GRE Quant, with a worked solution for every question.
The maths rarely goes past high school. The points are lost to traps, misreads, and the clock. So we do not hand you another answer bank: every question carries the full solution, the trap it sets, and the faster path, plus a per-question time analysis.
What GRE Quant actually tests.
Arithmetic
Fractions, ratios, percents, exponents, roots, number properties. The foundation most traps are built on.
Algebra
Linear and quadratic equations, inequalities, functions, word problems, and simplifying expressions under time.
Geometry
Lines and angles, triangles, circles, polygons, coordinate geometry, and 3D figures.
Data interpretation
Reading tables, bar and line graphs, and distributions, then answering fast without misreading the axis.
Each one fails in its own way.
Quantitative comparison
Compare two quantities and choose A, B, C, or D. The single biggest source of careless errors, and where strategy matters most.
Multiple choice
One answer, or select-all-that-apply where every correct option must be chosen for credit.
Numeric entry
Type the exact value, with an on-screen calculator available. No options to reverse-engineer.
GRE math formulas you must know.
The GRE math you need is compact: a short list of arithmetic, algebra, and geometry facts covers the overwhelming majority of Quant questions. Learn these cold so the calculator handles the arithmetic while you handle the setup. This is the core reference; the worked math questions below show them in action.
Arithmetic
- Percent change
- (new − old) / old × 100
- Average (mean)
- sum ÷ count
- Simple interest
- I = P · r · t
- Distance
- d = rate × time
- Exponent rule
- aᵐ · aⁿ = aᵐ⁺ⁿ
Algebra
- Slope
- (y₂ − y₁) / (x₂ − x₁)
- Quadratic formula
- x = (−b ± √(b²−4ac)) / 2a
- Difference of squares
- a² − b² = (a+b)(a−b)
- Square of a sum
- (a+b)² = a² + 2ab + b²
- Combinations
- C(n,k) = n! / (k!(n−k)!)
Geometry
- Pythagoras
- a² + b² = c²
- Circle area / circumference
- πr² · 2πr
- Triangle area
- ½ · base · height
- Sum of interior angles
- (n − 2) · 180°
- Cylinder volume
- πr²h
Worked GRE math questions
Three sample questions that put the formulas above to work, each with the setup that actually earns the point.
Sample 1 · Percents
A shirt priced at $80 is discounted 25%, then the sale price is discounted a further 10%. What is the final price?
Solution: Apply the cuts in sequence, not by adding 35%. After 25% off, 80 × 0.75 = 60. After a further 10% off, 60 × 0.90 = 54. Chaining the multipliers (0.75 × 0.90 = 0.675) is the faster path and avoids the add-the-percents trap.
Answer: $54
Sample 2 · Algebra
If x² − 9 = 0 and x < 0, what is x?
Solution: Factor with the difference of squares: x² − 9 = (x + 3)(x − 3) = 0, so x = 3 or x = −3. The constraint x < 0 selects the negative root. The trap is stopping at x = 3 and ignoring the second solution.
Answer: x = −3
Sample 3 · Geometry
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
Solution: Use Pythagoras: c² = 6² + 8² = 36 + 64 = 100, so c = 10. Recognising the 3-4-5 family scaled by 2 lets you read this off instantly without computing the square root.
Answer: 10
Solve, then learn the pattern.
- The trap, named
Every solution calls out the specific mistake the question is engineered to cause, so you stop repeating it.
- Per-question time analysis
See where you spent minutes you did not have, and which time-sinks to skip and guess on.
- The faster path
Many quant questions have a shortcut. We show the elegant route, not just the grind.
Practise Quant on its own, section by section. Pick a mixed set or a single-difficulty set, answer at your own pace, and see the worked solution and the trap on every question.