GRE Review of the Quantitative Section

Overview
The quantitative section measures your basic mathematical skills, your understanding of elementary mathematical concepts, and your ability to reason quantitatively and solve problems in a quantitative setting. There is a balance of questions requiring arithmetic, algebra, geometry, and data analysis. These are content areas usually studied in high school.
Arithmetic 
Questions may involve arithmetic operations, powers, operations on radical expressions, estimation, percent, absolute value, properties of integers (e.g., divisibility, factoring, prime numbers, odd and even integers), and the number line.
Algebra
Questions may involve rules of exponents, factoring and simplifying algebraic expressions, understanding concepts of relations and functions, equations and inequalities, solving linear and quadratic equations and inequalities, solving simultaneous equations, setting up equations to solve word problems, coordinate geometry, including slope, intercepts, and graphs of equations and inequalities, and applying basic algebra skills to solve problems.
Geometry
Questions may involve parallel lines, circles, triangles (including isosceles, equilateral, and 30°–60°–90° triangles), rectangles, other polygons, area, perimeter, volume, the Pythagorean Theorem, and angle measure in degrees. The ability to construct proofs is not measured.
Data Analysis
Questions may involve elementary probability, basic descriptive statistics (mean, median, mode, range, standard deviation, percentiles), and interpretation of data in graphs and tables (line graphs, bar graphs, circle graphs, frequency distributions).


Math Symbols and Other Information

It is important to familiarize yourself with the basic
mathematical concepts in the GRE General Test.
The publication Math Review is available as a download
on the GRE Web site at www.gre.org/
pracmats.html and provides detailed information on
the content of the quantitative section.
The quantitative section contains the following
question types:
• Quantitative Comparison Questions
• Problem Solving – Discrete Quantitative
Questions
• Problem Solving – Data Interpretation
Questions
Questions emphasize understanding basic principles
and reasoning within the context of given
information.






How the Quantitative Section is Scored

The quantitative section of the paper-based General Test is scored the same way as the verbal section. First, a raw score is computed. The raw score is the number of questions for which the best answer choice was given. The raw score is then converted to a scaled score through a process known as equating. The equating process accounts for differences in difficulty among the different test editions; thus a given scaled score reflects approximately the same level of ability regardless of the edition of the test that was taken.
Quantitative Comparison Questions
Quantitative comparison questions measure your ability to:
• reason quickly and accurately about the relative sizes of two quantities
• perceive that not enough information is provided to make such a decision
Directions*Each of the sample questions consists of two quantities, one in Column A and one in Column B. There may be additional information, centered above the two columns, that concerns one or both of the quantities. A symbol that appears in both columns represents the same thing in Column A as it does in Column B.
You are to compare the quantity in Column A with the quantity in Column B and decide whether:
(A) The quantity in Column A is greater.
(B) The quantity in Column B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Note: Since there are only four choices, NEVER MARK (E).**
Sample Questions

Strategies for Answering

• Avoid extensive computation if possible. Try to estimate the answer.

• Consider all kinds of numbers before deciding. If under some conditions Column A is greater than Column B and for others, Column B is greater than Column A, choose “the relationship cannot be determined from the information given,” and go to the next question.

• Geometric figures may not be drawn to scale. Comparisons should be made based on the given information, together with your knowledge of mathematics, rather than on exact appearance.

Answer to Question 1 

root 100 denotes 10, the positive square root of 100. (For any positive number x, root x denotes the positive number whose square is x.) Since 10 is greater than 9.8, the best answer is (B). It is important not to confuse this question with a comparison of 9.8 and x where x2 100. The latter comparison would yield (D) as the correct answer because x2 100 implies that either x 10 or x 10, and there would be no way to determine which value x would actually have.

Answer to Question 2

Since ( 6)4 is the product of four negative factors, and the product of an even number of negative numbers is positive, ( 6)4 is positive. Since the product of an odd number of negative numbers is negative, ( 6)5 is negative. Therefore, ( 6)4 is greater than ( 6)5 since any positive number is greater than any negative number. The best answer is (A). It is not necessary to calculate that

( -6)^4 = 1,296 and that (- 6)^5 = -7,776 in order to make the comparison.
Problem Solving – Discrete Quantitative Questions
Discrete quantitative questions measure
• basic mathematical knowledge
• your ability to read, understand, and solve a problem that involves either an actual or an abstract situation
Directions*
Each of the following questions has five answer choices. For each of these questions, select the best of the answer choices given.




Sample Question
When walking, a certain person takes 16 complete steps in 10 seconds. At this rate, how many complete steps does the person take in 72 seconds?
(A) 45
(B) 78
(C) 86
(D) 90
(E) 115
 Strategies for Answering 
• Determine what is given and what is being asked.
• Scan all answer choices before answering a question.
• When approximation is required, scan answer choices to determine the degree of approximation.
• Avoid long computations. Use reasoning instead, when possible.
Answer
72 seconds represents 7 ten-second intervals plus 2/10 of such an interval. Therefore, the person who takes 16 steps in 10 seconds will take (7.2)(16) steps in 72 seconds.

(7.2)(16)= (7)(16) + (0.2)(16)
= 112 + 3.2
= 115.2

Since the question asks for the number of complete steps, the best answer choice is (E).


Problem Solving – Data Interpretation Questions

Data interpretation questions measure your ability
• to synthesize information and select appropriate data for answering a question
• to determine that sufficient information for answering a question is not provided The data interpretation questions usually appear in sets and are based on data presented in tables, graphs, or other diagrams.
Directions*
Each of the following questions has five answer choices. For each of these questions, select the best of the answer choices given.
Sample Question

graduate student applicants increase the most from that of the previous year?

(A) 1985

(B) 1986

(C) 1988

(D) 1990

(E) 1991

Strategies for Answering

• Scan the set of data to see what it is about.

• Try to make visual comparisons and estimate products and quotients rather than perform computations.

• Answer questions only on the basis of data given.

Answer This question can be answered directly by visually comparing the heights of the bars in the graph. The greatest increase in height between two adjacent bars occurs for the years 1985 and 1986. The best answer is (B).