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 ability to reason quantitatively and to address problems with quantitative methods, or say basic 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 calculator in the test, but you cannot use your own calculator. In computer-based GRE test, the calculator is provided on-screen; as for paper-delivered test, 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 Content
GRE Quantitative Reasoning isn't real math test, it doesn't test all or main 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.

Find the sum of all two-digit natural numbers that are divisible by 4.



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 simple interest on a sum of money is 1/6 of the principal. The number of months is equal to twice the rate percent. Find the time in months of the investment.



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.

Find the radius of the circle x2+y2-4x+6y-51=0.

units


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.

Find the probability of the occurrence of exactly one of A and B when P(AUB) = 0.59 and the probability of the occurrence of both A and B is 0.01.[AUB = A union B]

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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 basic type in GRE quantitative reasoning; 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
The greatest prime factor of 36The greatest prime factor of 48
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.

How many three digit even numbers exist with distinct digits?



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

Exercises of word problem

Example:
Directions: Select answer choice or choices.

If a2 = 12, then a4 =

Exercise144

Exercise72

Exercise36

Exercise24

Exercise16



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

Exercises of data interpretation

Example:
Directions: The following question 1-2 are based on the bellow table, which shows per capita Mean Expenditure, Per capita Food expenditure, Number of Households and Per capita cereal consumption, in both quantity and value, for different expenditure classes of rural India. The sampled 41597 households are divided into 12 expenditure classes, starting from less than Rs.65 per month per capita and ending at more than Rs.385 per capita per month.

GRE quantitative test


1. According to the results of this sample survey, what is the proportion of total expenditure on food to total expenditure for all the sampled households taken together?

Exercise58%

Exercise36.7%

Exercise63.3%

Exercise71%

ExerciseCannot be determined

2. What is the difference, approximately, between the gross expenditure of the sampled households in the Rs.95-110 expenditure class and in the Rs.180-215 expenditure class?

Exercise372000

Exercise448000

Exercise496000

Exercise93.8

Exercise52.3

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