GRE Quantitative Reasoning

Quantitative Reasoning in GRE General Test covers arithmetic, algebra, geometry, and data analysis, and its question types are usually quantitative comparison, numeric entry, word problem, and data interpretation. Here we offer hundreds of GRE math exercises grouped by content and question type to practice online.

 Overview and Practice of GRE Quantitative Reasoning
1 Overview
GRE general test includes a math-related section: quantitative reasoning. It evaluates the ability to reason quantitatively and to address problems with quantitative methods, or say necessary mathematical skills.

The questions are in two sorts:
  • Pure mathematical problems: answer by math knowledge only
  • Word problems: answer by modeling problems mathematically
The mathematical symbols, terminology, and conventions in the Quantitative Reasoning worksheets are understandable at the high school level. Besides, there are some other assumptions listed in the Quantitative Reasoning section directions:
  • All numbers used are real numbers.
  • All figures are in a plane unless otherwise indicated.
  • Geometric figures are not necessarily drawn to scale.
  • Coordinate systems are drawn to scale
You can use a calculator in the test, but you cannot use your own calculator. In the computer-based GRE test, the calculator is provided on-screen; as for paper-delivered test, the test center will offer a basic calculator. You may get latest and official information of GRE Quantitative Reasoning from Quantitative Reasoning Measure.

2 GRE Quantitative Reasoning
GRE Quantitative Reasoning isn't real math test. It doesn't test all high school math skills; for example, it does not include trigonometry, calculus, or other higher-level mathematics. Instead, it just covers four primary math parts: arithmetic, algebra, geometry, and data analysis.

Arithmetic Topics include properties and types of integers, arithmetic operations, exponents and roots, and concepts of estimation, percent, absolute value, the number line, and decimal representation.

Example:
Directions: Enter your answer as an integer or a decimal if there is a single answer box OR as a fraction if there are two separate boxes — one for the numerator and one for the denominator.

How many times in a day are the hands of a clock in a straight line?

Exercises of arithmetic topics

Algebra Topics include operations with exponents; algebraic expressions; equations and inequalities; linear and quadratic equations and inequalities; and coordinate geometry, including graphs of functions, intercepts and slopes of lines.

Example:
Directions: Enter your answer as an integer or a decimal if there is a single answer box OR as a fraction if there are two separate boxes — one for the numerator and one for the denominator.

Let A = {1, 2, 3, 4, 5} and let f be a function from A to B defined by f(x) = y such that x+y = 6. Which is the greatest value of y?

Exercises of algebra topics

Geometry Topics include parallel and perpendicular lines, circles, triangles, quadrilaterals, other polygons, three-dimensional figures, area, perimeter, volume, and angle measurement in degrees. (Not need to construct proofs of geometry.)

Example:
Directions: Select answer choice or choices.

Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

GRE quantitative test


Exercise10

Exercise8

Exercise6

Exercise4

Exercise2

Exercises of geometry topics

Data Analysis Topics include basic descriptive statistics; interpretation of data in tables and graphs; elementary probability; conditional probability; random variables and probability distributions, including normal distributions; and counting methods, such as combinations and permutations.

Example:
Directions: Enter your answer as an integer or a decimal if there is a single answer box OR as a fraction if there are two separate boxes — one for the numerator and one for the denominator.

A box contains 5 chocolates with soft centers, 6 with nut centers, and 11 with hard caramel centers. Three students take turns to take a chocolate at random from the box and eat it. If the probability that all three students take soft centers is 1/x, what is the value of x?

Exercises of data analysis topics

3 GRE Quantitative Reasoning Question Type
GRE Quantitative Reasoning has four common types of questions. A question may be promoted in two ways: either independently as a discrete question or as part of a set of questions, the latter case is usually in Data Interpretation whose all questions are based on the same data source, like tables or graphs.

Quantitative Comparison is the primary type in GRE quantitative reasoning and usually ask you select one answer choice from multiple options.

Exercises of quantitative comparison

Example:
Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

A symbol that appears more than once in a question has the same meaning throughout the question.



Quantity AQuantity B
x + 11 – x
ExerciseQuantity A is greater.

ExerciseQuantity B is greater.

ExerciseThe two quantities are equal.

ExerciseThe relationship cannot be determined without further information.



Numeric Entry needs you calculate the answer; some Words Problem question also needs you give the numeric answer after modeling.

Exercises of numeric entry

Example:
Directions: Enter your answer as an integer or a decimal if there is a single answer box OR as a fraction if there are two separate boxes — one for the numerator and one for the denominator.

Which is the smallest number that is a perfect square and is a multiple of 7936?



Word Problem emphasizes to translate the problem to the mathematical model, you need to calculate the answer, select one or more choices from multiple options.

Exercises of word problem

Example:
Directions: Select answer choice or choices.

Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?

Exercise11

Exercise10

Exercise9

Exercise8

Exercise7



Data Interpretation usually has a set of questions based on the same data source; the problems are diversity, like calculating the answer, selecting one or more choices from multiple options.

Exercises of data interpretation

Example:
Directions: Questions 1 to 2 are based on the following data.

GRE quantitative test


1. The amount spent by country C in 1983 is what percentage more than the amount spent by Countries A and B together in 1977? (Find approximately)

Exercise50%

Exercise179%

Exercise75%

Exercise13%

Exercise70%

2. Which of the following statements must be true? i) Country A spends minimum amount of its budget on arms. ii) Throughout, Country C has spent the maximum amount on arms during the years shown. iii) An examination of the information for the last 3 years reveals that generally all 3 countries are reducing their expenditure on arms.

Exercisei only.

Exercisei and ii only

Exercisei and iii only

Exerciseii and iii only

ExerciseNone of the statements above.

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