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: 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
Twice an odd integer greater than 6Three times an odd integer greater than 2
ExerciseQuantity A is greater.

ExerciseQuantity B is greater.

ExerciseThe two quantities are equal.

ExerciseThe relationship cannot be determined without further information.

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.

The product of the positive numbers is 300 and the sum of their squares is 25 more than two times their product. Find the sum of the two numbers.

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: 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 square and an equilateral triangle have the same perimeter. If the diagonal of the square is 12*2cm, then how many times √3 sq.cm. is the area of the triangle?

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: Select answer choice or choices.

10. Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?


Exercise1 litre paint

Exercise1 litre water

Exercise1/2 litre water and one litre paint

Exercise1/2 litre paint and one litre water

Exercise1/2 litre paint

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
2(3 + 4)2 + 102 + (3 + 4)2 + 10
ExerciseQuantity A is greater.

ExerciseQuantity B is greater.

ExerciseThe two quantities are equal.

ExerciseThe relationship cannot be determined from the information given.



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.

Working together, two water pumps A and B can fill a water tank in 3 hours. Working alone pump A can fill the tank in 4 hours. How long does it take pump B, working alone, to fill the same tank?

hours


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.

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



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. Each of the following is a valid conclusion that can be drawn from the information in the graphs EXCEPT:

Exercisefrom 1970 to 1980, the number of stores increased by approximately 200

Exercisefrom 1970 to 2000, the number of stores approximately doubled

Exercisefrom 1980 to 2000, the average number of employees increased by approximately 50%

Exercisein 2000, there were about 75,000 employees

Exercisefrom 1970 to 2000, the number of employees increased each decade

2. According to the graphs, which of the following is the best estimate of the total number of employees in 1990?

Exercise75,000

Exercise62,000

Exercise57,000

Exercise50,000

Exercise48,000

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