GRE Quantitative Reasoning Portal
Select a sub-topic folder below to instantly expand its practice problems.
📁 Integers & Divisibility Foundations
Adapted from public-domain number theory ideas in The Theory of Numbers by R. D. Carmichael
If n is an integer, compare:
What is the greatest common divisor of 84 and 126?
Which of the following numbers is divisible by 6?
Compare:
What is the remainder when 210 is divided by 3?
📁 Fractions, Decimals, & Ratios
Adapted from public-domain number theory ideas in The Theory of Numbers by R. D. Carmichael
Compare:
What is the decimal form of ⅞?
A recipe uses a ratio of flour to sugar of 5:2. If 20 cups of flour are used, how many cups of sugar are needed?
Compare:
If ⅔ of a number is 18, what is the number?
📁 Percentages & Commercial Arithmetic
Adapted from public-domain number theory ideas in The Theory of Numbers by R. D. Carmichael
Compare:
A shirt originally costs 80 rupees and is discounted by 25%. What is the sale price?
A merchant buys an item for 200 rupees and sells it for 250 rupees. What is the profit percentage?
Compare:
A number is increased by 20% and becomes 180. What was the original number?
📁 Averages & Sequences
Adapted from public-domain number theory ideas in The Theory of Numbers by R. D. Carmichael
Compare:
What is the 10th term of the arithmetic sequence with first term 3 and common difference 4?
The first three terms of a geometric sequence are 2, 6, and 18. What is the next term?
Compare:
The sum of the first n positive integers is 55. What is n?
📁 Algebraic Manipulations
GRE-style questions inspired by elementary number theory ideas from the public-domain work The Theory of Numbers by R. D. Carmichael, and adapted into original algebra and functions practice.
Compare:
If 5a - 3 = 22, what is a?
Simplify 3(2x - 4) + x.
Compare:
If 2m + 3n = 18 and n = 2, what is m?
📁 Equations & Inequalities
GRE-style questions inspired by elementary number theory ideas from the public-domain work The Theory of Numbers by R. D. Carmichael, and adapted into original algebra and functions practice.
Compare:
Solve for x: 4x + 1 = 21
Which value of x satisfies 2x - 3 < 9?
If x < 0, compare:
Solve: 3(x - 2) = 15
📁 Exponents & Roots
GRE-style questions inspired by elementary number theory ideas from the public-domain work The Theory of Numbers by R. D. Carmichael, and adapted into original algebra and functions practice.
Compare:
What is the value of 161/2?
Simplify (x2)3.
Compare:
If √(49x) = 21, what is x?
📁 Coordinate Geometry
GRE-style questions inspired by elementary number theory ideas from the public-domain work The Theory of Numbers by R. D. Carmichael, and adapted into original algebra and functions practice.
Compare the slopes of the lines:
What is the distance between (1, 2) and (1, 7)?
What is the midpoint of the segment joining (2, 4) and (6, 8)?
Compare:
Find the slope of the line passing through (2, 3) and (6, 11).
📁 Lines & Angles
Adapted from classic geometry ideas in the public-domain book Pure Mathematics: Geometry (1874).
If two lines intersect, which angles are equal?
Two adjacent angles form a straight line. If one angle is 65°, what is the other angle?
Compare:
If one angle of a right triangle is 28°, what is the other acute angle?
If a line is perpendicular to another line, the angle between them is how many degrees?
📁 Triangles
Adapted from classic geometry ideas in the public-domain book Pure Mathematics: Geometry (1874).
Compare:
The angles of a triangle are in the ratio 2:3:4. What is the largest angle?
A triangle has sides 5, 7, and 12. Which statement is true?
Compare:
In a triangle, two sides are 6 and 8. What is the smallest possible integer length of the third side?
📁 Polygons & Circles
Adapted from classic geometry ideas in the public-domain book Pure Mathematics: Geometry (1874).
How many degrees are in the sum of the interior angles of a pentagon?
A circle has radius 7. What is its diameter?
Compare:
Which quadrilateral has all sides equal and all angles right angles?
What is the circumference formula of a circle in terms of radius \(r\)?
📁 Three-Dimensional Solids
GRE-style extension material, since the attached book is mainly plane geometry.
How many faces does a cube have?
A rectangular prism has length 4, width 3, and height 2. What is its volume?
Compare:
Which solid has exactly two circular bases?
What is the total number of vertices in a cube?
📁 Data Representation & Interpretation
Adapted from Introduction to Statistics by David M. Lane and collaborators, a public-domain work.
A table shows the number of books sold over four days: 12, 15, 9, and 14. What is the mean number of books sold per day?
The median of the data set 4, 7, 9, 12, 15 is what?
Compare:
A bar graph shows sales of 20, 25, 30, and 35 items. Which is the mode?
If a data set has values 6, 6, 8, 10, 12, what is the mode?
📁 Advanced Descriptive Statistics
Adapted from Introduction to Statistics by David M. Lane and collaborators, a public-domain work.
If the average of five numbers is 18, what is their total sum?
A data set has values 2, 4, 6, 8, and 10. What is the mean absolute deviation from the mean?
Compare:
Which measure is most affected by an extreme outlier?
The quartiles of a data set are 12 and 24. What is the interquartile range?
📁 Counting Methods & Combinatorics
Adapted from Introduction to Statistics by David M. Lane and collaborators, a public-domain work.
How many ways can 3 students be chosen from a group of 5?
How many permutations are there of the letters A, B, and C?
Compare:
A coin is tossed twice. How many possible outcomes are there?
How many 2-digit numbers can be formed using digits 1, 2, 3, and 4 without repetition?
📁 Probability
Adapted from Introduction to Statistics by David M. Lane and collaborators, a public-domain work.
What is the probability of rolling a 3 on a fair six-sided die?
A bag contains 3 red and 2 blue balls. What is the probability of drawing a blue ball?
Compare:
If two events are independent and each has probability 1/2, what is the probability that both occur?
What is the probability of selecting an ace from a standard deck of 52 cards?