# GRE Math Practice: Tips, Questions & Explanations

The GRE Quantitative Reasoning test assesses your understanding of basic arithmetic, algebra, geometry, and data analysis. This page contains everything you need to know to help you prepare for this section of the GRE, including what topics are covered, how many questions there are, and how to study effectively.

## 7 Tips to Ace GRE Test Math Section

You can easily crack the GRE Math section with these 7 secret tips and tricks that we are sharing: So, some GRE math tips and tricks that you could use in order to improve your test-taking skills are:

### 1. Practice Makes ‘Everyone’ Perfect

No matter how scared you have been of Math in your previous academic years, practicing can help you succeed in the GRE exam. It is advised that you start practicing for the test at least six months prior to your actual test date. Even if that seems impractical to you, it is crucial that you start practicing as early as possible.

### 2. Don’t Be Fast And Furious During The Test

The clock is ticking and you are running out of time yet more than half of your GRE test still remains unsolved, don’t panic cause it is natural to lose your cool.
You must memorize shortcuts to gain a strategic advantage during such moments.

Techniques such as mental math, Vedic math, an approximation, etc. can greatly help you solve a GRE math questions and answers quickly! This will help you keep calm and avoid silly mistakes made in haste.

### 3. Get Comfortable Using The GRE Onscreen Calculator

Despite being tech-geeks many students are not comfortable using the GRE calculator. We understand that using the onscreen calculator may not be user-friendly but it certainly comes in handy during the GRE math test. Learn to use the calculator for complex calculations and this will help you keep up with the time crunch and maintain your pace.

### 4. Skip But Don’t Miss

As there is no negative marking in the GRE Math section, the best strategy is to skip the difficult GRE math questions and come back to them later on (but before you complete the section). You can comfortably answer all GRE math questions whether or not you know the answer since there is no negative marking in the GRE exam. If you are unable to decide which question to skip, it is better to time yourself on each question. Do not spend over 1.5 minutes on any GRE math question unless you believe the solution is within your grasp.

### 5. Be Wary Of Word Problems

Often the most tricky questions in the GRE Maths section are the word problems. The key to solving these ‘complicated’ word problems is to read them thoroughly. Read and re-read until you are sure of what has been asked, what data is provided, etc. and only then start solving these GRE math questions.

Related Blog Post: How Much Time One Should Take to Prepare for the GRE?

### 6. Work On Your Mistakes

During GRE mock tests, you may come across a pattern of questions that you are most likely to answer wrong. On the contrary, there may be a certain topic in which you are unable to answer correctly sometimes.

Evaluate your knowledge by assessing your strengths and weaknesses in terms of topics during a GRE mock test. This can help you fare better during the actual GRE test. It is important that you work on your mistakes until you get them right.

### 7. Memorize Concepts Over Formulas

Although it is important to memorize all formulas, it is not mandatory. If you find yourself in the difficult situation of trying to learn everything, it always helps if you understand the underlying concept behind these formulas instead.

If you’re still studying for the GRE test, and you need help with your prep, then we at Manya-The Princeton Review are here to answer any questions you may have. We’ve helped many students score high in the quant section, and we can help you get the top GRE score as well. Reach out to us if you would like us to assist you with your GRE preparation.

## Can You Ace these GRE Practice Questions?

Start honing your skills with some GRE math practice questions and get a preview of what you can expect on test day.

Below are some of the GRE quantitative practice questions with which you can prepare for you GRE Math. Each sample GRE math question includes an explanation, so you can see how to crack it!

Note about calculators: On the GRE you’ll be given an on-screen calculator with the five basic operations: addition, subtraction, multiplication, division and square root, plus a decimal function and positive/negative feature. Don’t use anything fancier when you tackle this GRE math practice!

### Practice for GRE Quantitative Comparison Questions

Quantitative comparison in GRE math questions ask you to compare Quantity A to Quantity B. Your job is to compare the two quantities and decide which of the following describes the relationship:

• Quantity A is greater.
• Quantity B is greater.
• The two quantities are equal.
• The relationship cannot be determined from the information given.

1. The average (arithmetic mean) high temperature for x days is 70 degrees. The addition of one day with a high temperature of 75 degrees increases the average to 71 degrees.

(A) Quantity A is greater
(B) Quantity B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given

Answer: (B) Quantity B is greater

If the average high temperature for x days is 70 degrees, then the sum of those x high temperatures is 70x. The sum of the high temperatures, including the additional day that has a temperature of 75 degrees is, therefore, 70x + 75. Next, use the average formula to find the value of x:

In this formula, 71 is the average, 70x + 75 is the total, and there are x + 1 days. Substituting this information into the formula gives:

To solve, cross-multiply to get 71x + 71 = 70x + 75. Next, simplify to find that x = 4. Therefore, Quantity B is greater. The correct answer is (B).

2.
and are integers.
= b 3

(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.

Answer: (D) The relationship cannot be determined from the information given.

Try different integers for a and b that satisfy the equation a 2 = b 3 such as a = 8 and b = 3. These numbers satisfy the equation as 8 2 = 4 3 = 64. In this case, Quantity A is greater. Because Quantity B is not always greater nor are the two quantities always equal, choices (B) and (C) can be eliminated. Next, try some different numbers. When choosing a second set of numbers, try something less common such as making a = b = 1. Again, these numbers satisfy the equation provided in the problem. In this case, however, the quantities are equal. Because Quantity A is not always greater, choice (A) can now be eliminated. The correct answer is (D).

### Practice for Multiple-Choice GRE Math Questions

For question 3, select one answer from the list of five answer choices.

3. A certain pet store sells only dogs and cats. In March, the store sold twice as many dogs as cats. In April, the store sold twice the number of dogs that it sold in March and three times the number of cats that it sold in March. If the total number of pets the store sold in March and April combined was 500, how many dogs did the store sell in March?

(A) 80
(B) 100
(C) 120
(D) 160
(E) 180

Plug-In the Answers, starting with the middle choice. If 120 dogs were sold in March, then 60 cats were sold that month. In April, 240 dogs were sold, along with 180 cats. The total number of dogs and cats sold during those two months is 600, which is too large, so eliminate (C), (D), and (E). Try (B). If there were 100 dogs sold in March, then 50 cats were sold; in April, 200 dogs were sold along with 150 cats. The correct answer is (B) because 100 + 50 + 200 + 150 = 500.

4

▵ ABC has an area of 108 cm 2. If both x and y are integers, which of the following could be the value of x?

Indicate all such values.

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9

Answer: (A), (C), (D) and (E)

Plug the information given into the formula for the area of a triangle to learn more about the relationship between x and y:

The product of x and y is 216, so x needs to be a factor of 216. The only number in the answer choices that is not a factor of 216 is 5. The remaining choices are the possible values of x.

### Practice for GRE Math Numeric Entry Questions

Some questions on the GRE won’t have answer choices, and you’ll have to generate your own answer.

5. Each month, Renaldo earns a commission of 10.5% of his total sales for the month, plus a salary of \$2,500. If Renaldo earns \$3,025 in a certain month, what were his total sales?

If Renaldo earned \$3,025, then his earnings from the commission on his sales are \$3,025 – \$2,500 = \$525. So, \$525 is 10.5% of his sales. Set up an equation to find the total sales:

Solving this equation, x = 5,000.

6. At a recent dog show, there were 5 finalists. One of the finalists was awarded “Best in Show” and another finalist was awarded “Honorable Mention.” In how many different ways could the two awards be given out?

In this problem order matters. Any of the 5 finalists could be awarded “Best in Show.” There are 4 choices left for “Honorable Mention,” because a different dog must be chosen. Therefore, the total number of possibilities is 5 x 4, or 20.

## Key Concepts and Formulas: GRE Math

The GRE test will analyze your ability to solve a problem using essential concepts. Therefore, simply learning a formula by heart won’t help you much.

What you need to do is: Understand the concept, remember some crucial formulas and practice the application.

### What are These Formulas We are Talking About?

Arithmetic, Algebra, Geometry, and Data Analysis are the four major areas that are tested in the GRE Quantitative section.

#### Roots:

• All positive numbers have two square roots, one positive and one negative. Though, the square root of 0 is 0.
• The square root of a number “x” is “y” where y raised to the power 2 is x. And so on.
• Four crucial rules to remember:

#### Algebra:

This section comprises algebraic expressions, equations, inequalities, and functions. All these concepts are used to check application power to solve real-life word problems.

Following are a few more rules to remember about exponents (we talked about a couple already) in an algebraic expression.

Following are the basic rules for solving linear equations:

#### Coordinate Geometry:

Slope intercept form y = mx + b (slope formula of a straight line in the xy-plane, where m is called the slope and b is called the y-intercept.) See an example below:

Here, y= -13 + 7x form.

Intercept is (0, -13). Slope is 7.

Polygons, Triangles, and Circles

• A geometrical figure with 3 or more sides is known as a Polygon. If a polygon has n sides, it can be divided into (n – 2) triangles. The measure of the interior angles is 180 degrees. Thus, the sum of the measures of the interior angles of an n-sided polygon is (n – 2)(180 degrees).
• Pythagorean theorem: This theorem says that in a right triangle, the square of the length of the hypotenuse (line opposite the right angle) is equal to the sum of the squares of the lengths of the legs.

It can also be expressed as:

where DEF is a triangle with EF being the hypotenuse.

For all parallelograms, including rectangles and squares, area A is given by the formula

• A = bh
• b is the length of the base and h is the corresponding height.

There are two ways to find a circle’s circumference:

• C = 2πr
• C = πd

#### Exponents:

• You can multiply numbers as many times as you want, the exponent/ power tells you how many times multiplication has been done.

n x n x n x n x n = n5

• Any number raised to the power of 0 equals to 1.

• When base numbers with different powers are multiplied, the powers add up. Similarly, if you divide the same base number with different powers, the lower power is subtracted from a higher power.

#### Distance:

• d=rt
• Where d is the distance, r is the rate, and t is the time spent.

#### Interest rate :

• Let p = principal, r = rate, and t = time
• V = P [1+(rt/100)]
• Compound Interest
• V = P [1+(r/100n)]^nt

Remember to refer to your high school book and memorize the important formulas related to the above-stated concepts. Following this plan and solving GRE Maths Questions will be a cakewalk.

You can also enroll in GRE Classes for regular assessments and a deep understanding of the concepts.

As a final word of advice, always remember to use PEMDAS (the order of operations), consult your calculator when necessary, and, above all, practice, practice, practice!

## Ballparking in GRE Math – Arithmetic

Sometimes you might just get stuck on a GRE math question and not know how to proceed. It may also happen that you know how to solve the GRE arithmetic question but have very little time to complete. At such times, Ballparking may just help you to get your answer right on the GRE. Ballparking is a strategy which involves eliminating wrong answer choices and estimating the possibly right answer by doing some approximate calculations.

Let’s understand this better with an example.

1. If P=91/2 -91/3-91/5, Then P is

A. less than 0
B. Between 0 and 1
C. Between 1 and 2
D. Between 2 and 3
E. Greater than 3

A normal way of solving this question would be to use the calculator, but it is not possible on the GRE. As the onscreen calculator will not help you to find the cube root or the fifth root!

Now the square root of 9 is 3 and if you have to subtract 91/3 and 91/5 from 3 then P’s got to be less than 3! So answer choice E gets eliminated.

Now since 81/3 is 2, we can say that 91/3> 2. So 3 – (some no >2) means P must be less than 1. Eliminate C and D.

Since 11/5 = 1, we can say that 91/5>1.

That means P = 3 – (some no. >2) – (some no. >1) and this makes P negative. The answer is A

Ballparking works very well when the answer choices are far apart as in the example below:

Related Blog: How to Prepare For GRE in a Month

2. Which of the following is nearest to

A. 15
B. 10
C. 7
D. 3
E. 1

The numbers look quite horrible but let’s just replace the decimals with whole numbers and compute. First let’s round off the decimal numbers and then do some approximation.

Wait a moment! E is not the answer!

Be careful! The question has a 3 in the beginning and hence the answer is D!

## Ballparking in GRE Math – Geometry

The Ballparking technique works really well on the Geometry questions asked on the GRE test. It involves eliminating answer choices of wrong size and estimating the right answer by doing some approximation. Whenever you get stuck or are running out of time on your GRE math exam, you should try to use this technique to get your answer right.

Let’s see an example and try finding areas of the shaded region.

1. In the circle given below with center O, the diameter is 12 and the smaller angle AOB is 150˚ as shown. What is the area of the shaded region?

a) 27π
b) 18π
c) 15π
d)12π
e)9π

Well this involves knowing the relationship between sector area and central angle and for that you need to know the formula. However you can solve this just by doing some Ballparking!

Related Blog Post: How to Score 320+ on the GRE Exam in 30 Days?

Now since the diameter is 12, the radius becomes 6. The area of the circle is 36π (Everyone knows the area of the Circle formula is πr2). That means the area of the semicircle would be 18π. Well since the shaded region is less than the area of a semicircle the answer choices A and B get eliminated. As the area of the shaded region is surely more than the area of a quarter circle, that is 9π, answer choice E too gets eliminated.

Now we are left with answer choices C and D as both are between 9π and 18π. A closer observation of the diagram will tell you that the area of the shaded region is surely more than 1/3rd the area of the circle, that is more than 12π. Hence the answer choice D gets eliminated and C is the answer!

Ballparking works well in the Coordinate Geometry question as well.

2. In the rectangular coordinate system line y = x is the perpendicular bisector of the line segment AB and the X – axis is the perpendicular bisector of the line segment BC. If the coordinates of A are (3, 4), what are the coordinates of point C?

a) (-4,-3)
b) (-4, 3)
c) (3, -4)
d) (4,-3)
e) (4, 3)

Now this question involves drawing the X and Y axes, plotting the point A and the line y = x as shown below. As the line y = x is the perpendicular bisector of the line segment AB, the coordinates of B will be (4,3) (mirror image)as shown below.

As it is given that the X – axis is the perpendicular bisector of the line segment BC, it clearly means that the point C will be in the fourth quadrant with the x coordinate being positive and the y coordinate being negative. That means we can eliminate choices A, B and E.

A closer look at the diagram will tell us that (3, -4) is just the mirror image of point A in the X – axis and not point B. Hence eliminate C and the answer is D!
The diagram below shows points A, B and C.

This same question would have involved slope, equation of line and other formulae if you had solved it normally. However, Ballparking makes it look pretty simple!

## Tackle GRE Probability Questions With These Simple Tricks

The GRE quant section has several questions on probability. These GRE math questions generally test two basic concepts of the candidates – simple probability and permutation and combination. Broadly all questions in the GRE exam section will test only these two aspects. Simple probability is used to ascertain the likelihood of that particular event to happen.

On the other hand, permutation and combination are slightly complex where permutation refers to sequences and combination refers to groups. In permutations, the order is important while it is not the same with combinations.

### An Introduction to GRE Probability

Probability is a sub-topic of data analysis, one of the 4 major math topics tested on Quant (arithmetic, algebra, and geometry). Unlike these broader topics, however, probability doesn’t play a significant role in the GRE. In fact, you’ll probably have to answer only a couple of GRE probability questions – no more than two or three.

Still, it’s very important for you to understand what probability is and how it’s usually tested on the GRE. This way, you’ll be able to solve for the right answer, and as a result, raise your chance of achieving a high Quant score on the GRE.

So what exactly is the probability? Well, in math, probability is a way to describe uncertainty and the possible outcomes of an experiment using numbers. These numbers indicate the prospect of a certain event or group of events occurring and can be written as fractions, integers, or decimals.

Probability questions on the GRE can take on a variety of formats, such as numeric entry, multiple-choice, and Quantitative Comparison. Whether a GRE probability question calls for fractions or decimals is usually clarified by the question or answer choices. So, a GRE probability question discussing probabilities in fractions will probably ask for an answer in fractions. Answer choices, if supplied, are typically written either all in fractions or all in decimals.

If you are answering a Numeric Entry probability question, look closely at the blank to determine how you should write your answer. A single blank means the question is looking for either a decimal or an integer. A double blank means the question is looking for a fraction.

### Concepts Tested in GRE Probability Questions

All GRE probability questions will test your knowledge of two basic concepts:

• Simple Probability
• Permutation and Combination

### Tips to Master GRE Probability Questions

Here are few things to remember in order to tackle GRE probability questions

#### Tip 1 – Ensure the Question is on Probability

In the GRE exam, questions are not tagged as arithmetic or probability. You need to decide if it is from probability by looking for the “probability” word. If you can’t find it, then look for related keywords such as “outcome”, “random selection”, etc.

#### Tip 2 – Memorize the Formulas

For a great quant score, it is advised to memorize key GRE Quant Formulas of probability. Since time is extremely limited, try not to waste time in figuring out the exact formula. Most of the top-scoring GRE aspirants spend more time learning the formula and concept by heart rather than practicing sums.

Below are some of the key probability formulas that you should memorize if you want to clear the GRE quant section with a higher percentile:

• The probability of an event = Favorable number of event: Number of total outcomes
• Odds in favor of an event = Number of favorable outcomes: Number of total outcomes
• Odds against an event = Number of unfavorable outcomes: Number of total outcomes
• Take the mock GRE quant test

#### Tip 3 – Practice A Lot

To score a higher percentile on the GRE Quant section, it is imperative that you have a clear and thorough understanding of probability concepts. In fact, getting the perfect 170 in GRE Quants is not that difficult if you practice and have proper guidance related to preparation. Understand and avoid some common mistakes that aspirants often make during the GRE exam.

## How to Practice Probability Questions on the GRE?

Two events are said to be independent if the probability of any one of the events occurring is not affected by the probability of the other event occurring. If A and B are two independent events then the probability of both occurring is given by:
P (A and B) = P (A) x P (B).

### Sample Question 1

Q1. A jar contains 20 coins numbered from one to twenty. Amit selects a coin at random and then replaces it. He then selects another coin at random. What is the probability that both the coins will be odd-numbered ones?

Answer: The number of odd-numbered coins in the jar = 10.

The total number of coins = 20

The probability of selecting an odd-numbered coin the first time = 10/20 = 1/2

Since the first coin that was selected was replaced, the number of odd-numbered coins and a total number of coins do not change when the next coin is selected.

Hence the probability of selecting an odd-numbered coin the second time = 10/20 = 1/2

Now P(odd and odd) = P(odd) x P(odd)

= 1/2 x 1/2 = 1/4

Two events are said to be dependent if the probability of any one of the events occurring is affected by the occurrence of the other event. If A and B are two dependent events then the probability of both occurring is given by:

P (A and B) = P (A) x P (B).

### Sample Question 2

Q2. A jar contains 20 coins numbered from one to twenty. If Bob selects two coins at random one after the other without replacement, what is the probability that both the coins will be odd numbered ones?

Answer: In the beginning the number of odd numbered coins = 10

Total number of coins in the jar = 20.

Probability of selecting an odd numbered coin the first time = 10/20 = 1/2
After an odd numbered coin is selected and not replaced,

The total number of odd-numbered coins currently in the jar = 9

The total number of coins currently in the jar = 19.

Therefore the probability of selecting an odd-numbered coin the second time = 9/19

Now P (odd and odd) = P (odd) x P (odd)
= 1/2 x 9/19 = 9/38

There are some formulae required for solving almost every basic problem of Probability. Here, we have mentioned them all for your ease.

• Probability of an event happening = Capture
• The probability of an event will range from 0 to 1, that is 0 ≤ P (E) ≤ 1
• P (event occurring) + P (event not occurring) = 1

Sample Question 3

Q3. A problem is given to Alan, Bob & Carl, and the probability of their solving it is 1/2, 1/3 and 2/5 respectively. What is the probability that none of them solves the problem?

a) 1/5
b) 1/3
c) 1/2
d) 3/4
e) 11/12

Answer: The question asks for the probability of the problem not being solved by all three students.

P (Alan not solving AND Bob not solving AND Carl not solving) is what is asked.

It is given that P (Alan solving) = 1/2 , P (Bob solving) = 1/3 and P (Carl solving) = 2/5

P (Alan solving)

= 1/2

P (Alan not solving) = 1- P (Alan solving)

= 1 – 1/2 = 1/2

P (Bob solving) = 1/3

P (Bob not solving) = 1-1/3

= 2/3

P (Carl solving) =2/5

P (Carl not solving) = 1-2/5 = 3/5

Therefore, P (Alan, and Bob, and Carl not solving)

Answer= 1/2 x 2/3 x ⅗ = 1/5

The point to be noted here is that when we use the conjunction “and” we multiply.

The correct answer is option B.

### Sample Question 4

Q4. Annie and Chris write the GRE on the same day. The probability of Annie getting 170 in Maths is 1/7 and the probability of Chris getting 170 in Maths is 1/5. What is the probability that only one of them gets 170 in Mathematics?

(a) 1/7
(b) 2/7
(c) 1/2
(d) 3/4
(e) 4/5

Answer: In this question, we have to find P (Exactly one of them getting 170).

So P (Exactly one of them getting 170) can be written as:

P (Annie getting a 170 in Math AND Chris not getting a 170 in Math) OR

P (Chris getting a 170 in Math AND Annie not getting a 170 in Math)

Here, we see the use of both ‘AND’ and ‘OR’.

For ‘AND’ we multiply and for ‘OR’ we add.

Now, P (Annie getting 170 in Maths) = 1/7

P (Annie not getting 170 in Math) = 6/7

P (Chris getting 170 in Math) = 1/5

P (Chris not getting 170 in Math) = 4/5

P (Annie getting 170 in Math AND Chris not getting 170 in Math) = 1/7 x 4/5

= 4/35

P (Chris getting 170 in Math AND Annie not getting 170 in Math) = 1/5 x 6/7

= 6/35

Putting both together, we have this:

P (Annie getting a 170 in Math AND Chris not getting a 170 in Math) OR

P (Chris getting a 170 in Math AND Annie not getting a 170 in Math)

= 4/35+6/35

= 10/35

= 2/7

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### Can I use a calculator on the GRE Quantitative section?

As part of the testing software, you will have access to a digital calculator. This cuts down on the time it takes to compute, giving you more time to check your understanding of mathematical concepts.

### How many questions are under GRE Quantitative Reasoning?

There are two quant sections on the GRE test. Both these sections have 20 questions each to be completed in 35 minutes duration.

### What does the GRE Quantitative Test include?

GRE Quantitative test includes topics from high school mathematics. There are two math sections present on the GRE test. Each section consists of 20 questions to be solved in 35 minutes. If the experimental section turns out to be quant, test-takers will have to face a total of three math sections(only two sections will be scored). Topics in the quant section include problems from Algebra, Geometry, Rates, Word Problems, Ratios, and Data Analysis(Chart problems).

### How hard is it to get a 160 on the Quantitative section?

To start with, the topics of GRE Math are familiar to most of the test-takers as they would have studied them in their high school education. Once this is established, students can hone their quantitative skills through rigorous practice by doing mock drills and practice tests.

The only difficult part for test-takers would be to comprehend lengthy word problems on the math section. Through structured practice and proper implementation of techniques, the trouble caused by word problems can be eliminated and scoring 160 will thus become easier.

### What is the syllabus of GRE Quantitative Reasoning?

The GRE quantitative reasoning section tests the student’s ability to create mathematical models to solve real-world and theoretical problems. The topics covered in the quants sections include Algebra, Arithmetic, Geometry, and Data Analysis.