Quantitative Reasoning in the GRE General Test covers arithmetic, algebra, geometry, and data analysis. 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.

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Quantitative comparison

Numeric Entry

Word Problem

Data Interpretation

Arithmetic

Algebra

Geometry

Data Analysis

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

- 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

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.

Which is the smallest number that should be added to 192 to make it a perfect square?

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.

10. The average of 1/2, 1/4, 2/3 and x is equal to 3/4. Find:

/

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.

The height and radius of the base of a right circular cone are in the ratio 3:4. The ratio of the total surface area to the curved surface area is 9:5. The sum of the total surface area and the curved surface area of the cone is 224*pi sq.cm. Find the radius of the base.

cm

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:

RESULTS OF A USED-CAR AUCTION

For the large cars sold at an auction that is summarized in the table above, what was the average sale price per car?

Small Cars | Large Cars | |

Number of cars offered | 32 | 23 |

Number of cars sold | 16 | 20 |

Projected sales total for cars offered (in thousands) | $70 | $150 |

Actual sales total (in thousands) | $41 | $120 |

For the large cars sold at an auction that is summarized in the table above, what was the average sale price per car?

$

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 comparisonExample:

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 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 A | Quantity B |

The greatest prime factor of 36 | The greatest prime factor of 48 |

Quantity A is greater. | |

Quantity B is greater. | |

The two quantities are equal. | |

The 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 entryExample:

How many three digit even numbers exist with distinct digits?

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 problemExample:

Directions: Select answer choice or choices.

If a^{2} = 12, then a^{4} =

144 | |

72 | |

36 | |

24 | |

16 |

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 interpretationExample:

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.

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?

58% | |

36.7% | |

63.3% | |

71% | |

Cannot 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?

372000 | |

448000 | |

496000 | |

93.8 | |

52.3 |

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