An Elaborate Overview of the GRE Math Section
What is GRE?
GRE stands for Graduate Record Exam. It is basically a test which is taken by students all over the world in order to get admission in national and international universities for higher education. Students who are interested to pursue Masters and even Doctoral degrees in various fields like Business, Biological Science, Engineering, etc. are supposed to take this test.
If you’re planning to sit in the GRE general exam and are wondering about the ways to prepare for the Quantitative section of GRE, then we're here to help you out. Here in this article, we would have a detailed discussion on the Quant, i.e. GRE Math section and clear all your doubts.
Skills which GRE Math Intend to Measure
Students who are planning to do their graduation or post-graduation in reputed universities generally take-up the GRE exam. Hence the Quantitative section of GRE exam intends to measure a student’s basic problem solving skills, their understanding of the rudiments of mathematics and obviously their ability to solve problems quickly by using proper formulations and tricks and their potentiality to apply the mathematical concepts logically.
Level of Math in GRE Exam
The level of questions in the GRE math section is of very basic type. The syllabus is limited to the sums you've practiced in high school. The only difference between the typical high school sums and that of the GRE Quant section is the difficulty and trickiness. While you could easily score good marks in high school by practicing 2 or 3 types of sums, for GRE you need to practice thoroughly and rigorously. Until you gain the ability to solve tricky problems within a short span of time, it is quite impossible to score good marks in GRE.
GRE Quant is Adaptive:
The GRE math section is divided into two sections, with 20 questions each and the time allocated to each section is 35 minutes. GRE Quant section is adaptive in nature between the sections. That is, the difficulty level of the second section depends on the performance of the first section. In simple words, if you aim for a perfect score, then you have to go through a more difficult path in the second section of Quant.
GRE Quant: Content
The Quant section of GRE comprises of basic questions from the fields of
- Arithmetic
- Algebra
- Geometry
- Data Analysis
Arithmetic:
First, let us discuss the topics which you should cover for the Arithmetic questions. As we have already stated, the GRE Math section aims to test your basic mathematical skills; you should never neglect the basics of Arithmetic. Topics like
- Prime numbers
- Factorization odd and even numbers
- Divisibility
- Ratio-proportion-variation
- Percentage and rate calculation
- Absolute value determination
- Number system
Algebra:
Next, we come to the Algebra part. As you may know, Algebra is a vast section of Mathematics. There are innumerable number of topics in this part; it might not be possible for you to cover all of them, but the topics which you can never neglect are,
- Linear and Quadratic Equations
- Simultaneous Equations
- Functions
- Inequalities
- Roots and surds
- Exponents
- Coordinate geometry
- straight lines
- slopes
- parabola-hyperbola-ellipse
- circle
Geometry:
For the Geometry section, you can hardly skip a topic. You’ll have to cover everything starting from
Lines and Circles
- Polygons
- Triangles
- Quadrilaterals
- Lot more
- Three-dimensional figures
- Pythagoras theorem
- Angle measurements
- Mensuration
- Area
- Perimeter
- Volume
Data Analysis:
In Data Analysis section topics include,
- Statistics:
- Mean
- Median
- Mode
- Standard deviation
- Quartiles
- Percentiles
- Data Interpretation Set:
- Interpretation of data in tables
- Graphs like line graph
- Bar graph
- Probability:
- Individual and compound events
- Random variables
- Probability distribution
- Counting methods:
- Combination and Permutation
- Venn diagram
GRE Quant: Test Pattern
GRE Quant section consists of four types of question pattern. They are,
Comparison Questions
- Multiple choice Question - one correct answer
- Multiple choice Question – one or more correct answers
- Numeric entry questions
Comparison Questions
In comparison question type, you will be asked to compare two entities to derive a relationship between them. You will be given four answer choices and the choices are always standard for all comparison type questions. In other words, the choice list and the order of the choice list are static.
Sample Question
Quantity A | Quantity B |
---|---|
54% of 360 | 150 |
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Explanation
Without doing the exact computation, you can see that 54 percent of 360 is greater than one half of 360, which is 180, and 180 is greater than Quantity B, 150. Thus the correct answer is Choice A; Quantity A is greater.
(This Question is taken from the following URL - https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/comparison/sample_questions)
Cracking Comparison Questions:
- Don't waste time in unnecessary calculations. Just simplify and evaluate the value of one or both the numbers.
- If the comparison is based on a geometrical figure, quickly redraw the figure with the details which are fully determined by the information and check what changes happen to the undetermined part.
- If the comparison is between algebraic equations, quickly substitute comfortable numbers to the variables in the equation and then compare the results.
- If finding a relation between two algebraic or arithmetic expressions seems difficult, then first simplify them as much as possible and then try to compare.
Multiple Choice Questions (one correct answer)
This type is a simple Multiple Choice Question, where there will be one correct answer in the choice list and you have to find it. You will be given five choices.
Sample Question
A car got 33 miles per gallon using gasoline that cost $2.95 per gallon. Approximately what was the cost, in dollars, of the gasoline used in driving the car 350 miles?
- $10
- $20
- $30
- $40
- $50
Explanation
Scanning the answer choices indicates that you can do at least some estimation and still answer confidently. The car used (350/ 33) gallons of gasoline, so the cost was Open parenthesis, (350/33)(2.95) dollars. You can estimate the product (350/ 33)(2.95) by estimating (350/ 33) a little low, 10, and estimating 2.95 a little high, 3, to get approximately (10)( 3) = 30 dollars. You can also use the calculator to compute a more exact answer and then round the answer to the nearest 10 dollars, as suggested by the answer choices. The calculator yields the decimal 31.287… which rounds to 30 dollars. Thus the correct answer is Choice C, $30.
(This Question is taken from the following URL - https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/multiple_choice_one/sample_questions)
Cracking Multiple Choice Questions-(One Correct Answer)
Try elimination method to reject the choices that seem totally irrelevant quickly.
- For algebraic and arithmetic equations, you can Simply substitute the answer choices one by one in the equation and find the right answer.
- Pay attention to the units as sometimes there may be a trap in the answer choices.
- The right answer may be in decimals or as a whole number or a fraction. So be quick to convert your answer to required form and find its nearest possible choice.
Multiple Choice Questions (one or more correct answers):
These are also multiple choice questions with one or more than one correct answers in the choice list. You have to find all correct answers in the choice list or sometimes a specific number of correct answers if specified in the question. There is no credit for partially correct answers.
Sample Question
Which of the following integers are multiples of both 2 and 3?
Indicate all such integers.
- 8
- 9
- 12
- 18
- 21
- 36
Explanation
You can first identify the multiples of 2, which are 8, 12, 18 and 36, and then among the multiples of 2 identify the multiples of 3, which are 12, 18 and 36. Alternatively, if you realize that every number that is a multiple of 2 and 3 is also a multiple of 6, you can identify the choices that are multiples of 6. The correct answer consists of Choices C (12), D (18) and F (36).
(This Question is taken from the following URL - https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/multiple_choice_more/sample_questions)
Cracking Multiple Choice Questions-(One or More Correct Answers)
Check whether the number of right answers to be chosen is specified in the question. This may save your time. If there is no specification, you have to find all the possible right answers.
Remember, sometimes there may be only one right answer in the choice list. This type of question and choice list can easily make you fit in the trap or waste your time too much.
Numeric Entry Questions
In this section, you won't find answer choices, and you need to type the correct answer in a box. There will be a single box if the answer is an integer or a decimal and two boxes if the answer is a fraction. Rounding off should be done if specified.
Sample Questions
One pen costs $0.25 and one marker costs $0.35. At those prices, what is the total cost of 18 pens and 100 markers?
Explanation
Multiplying $0.25 by 18 yields $4.50, which is the cost of the 18 pens; and multiplying $0.35 by 100 yields $35.00, which is the cost of the 100 markers. The total cost is, therefore, $4.50+ $35.00=$39.00. Equivalent decimals, such as $39.5 or $39.500, are considered correct. Thus the correct answer is $39.50 (or equivalent).
(This Question is taken from the following URL - https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/numeric_entry/sample_questions)
Cracking Numeric Entry Questions
- Pay attention to labels given before or after the answer box as they may indicate the format of answer you need to enter.
- Pay attention to the degree of accuracy you are directed to round-off the answer. If not specified enter the exact answer.
- As there is no choice list to confirm your answer, always double check your computations and if possible solve it with an alternate method to be sure.
Data Interpretation Set:
Questions from the section of Data Analysis may appear individually separate and distinct or as a set of questions based on a group of data. This pattern is called Data Interpretation questions. Data Interpretation Set questions may be based on a set of data from a table or a graph or a statistical chart.These type of questions may fall either into multiple choice type or numeric entry type.
Sample Question
Store | Percent Change from 2006 to 2007 | Percent Change from 2007 to 2008 |
---|---|---|
P | 10 | -10 |
Q | -20 | 9 |
R | 5 | 12 |
T | 17 | -8 |
If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- $727,200
- $792,000
- $800,000
- $880,000
- $968,000
Explanation
If the dollar amount of sales at Store P was $800,000 for 2006, then it was 10 percent greater for 2007, which is 110 percent of that amount, or $880,000. For 2008 the amount was 90 percent of $880,000, which is $792,000. The correct answer is Choice B, $ 792,000.
Note that an increase of 10 percent for one year and a decrease of 10 percent for the following year do not result in the same dollar amount as the original dollar amount because the base that is used in computing the percentage is $800,000 for the first change but $880,000 for the second change.
(This Question is taken from the following URL - https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/data_interpretation/sample_questions)
Cracking Data Interpretation Set:
- Stay focused only on the part which you have to solve and information regarding it.
- There may be too many information present in the question which may not be needed to solve the problem. Focusing on all given information can confuse or waste your time.
Breaking the Barrier: Word Problems
One of the most important parts of GRE Quant, which is often dreaded by the students is the word problems of Algebra. But in reality, they are not that hard and can fetch you good marks once you apply the right tricks. For word problems, it is very important that you read the problem carefully. Without reading it, you won’t be able to figure out the process in which you should carry on.
Most of the algebraic word problems are need to be started by picking up a variable and forming the right equation. Once the equation is formed, there is nothing much left to do. But don’t just rush to form the equation until you collect all data. For that, it is advised to write down all the relevant data provided to you in the sum. The variable which you would assume is the one (or more than one) entity which needs to be found out. It won’t be ascertained with a quantity. The common word problems in GRE math comes from topics like time and distance, percentage, age, cost and profit etc. Make sure you practice these parts thoroughly.
Special Tips for Statistics:
The level of GRE Statistics questions in GRE is not very hard and can be solved easily if you practice smartly. Here I’m providing some free URLs to GRE statistics sample questions and formulas. Hopefully, they would help you in preparing for the Statistics questions in a better way.
Statistics Formula Flash Cards
Statistics GRE Math Questions
Cracking overall GRE Quant:
Choose right preparation materials.
- Evaluate a study plan with respect to time period you are left with.
- Get familiar with basic formulas and conventions.
- Take practice tests regularly and focus on the areas where you seem weak. Timed practice tests will help you to get used to the time management.
- Get used to all types of expected question formats.
How to Choose Right Preparation Books:
Following are the factors which you must take into account before you buy yourself a proper practice book for GRE math:
- A proper GRE practice book should maintain the standard and pattern of the GRE questions. Honestly, if you buy a GRE prep book which covers question patterns of other tests, it is of no use to you, no matter how good the book is.
- The book should explain each and every problem in an elaborate way. Just solving a problem in two lines is definitely not going to help the test takers. If the book contains a proper study plan and time management strategies, then that would be an additional bonus.
- Finally, the book should have enough number of practice sets so that the test takers can perform tons of tests before they actually sit for the exam.
Best GRE Math Books: Recommended
- Magoosh ($14.24) – Magoosh is a California based publishing house which has been bringing books on GRE and SAT exams for a long time. This book would help you in preparing all the sections of GRE as well as help you in coming up with various exam strategies. Add to that they have their own app and online practice tests to help you further. But some users claim that this book lacks a bit when it comes to explaining the solutions properly. You can buy this book from Amazon.
- ETS ($17.40) – ETS offers several books to the GRE test takers; the speciality of these books is they come with exam guides and CDs which let the examinees take online tests. But some test takers find it too difficult to understand the explanations given in these books. You can buy their book from Amazon.
- Manhattan ($20.52) – At an affordable price, this book is quite a hit among the GRE examinees due to its extensive set of resources when it comes to the GRE exam. This book elaborates each unit of the GRE math section and is available on Amazon in various price ranges. While a few examinees find this book and its formatting a bit confusing, most of the test takers are thoroughly satisfied with this book.
Also, there are ample numbers of free GRE Tests available on the internet which you can try to sharp-up your skills.
How to Choose a Study Plan:
This question is a bit difficult to answer as it depends on a number of factors. GRE math syllabus is largely based on the syllabus of your high school. So, if you're fresh from school, then it might be easier for you to crack the Math section. Also, it depends on your problem solving speed. On an average, a student should at least take a period of 3 months to prepare.
There are various online GRE prep courses to help you out. But the GRE math prep course from Khan Academy is possibly the best one as it covers all the parts of GRE math methodically. Here we’re providing some URLs to various online GRE math prep courses. The duration of these courses varies from 1 month to 3 months to 6 months.
https://www.ets.org/gre/revised_general/prepare/khan_academy
https://gre.magoosh.com/prep-app
https://www.manhattanprep.com/gre/
Formulas and Conventions
There are tons of formulas which you need to keep track of, if you’re thinking of appearing for the GRE. But here we’re listing only those set of formulas which are an integral part of the GRE examination:
- Circles (Let r = radius and d = diameter)
- Squares (Let s = side length)
- Rectangles (Let L = length and W = width)
- Triangles (Let b = base and h = height)
- Trapezoids (a = top parallel side, b = bottom parallel side, h = height)
- Slope
- Distance, rate, time
- Interest rate
Area: A = π r^2
Circumference: C: π2r or πd
Area: s2
Perimeter: 4s
Area: L x W
Perimeter: 2L + 2W
Area: 1/2bh
Area: (a+b)/2 x h
y=mx + b
The steepness of a line on the coordinate plane can be calculated using the slope formula. The b is where the line crosses the y-axis and is called the "y-intercept." The x and y can be any point along the line; you'll always have these three numbers. Simply solve for y to get your m.
d = rt
Simple interest is the type of interest where the rate of growth is always applied to the original principal. Let p = principal, r = rate, and t = time
V = P [1+(r/100n)]
Compound interest is when the rate of growth is applied to the current principal. Let n = number of times compounded annually.
V = P [1+(r/100n)]^nt
If you’re planning to get a decent score in the GRE Math section, don’t even think of sitting for the exam without memorizing these basic formulas.
(These Formulas are taken from the following URL - https://gre.economist.com/gre-advice/gre-quantitative-section/overview-gre-math/most-important-gre-math-formulas)
Conventions:
Conventions are assumptions to be considered while solving mathematical concepts. The assumptions about geometric figures, numbers, quantities, etc. in GRE Quant is conventional to the high school level.
Some Examples:
Arithmetic:
All numbers are Real Numbers.
Prime number is an integer > 1
One dozen= 12
Algebra:
|x| = absolute value of x; Q || R = lines Q and R are parallel
Algebraic equations are to be solved in the
Order Of Operations.
Geometry:
All figures are assumed to lie on the same plane, unless specified.
Geometrical figures are not drawn to scale
Data Analysis:
Bar graphs, circle graphs, line graphs are all drawn to scale.
IF E and F are two events and they are mutually exclusive, then P(E and F) =0
To know more about mathematical conventions, click here https://www.ets.org/s/gre/pdf/gre_math_conventions.pdf
Why should you take the GRE Practice tests?
Taking the practice tests is important because they help the test takers in getting familiar with the GRE Math question pattern and the syllabus. Also, the potential examinees can be habituated with the usage of online calculators and practice their time management skills. The scores they achieve in these practice tests would help them in identifying their strengths and weaknesses as well.
Here are a set of online GRE Math preparation tests which would be handy for the test takers;
GRE Math MCQ Questions with one correct answerGRE Math MCQ Questions with more than one correct answer
GRE Math Numerical Entry Questions
GRE Math Comparison Questions
To find more such sample questions you can visit http://www.greguide.com/ where you would be able to practice sample questions on GRE Math in proper format with the timer and online calculator.
One important thing is, students must not take these practice tests just a day before the exam. Because, if for any reason the score of the practice test is not satisfactory, the student might start getting anxious and that would be bad for the actual exam. So, keep the last 2-3 days for revision purpose only and don’t stress out unnecessarily.
Time Management Strategies for the GRE Math Section
Managing the time properly is a must for any competitive examination. No matter how good students are you, if you lack the time management skills, you are pretty much in trouble. So, here are a few time management tricks to help you out:
- Don't forget to maintain a proper sequence even when you're doing rough work. Neat rough work is mandatory to keep your cool at the time of the exam. Also, avoid leaving sums in the middle. It is quite rare that you would get a chance to return to all those questions at the end. So it is better that you solve them at one go and in case you can’t, just move forward.
- Here is a table to help you:
- There would be an online calculator provided to you. Don’t use it unnecessarily for simple calculations. In fact, try to spend less time on the simple questions. And, don’t forget to keep track of the background timer.
Question Type | Approximate no. of Questions | Average Time to be Spent on Each Question (Minutes) |
---|---|---|
Comparison Questions | 8-9 | 2 |
MCQ with one answer | 7-8 | 2 |
MCQ with more than one answer | 2-3 | 3 |
Numerical Entry | 1-2 | 3 |
Note: Spend the rest of the times for the Data Interpretation questions.
GRE Quant Scores:
When you’re sitting for a competitive examination, no score is a sufficient score unless you score the full marks. Same goes for GRE. Still, to help you out we're providing you with a rough sketch of the levels of scores in GRE exam. Take a look:
- Perfect GRE Math Score:165-170
- Good GRE Math Score:155-164
- Average GRE Math Score: 150-160
- Not Good Enough GRE Math Score: Below 150
ETS the organization which organizes the GRE exam keeps the record of your GRE score for five years. Also, there is no limitation in appearing for this exam. Hence, it is better that you apply with your best GRE score when it comes to applying for the Grad schools. If your latest score of GRE is your best till date score then send that, and if not then it is advised that you send your highest achieved score till date.
Availability of Online Calculator
To make your task easier, there is an online calculator available in the GRE examination. Though it is there to simplify your quantitative calculations and measurements, make sure you don't rely on it completely as there would definitely be those questions where you would have to apply your own analytical skills and the calculator won't be of that much help.
Availability of Scratch Paper
Like any other competitive exams, GRE too does not impose any restrictions on you when it comes to using the Scratch paper. You can have as many as you want. Also, you can't use your own pen or pencil. A pencil would be provided from the exam organizing authorities. Though there are no bounds in the number of scratch papers, yet we suggest you to use your scratch sheets very carefully. Especially, when it comes to the Quant section, the usage of rough sheets has the ability to make or break your exam. You need to keep your GRE scratch paper properly sequenced. Don't forget to put a number on them from the very first paper you use. That way it would be easier for you to identify the order in which you have solved the problems.
How is GRE General Test different from GRE subject Test?
The GRE general test is a type of GRE exam which tries to measure the overall skills and intelligence of a student rather than considering only an individual subject. While in the GRE subject test, more focus is given on each subject like Mathematics, Biology, English, Chemistry, Physics, and Psychology.
The math section in GRE general test is easier compared to the math section in GRE subject test. While there are no questions on Trigonometry and Calculus in the general test; 50% of the GRE subject test contains Calculus. GRE general math test is based on High school level math while GRE subject test has some high level of conceptual topics like Linear and Abstract Algebra, Discrete mathematics, Trigonometry etc.
Overview of GRE General Test
The GRE exam mainly contains a total of three sections, and apart from the Quant section the other two sections are Analytical Writing and Verbal Reasoning. With the total duration of 3 hours and 40 minutes, times allocated to the Analytical Writing, Verbal Reasoning and Quantitative Reasoning sections are 60 minutes, 30 minutes per section and 35 minutes per section respectively.
Click on the following URLs to find more about the other two sections apart from the Quant section;
Analytical Writing
Verbal Reasoning
(Credit-Official website of ETS)