible. If both quantities are fixed numbers with no variables, the answer can't be D.
• Estimate before you calculate. Many answer choices are far enough apart that a rough estimate picks the winner in seconds.
• Use the calculator as a backup, not a crutch. It's worth it for ugly arithmetic like 63 ÷ 160. It's slow for anything you can do in your head. On Numeric Entry, the Transfer Display button copies the result straight into the answer box.
• Reread the last line before you answer. “What is x − y?” and “what is x?” have different answers. A lot of wrong choices are the right answer to the wrong question.
• Mark and move. Every question counts the same. If one is eating time, mark it, bank the easier points, and come back if time allows. Never leave a blank, since there's no penalty for guessing.

• Percent change with the wrong base. Change is always divided by the original value. Up 20% then down 20% leaves you at 96%, not 100%.
• Assuming a variable is a positive integer. Unless the question says so, x can be negative, zero or a fraction.
• Trusting the figure. Figures aren't necessarily drawn to scale. Use the given numbers and properties, not what the picture looks like.
• “Must be” versus “could be.” “Must” means true in every allowed case, so one counterexample kills it. “Could” means one working case is enough.
• Share versus amount. In data sets, a category can grow in dollars while shrinking as a share of the total.
• Inclusive versus strict inequalities. |x − 4| < 3 excludes 1 and 7. Endpoint mistakes are cheap points to lose.
• Averages without sums. Mean problems nearly always get easier when you convert to totals (sum = mean × count).

Six to eight weeks at 5–8 hours a week is a sensible starting point for most people. Stretch it if your math is rusty.

1. Week 1: Baseline. Take ETS's free timed POWERPREP test (or our full-length practice test) under real conditions. Log every miss by content area and by cause (didn't know it, careless, ran out of time).
2. Weeks 2–4: Rebuild the weak areas. Work through the matching parts of the ETS Math Review, then drill by topic. Fix concepts before speed.
3. Weeks 5–6: Timed mixed sets. Do 12- and 15-question sets at real timing (21 and 26 minutes). Keep an error log and redo missed questions a week later without looking at your notes.
4. Weeks 7–8: Full tests. Take whichever of our full-length GRE practice test and the timed POWERPREP test you didn't use in Week 1, plus paid POWERPREP PLUS tests if you want more scored practice. Review every miss and every lucky guess.

Pair this with the GRE Verbal guide, and see the best GRE prep books if you want more practice material.