• 100 questions

GRE Quantitative Practice Test

Unofficial Quantitative Reasoning questions in ETS's four content areas, with quantitative comparisons and a worked solution under every answer.

m is an odd integer and n is an even integer. Which of these must be odd?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

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Unofficial practice questions, not affiliated with ETS. Bank checked October 11, 2026.

Next step GRE practice test: Verbal and QuantitativeGRE Math Subject Test practice exam

All 100 questions

Arithmetic 25

  • $2,000 is invested at 5 percent interest, compounded once a year. How much is it worth after 2 years? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, percent. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A jar holds red and blue marbles in the ratio 3 to 5, and there are 16 more blue marbles than red. How many marbles are in the jar? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, ratio. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A price is raised by 20 percent, and the new price is then cut by 25 percent. How does the final price compare with the original? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, percent. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A sequence starts with a₁ = 3, and each later term is 1 less than twice the term before it. What is a₅? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, sequences of numbers. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
Show all 100 questions (96 more)

Arithmetic, continued

  • How many digits does the number 2¹⁰ · 5⁷ have when it is written out? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, exponents. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • How many integers from 1 to 100, inclusive, are divisible by 6 or by 8? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, properties of integers: divisibility. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • m is an odd integer and n is an even integer. Which of these must be odd? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, properties of integers: odd and even integers. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • n is a positive integer. Quantity A is the remainder when n is divided by 6. Quantity B is the remainder when n is divided by 3. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, properties of integers: remainders. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • On a number line, which number is the same distance from −7 as it is from 13? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, the number line; absolute value. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • The price of a coat rose by 10 percent. Quantity A is the increase in dollars. Quantity B is 10. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, percent. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is 4¹⁵. Quantity B is 8⁹. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, exponents. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is 7/15. Quantity B is 8/17. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, arithmetic operations; the number line. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is 35 percent of 60. Quantity B is 60 percent of 35. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, percent. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is the greatest common divisor of 84 and 126. Quantity B is 42. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, properties of integers: divisibility and factorization. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is the number of positive divisors of 36. Quantity B is the number of positive divisors of 48. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, properties of integers: divisibility and factorization. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is √50 + √18. Quantity B is √128. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, roots. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • What is (3/4 − 1/6) divided by 7/8? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, arithmetic operations. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • What is the 20th digit to the right of the decimal point in the decimal form of 3/7? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, decimal representation. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • What is the greatest prime factor of 1,001? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, properties of integers: prime numbers. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • What is the value of (2⁻³ · 6²)/3⁻¹? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, exponents. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • When the integer n is divided by 5, the remainder is 3. Quantity A is the remainder when 3n is divided by 5. Quantity B is 2. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, properties of integers: remainders. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • When the positive integer n is divided by 12, the remainder is 7. What is the remainder when n is divided by 4? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, properties of integers: remainders. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Which of these is closest to (0.498 × 61.2)/0.102? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, estimation. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Working alone, one printer finishes a job in 6 hours and a second printer finishes it in 3 hours. At those rates, how long do the two take working together? ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, rate. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • x is a nonzero number. Quantity A is |x|. Quantity B is x. ETS, Overview of the Quantitative Reasoning Measure: Arithmetic, absolute value. Quantitative Comparison question. The answer is worked out from the numbers in the question.

Algebra 25

  • 0 < x < 1. Quantity A is x³. Quantity B is x². ETS, Overview of the Quantitative Reasoning Measure: Algebra, operations with exponents. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • 2x + 3y = 12 and x − y = 1. Quantity A is x. Quantity B is y. ETS, Overview of the Quantitative Reasoning Measure: Algebra, solving simultaneous equations. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • 2x − 7 > 5. Quantity A is 6. Quantity B is x. ETS, Overview of the Quantitative Reasoning Measure: Algebra, solving linear inequalities. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • A club sold 60 mugs for $510 in all. Large mugs cost $10 and small mugs cost $7. How many large mugs were sold? ETS, Overview of the Quantitative Reasoning Measure: Algebra, setting up equations to solve word problems. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A driver covers 150 miles at 50 miles per hour and returns over the same road at 75 miles per hour. What is the average speed for the whole trip? ETS, Overview of the Quantitative Reasoning Measure: Algebra, setting up equations to solve word problems. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A plumber charges a flat fee plus an hourly rate. A 2-hour job costs $130, and a 5-hour job costs $250. What is the flat fee? ETS, Overview of the Quantitative Reasoning Measure: Algebra, setting up equations to solve word problems. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • f(x) = 2x − 3 for all numbers x. Quantity A is f(f(2)). Quantity B is −1. ETS, Overview of the Quantitative Reasoning Measure: Algebra, functions. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • For how many integers n is n² − 3n − 10 < 0? ETS, Overview of the Quantitative Reasoning Measure: Algebra, solving quadratic inequalities. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • For x not equal to 4 or −3, which expression equals (x² − 16)/(x² − x − 12)? ETS, Overview of the Quantitative Reasoning Measure: Algebra, factoring and simplifying algebraic expressions. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • g(x) = x² − 2x for all numbers x. For which values of x is g(x) = 15? ETS, Overview of the Quantitative Reasoning Measure: Algebra, functions; solving quadratic equations. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • How many liters of water must be added to 12 liters of a drink that is 30 percent juice to make a drink that is 20 percent juice? ETS, Overview of the Quantitative Reasoning Measure: Algebra, setting up equations to solve word problems. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • If 3^(x + 1) = 27^(x − 1), what is x? ETS, Overview of the Quantitative Reasoning Measure: Algebra, operations with exponents. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • In the xy-plane, a line passes through the points (−2, 5) and (4, −7). What is its y-intercept? ETS, Overview of the Quantitative Reasoning Measure: Algebra, coordinate geometry: intercepts and slopes of lines. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • In the xy-plane, the line y = 3x − 12 crosses the x-axis at (a, 0) and the y-axis at (0, b). Quantity A is a. Quantity B is b. ETS, Overview of the Quantitative Reasoning Measure: Algebra, coordinate geometry: intercepts. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • In the xy-plane, what is the lowest point on the graph of y = x² − 4x + 7? ETS, Overview of the Quantitative Reasoning Measure: Algebra, coordinate geometry: graphs of functions. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Quantity A is the slope of the line 3x + 2y = 6. Quantity B is the slope of the line 2x − 3y = 6. ETS, Overview of the Quantitative Reasoning Measure: Algebra, coordinate geometry: slopes of lines. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Two numbers have a sum of 20 and a product of 96. What is the positive difference between them? ETS, Overview of the Quantitative Reasoning Measure: Algebra, solving quadratic equations. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Which expression equals (x + 3)² − (x − 3)²? ETS, Overview of the Quantitative Reasoning Measure: Algebra, factoring and simplifying algebraic expressions. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Which line is perpendicular to y = (2/5)x + 1 and crosses the y-axis at 4? ETS, Overview of the Quantitative Reasoning Measure: Algebra, coordinate geometry: intercepts and slopes of lines. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Which point (x, y) satisfies both y > x + 1 and y < −x + 5? ETS, Overview of the Quantitative Reasoning Measure: Algebra, solving simultaneous inequalities. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Which values of x satisfy |2x − 5| < 3? ETS, Overview of the Quantitative Reasoning Measure: Algebra, solving linear inequalities. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • x + y = 9 and x − y = 3. Quantity A is x² − y². Quantity B is 27. ETS, Overview of the Quantitative Reasoning Measure: Algebra, factoring and simplifying algebraic expressions. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • x > 0. Quantity A is (x + 2)². Quantity B is x² + 4. ETS, Overview of the Quantitative Reasoning Measure: Algebra, factoring and simplifying algebraic expressions. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • x² − 5x + 6 = 0. Quantity A is x. Quantity B is 2.5. ETS, Overview of the Quantitative Reasoning Measure: Algebra, solving quadratic equations. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • y = 2x + 1. Quantity A is x. Quantity B is y. ETS, Overview of the Quantitative Reasoning Measure: Algebra, relations, functions, equations and inequalities. Quantitative Comparison question. The answer is worked out from the numbers in the question.

Geometry 25

  • A 29-foot wire runs straight from the top of a vertical pole to a stake in level ground 20 feet from the pole's base. How tall is the pole? ETS, Overview of the Quantitative Reasoning Measure: Geometry, the Pythagorean theorem. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A circle has circumference 10π. Quantity A is the area of the circle. Quantity B is 75. ETS, Overview of the Quantitative Reasoning Measure: Geometry, circles; area. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • A circle has radius 6. What is the area of the sector cut off by a central angle of 60°? ETS, Overview of the Quantitative Reasoning Measure: Geometry, circles; area. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A rectangle has a diagonal of length 25 and one side of length 7. What is its area? ETS, Overview of the Quantitative Reasoning Measure: Geometry, quadrilaterals; the Pythagorean theorem; area. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A rectangle has perimeter 20. Quantity A is the area of the rectangle. Quantity B is 24. ETS, Overview of the Quantitative Reasoning Measure: Geometry, quadrilaterals; area; perimeter. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • A rectangular tank is 5 feet long and 4 feet wide and holds water 3 feet deep. When 20 cubic feet of water are added, by how many feet does the water level rise? ETS, Overview of the Quantitative Reasoning Measure: Geometry, three-dimensional figures; volume. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A right circular cylinder has a base of radius 3 and a height of 8. What is its volume? ETS, Overview of the Quantitative Reasoning Measure: Geometry, three-dimensional figures; volume. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A right triangle has angles of 30°, 60° and 90°, and its hypotenuse has length 10. How long is the longer leg? ETS, Overview of the Quantitative Reasoning Measure: Geometry, triangles, including 30°-60°-90° triangles. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A square is drawn inside a circle of radius 5 so that all four corners lie on the circle. What is the area of the square? ETS, Overview of the Quantitative Reasoning Measure: Geometry, circles; quadrilaterals; the Pythagorean theorem. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A trapezoid has parallel sides of length 7 and 13, and the distance between them is 6. What is its area? ETS, Overview of the Quantitative Reasoning Measure: Geometry, quadrilaterals; area. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A triangle has sides of 6, 8 and 10. A similar triangle has a shortest side of 9. What is the perimeter of the second triangle? ETS, Overview of the Quantitative Reasoning Measure: Geometry, congruent and similar figures; perimeter. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A triangle has sides of length 4, 7 and x. Quantity A is x. Quantity B is 11. ETS, Overview of the Quantitative Reasoning Measure: Geometry, triangles. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • The diagonals of a rhombus measure 10 and 24. What is its perimeter? ETS, Overview of the Quantitative Reasoning Measure: Geometry, quadrilaterals; the Pythagorean theorem; perimeter. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Each exterior angle of a regular polygon measures 30°. Quantity A is the number of sides of the polygon. Quantity B is 12. ETS, Overview of the Quantitative Reasoning Measure: Geometry, other polygons; angle measurement in degrees. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • In a circle of radius 10, how long is the arc cut off by a central angle of 72°? ETS, Overview of the Quantitative Reasoning Measure: Geometry, circles; angle measurement in degrees. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • In the xy-plane, what is the area of the triangle with vertices (0, 0), (8, 0) and (3, 5)? ETS, Overview of the Quantitative Reasoning Measure: Geometry, triangles; area. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • In triangle ABC, sides AB and AC have the same length and angle A measures 40°. Quantity A is the measure of angle B. Quantity B is 70°. ETS, Overview of the Quantitative Reasoning Measure: Geometry, triangles, including isosceles triangles. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • In triangle PQR, the angle at P measures 55°, and the exterior angle at R measures 130°. What is the measure of the angle at Q? ETS, Overview of the Quantitative Reasoning Measure: Geometry, triangles; angle measurement in degrees. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Lines m and n are parallel, and a third line crosses both. On one side of the third line, the two angles between m and n measure (4x + 15)° and (x + 40)°. What is x? ETS, Overview of the Quantitative Reasoning Measure: Geometry, parallel and perpendicular lines. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Quantity A is the perimeter of a square with area 36. Quantity B is the circumference of a circle with radius 4. ETS, Overview of the Quantitative Reasoning Measure: Geometry, circles; quadrilaterals; perimeter. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is the surface area of a cube with edges of length 3. Quantity B is the surface area of a rectangular box that measures 2 by 3 by 5. ETS, Overview of the Quantitative Reasoning Measure: Geometry, three-dimensional figures; area. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is the volume of a rectangular box that measures 2 by 4 by 8. Quantity B is the volume of a cube with edges of length 4. ETS, Overview of the Quantitative Reasoning Measure: Geometry, three-dimensional figures; volume. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Two sides of a triangle have lengths 5 and 12. Quantity A is the length of the third side. Quantity B is 13. ETS, Overview of the Quantitative Reasoning Measure: Geometry, triangles; the Pythagorean theorem. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • What is the area of an equilateral triangle with sides of length 6? ETS, Overview of the Quantitative Reasoning Measure: Geometry, triangles, including equilateral triangles; area. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • What is the measure of each interior angle of a regular polygon with 9 sides? ETS, Overview of the Quantitative Reasoning Measure: Geometry, other polygons; angle measurement in degrees. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.

Data analysis 25

  • A bar graph shows a shop's sales by month: January $12,000, February $15,000, March $9,000 and April $18,000. March's sales were what fraction of the four-month total? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, interpretation of data in bar graphs. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A box holds 5 green and 7 yellow tiles. Two tiles are drawn at random, one after the other, and the first is not put back. What is the probability that both are green? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, elementary probability: compound events. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A boxplot of 40 delivery times shows a least value of 12 minutes, a first quartile of 18, a median of 23, a third quartile of 30 and a greatest value of 45. About how many of the deliveries took between 18 and 30 minutes? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, interpretation of data in boxplots; quartiles. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A class of 20 students has a mean score of 80, and a class of 30 students has a mean score of 90. What is the mean score of all 50 students? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, basic descriptive statistics: mean. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A code is 2 letters followed by 2 digits. Each letter is A, B, C or D, and a letter may repeat. Each digit is from 0 to 9, and the two digits must differ. How many codes are possible? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, counting methods. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A fair coin is tossed 3 times. Quantity A is the probability of exactly 2 heads. Quantity B is the probability of exactly 1 head. ETS, Overview of the Quantitative Reasoning Measure: Data analysis, elementary probability. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • A fair coin is tossed 4 times. What is the probability of at least one head? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, elementary probability: compound events. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A fair six-sided die is rolled twice. What is the probability that both rolls show a number greater than 4? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, elementary probability: independent events. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A frequency table of quiz scores reads: score 6, 3 students; score 7, 5 students; score 8, 8 students; score 9, 4 students. What is the median score? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, interpretation of data in frequency distributions; median. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A list holds the five numbers 2, 3, 3, 3 and 9. Quantity A is the range of the list. Quantity B is the mode of the list. ETS, Overview of the Quantitative Reasoning Measure: Data analysis, basic descriptive statistics: mode and range. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • A list holds the five numbers 2, 4, 4, 6 and x. Quantity A is the mean of the list. Quantity B is 4. ETS, Overview of the Quantitative Reasoning Measure: Data analysis, basic descriptive statistics: mean. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • A list holds the five numbers 3, 7, 7, 9 and 14. Quantity A is the mean of the list. Quantity B is the median of the list. ETS, Overview of the Quantitative Reasoning Measure: Data analysis, basic descriptive statistics: mean and median. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • A random variable X takes the value 0 with probability 0.5, the value 1 with probability 0.3 and the value 2 with probability 0.2. What is the mean of X? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, random variables and probability distributions. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • A table lists cups sold at a stand: Monday 40, Tuesday 55, Wednesday 35, Thursday 70. What was the percent increase from Wednesday to Thursday? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, interpretation of data in tables. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • The eight values 2, 4, 5, 7, 8, 10, 13 and 15 are split into a lower half and an upper half, and each quartile is the median of its half. What is the interquartile range? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, basic descriptive statistics: quartiles and interquartile range. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Events E and F each have probability 0.5. Quantity A is the probability that both E and F occur. Quantity B is 0.25. ETS, Overview of the Quantitative Reasoning Measure: Data analysis, elementary probability: independent events. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Every value in a data set is increased by 5. What happens to the mean and the standard deviation of the set? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, basic descriptive statistics: mean and standard deviation. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Five numbers have a mean of 12. When a sixth number is added, the mean of the six is 13. What is the sixth number? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, basic descriptive statistics: mean. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • In a group of 60 people, 35 own a dog, 28 own a cat and 10 own neither. How many own both a dog and a cat? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, counting methods: Venn diagrams. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • List S is 10, 20, 30, 40, 50. List T is 28, 29, 30, 31, 32. Quantity A is the standard deviation of S. Quantity B is the standard deviation of T. ETS, Overview of the Quantitative Reasoning Measure: Data analysis, basic descriptive statistics: standard deviation. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Nine runners enter a race with no ties. In how many different ways can first, second and third place be awarded? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, counting methods: permutations. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Of 200 students, 120 take Spanish, 80 take art and 50 take both. One of the students who take art is picked at random. What is the probability that this student takes Spanish? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, conditional probability. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.
  • Quantity A is the number of ways to choose 2 books from 7 different books. Quantity B is the number of ways to choose 5 of the same 7 books. ETS, Overview of the Quantitative Reasoning Measure: Data analysis, counting methods: combinations. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Quantity A is the number of ways to choose 3 people from a group of 6. Quantity B is the number of ways to line up 4 different books on a shelf. ETS, Overview of the Quantitative Reasoning Measure: Data analysis, counting methods: combinations and permutations. Quantitative Comparison question. The answer is worked out from the numbers in the question.
  • Scores on a test are normally distributed with a mean of 500, and 16 percent of the scores are above 600. What percent of the scores lie between 400 and 600? ETS, Overview of the Quantitative Reasoning Measure: Data analysis, probability distributions, including normal distributions. Multiple-choice question, select one answer. The answer is worked out from the numbers in the question.

How this list was compiled: Our own questions, written to ETS's Overview of the Quantitative Reasoning Measure of the GRE General Test (https://www.ets.org/gre/test-takers/general-test/prepare/content/quantitative-reasoning.html, read 2026-10-11): four content areas (arithmetic, algebra, geometry, data analysis) and four question types, of which this bank uses two, Quantitative Comparison and Multiple-choice with one answer. ETS publishes no share for the content areas, so the bank holds 25 questions in each; 37 of the 100 are Quantitative Comparison questions. Section lengths (12 and 15 questions, 21 and 26 minutes) from https://www.ets.org/gre/test-takers/general-test/prepare/test-structure.html, read 2026-10-11. Every answer is arithmetic, algebra or geometry on what the question prints, and each was worked out a second time on 2026-10-11. Licence: Questions, choices and explanations are original work of this site.

How it works

This free GRE quantitative practice test, on screen or printed, has 100 questions of our own in arithmetic, algebra, geometry and data analysis, each with a worked solution. It is unofficial and is not affiliated with, endorsed by or sponsored by ETS.

Read the full guide

Four content areas

ETS's overview of the Quantitative Reasoning measure, read October 11, 2026, lists arithmetic, algebra, geometry and data analysis, at a level that stops at a second algebra course, with no trigonometry or calculus. It gives no share for each area, so this bank holds 25 questions in each.

Quantitative comparisons

37 questions give a Quantity A and a Quantity B with the four fixed answers the real test uses. The other 63 are multiple choice with one answer. Numeric entry and questions with several right answers are not here.

Timing

The real measure has two sections: 12 questions in 21 minutes, then 15 in 26. Exam mode gives 27 questions in 47 minutes, a full GRE quant practice test.

  • ETS's advice: never choose "cannot be determined" when both quantities can be worked out by computation.
  • The real test puts a calculator on the screen for this measure, so practice with a basic one beside you.

Questions and answers

Is this a GRE quantitative practice test with solutions?

Yes. In practice mode each answer is marked at once and its worked solution is shown under it. Exam mode holds the solutions back until the end, then lists every question you missed with its working.

Can I get a GRE quantitative practice test with solutions as a PDF?

Yes. Print the question sheet opens 27 questions, the length of the real measure, across the four content areas. Tick With answer key to add the answers, then choose Save as PDF in the print window to keep the file.

Is this a GRE math practice test?

Yes. Quantitative Reasoning is the measure most people call GRE math, so this is GRE General Test math practice. The GRE Mathematics Test is a different, college-level Subject Test, with its own practice exam.

Is this GRE Quantitative Reasoning practice test official?

No. All 100 questions were written for this page from ETS's published content areas and question types. None is taken or reworded from a real test, a POWERPREP test, ETS's sample questions or its Math Review.

How is GRE Quantitative Reasoning scored?

ETS counts your correct answers across both sections and converts the count to a scaled score through equating. The second section is chosen by how you did on the first. This page reports a percent and estimates no scaled score.

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