# GRE Quant Formulas - Cheat sheet for GRE Preparation

#### What are the components of the GRE^{®} Quants section?

The GRE^{®} General Test has three main divisions: Analytical Writing; Verbal Reasoning; and Quantitative Reasoning.

The quantitative reasoning section has two kinds of multiple choice questions: Quantitative comparisons and problem solving. The test also contains questions where students have to provide their own answers. There are approximately 20 questions to be completed in 35 minutes. The math that will be tested is around the basic math formula and should be within the level of a 10th grade student. Some of the questions involve data interpretation. For the computer based test a calculator that is available onscreen is provided to students. Students taking the paper based test are provided with a calculator at the test center on test day.

The GRE^{®} General Test has three main divisions: Analytical Writing; Verbal Reasoning; and Quantitative Reasoning.

The quantitative reasoning section has two kinds of multiple choice questions: Quantitative comparisons and problem solving. The test also contains questions where students have to provide their own answers. There are approximately 20 questions to be completed in 35 minutes. The math that will be tested is around the basic math formula and should be within the level of a 10th grade student. Some of the questions involve data interpretation. For the computer based test a calculator that is available onscreen is provided to students. Students taking the paper based test are provided with a calculator at the test center on test day.

#### Prepping for the GRE^{®} quantitative Section:
The best way to prepare for the GRE^{®} Quant section is to seek out the right GRE^{®} Quant materials, mainly the Quant formulas. These can be found for free on the internet which has a wealth of online GRE^{®} prep aids, ranging from iPhone apps to practice tests.

The best way to prepare for the GRE^{®} Quant section is to seek out the right GRE^{®} Quant materials, mainly the Quant formulas. These can be found for free on the internet which has a wealth of online GRE^{®} prep aids, ranging from iPhone apps to practice tests.

#### What are some of the basic GRE^{®} Quant formulas?
Below you will find some of the most important and basic math formulas that will be helpful in your GRE^{®} quantitative section. They can also be called GRE^{®} Quant formulas or GRE^{®} math formulas.

**1. Square**

**Perimeter**

P = 4S

- Multiply any one side (s) by four.

**Area**

A = (side)^2

- Multiply any two sides together (i.e., square one side).

**2. Rectangle**

**Perimeter**

P = 2(l+w)

- Multiply the length (l) by 2 and the width (w) by 2, and then add the products together.

**Area**

A = l*w

- Multiply the length by the width.

**3. Circle**

**Perimeter**

P = 2πr or πd

- Multiply 2, π (pi), and the radius (r) (the length of a line connecting the center of the circle to the edge).
- Alternatively, multiply π by the diameter (d) (the length of a line cutting the circle in half).
- Two radii (the plural of radius) equal the diameter, so 2r=d.
- π can be rounded to 3.14 (or 3.14159).

**Area**

A =πr^2

- Square the radius and multiply it by π.
**Note: all circles equal 360 degrees.**

**4. Triangle**

**Pythagorean Theorem**

(a)^2 + (b)^2 = c^2

**This theorem can only be used for right triangles (triangles with a 90-degree angle).***a* and *b* are the two shorter sides, or “legs,” and *c* is the hypotenuse (the longest side of a right triangle).- Certain triangle-side combinations (a:b:c), called Pythagorean triples, are easy to memorize. Common ones you may come across on the GRE
^{®} are:- 3:4:5
- 5:12:13
- 8:15:17

**Area**

A =1/2 bh

- Multiply the base (b) by the height (h) and divide by 2.
**Note: angles in a triangle always add up to 180 degrees.**

**5. Trapezoid**

**Area**

A = a+b2h

- a and b are parallel sides.
- Add a and b, divide by 2, and then multiply by the height (h).

**6. Laws of Exponents**

x 0 = 1x -1 =1x, x-2 =1x2, etc

xa xb = xa + bx axb = x(a-b)=1xb-axaya=(xy)a(xy)a=xaya(xa)b=xab

**7. Laws of Square Roots**

a square =aab=abab=ab

**8. Laws of Even and Odd Numbers**

even + even = even

odd + odd = even

even + odd = odd

even * even = even

odd * odd = odd

even * odd = even

**9. Distance**

D =rt

- Multiply the rate (r) by the time (t) to find the distance (D).
- You can also solve for the time or rate by rearranging this formula to equal either r or t: R =Dt or t=Dr

**10. Slope of a Line**

**Using the Equation of a Line**

y=mx+b

- A slope is the steepness of a line in a coordinate system.
- m is the slope.
- x and y are a pair of coordinates.
- b is the y-intercept, or where the line passes through the y-axis.
- You may occasionally see this equation written in a different way.
**Always convert it to the format above to ease calculations and avoid confusion.** - A line increasing as it moves left to right has a positive slope, whereas a decreasing line has a negative slope. A completely horizontal line has a slope of 0.
- If the y-intercept of a line is 0, the formula for it is y=mx+0 or y=mx. Here is an example:

**Using Two Sets of Coordinates**

m = (y2 – y1)/(x2- x1)

*or*

slope=rise/run

- x1 and y1 are a corresponding pair of coordinates on a line. (x2 and y2 are a separate pair of coordinates on the same line).
- This equation is known as rise over run (the change in vertical distance over the change in horizontal distance).

**11. Average**

average = sum of n numbers/n

average speed = total distance/total time

- The average is also called the mean.
- Don’t confuse the average for other statistical terms. Common terms you may see on the GRE
^{®} test are:**Mode:** the most common number of a data set**Range:** the difference between the highest number and the lowest number of a data set.**Median:** the middle number of a data set.

**12. Probability**

Probability of an event occurring = number of successful outcomes/ total number of possible outcomes.

Probability of two independent events occurring = probability of event A * probability of event B

**Probabilities are usually written as fractions**, though you may see them written as decimals or ratios (e.g., 3:4).

**13. Percentages**

**Percent Basics**

**Solve for x percent of number n**

N x 100

- Alternatively, a faster way to solve this is by moving the decimal point of the percent to the left two places and multiplying it by n. For example, what is 12 percent of 50? Answer: 50*(12/100) = 6.

**Solve for what number n is x percent of:**

100 nx

**Solve for what percent is number n of number m:**

100 nm

**Percent Change**

Percent Increase

Final amount – original amount/original amount *100.

The numerator is equivalent to the actual increase in the amount.

**Percent Decrease**

((Original amount –final amount)/(original amount)) *100

The numerator is equivalent to the actual decrease in the amount.

**Do you need to memorize GRE**^{®} Quant formulas?

While the GRE^{®} is not a test of knowledge, you will need to show up on the test day with some basic math formula memorized. Though memorizing Quant formulas isn't the only way to study for the GRE^{®} Quant, memorizing certain frequently-tested math formulas will help you improve your speed on test day. Once you learn these GRE^{®} math formulas, be sure to practice using them! Timed practice will ensure you can answer all the questions giving you a higher chance to ace your test.

**Time allocated for the GRE**^{®} Quant section and knowing your GRE^{®} Quant formulas.

The Quant section has 40 questions in total which are divided into 2 sections each containing 20 questions and the time allocated for each part is 35 minutes. In total, the GRE^{®} Quant sections take 1 hour 10 minutes. Therefore, knowing your quant formulas and keeping a handy math formula chart for your practice sessions is key.

Below you will find some of the most important and basic math formulas that will be helpful in your GRE^{®} quantitative section. They can also be called GRE^{®} Quant formulas or GRE^{®} math formulas.

**1. Square**

**Perimeter**

P = 4S- Multiply any one side (s) by four.

**Area**

A = (side)^2- Multiply any two sides together (i.e., square one side).

**2. Rectangle**

**Perimeter**

P = 2(l+w)- Multiply the length (l) by 2 and the width (w) by 2, and then add the products together.

**Area**

A = l*w- Multiply the length by the width.

**3. Circle**

**Perimeter**

P = 2πr or πd- Multiply 2, π (pi), and the radius (r) (the length of a line connecting the center of the circle to the edge).
- Alternatively, multiply π by the diameter (d) (the length of a line cutting the circle in half).
- Two radii (the plural of radius) equal the diameter, so 2r=d.
- π can be rounded to 3.14 (or 3.14159).

**Area**

A =πr^2- Square the radius and multiply it by π.
**Note: all circles equal 360 degrees.**

**4. Triangle**

**Pythagorean Theorem**

(a)^2 + (b)^2 = c^2**This theorem can only be used for right triangles (triangles with a 90-degree angle).***a*and*b*are the two shorter sides, or “legs,” and*c*is the hypotenuse (the longest side of a right triangle).- Certain triangle-side combinations (a:b:c), called Pythagorean triples, are easy to memorize. Common ones you may come across on the GRE
^{®}are:- 3:4:5
- 5:12:13
- 8:15:17

**Area**

A =1/2 bh- Multiply the base (b) by the height (h) and divide by 2.
**Note: angles in a triangle always add up to 180 degrees.**

**5. Trapezoid**

**Area**

A = a+b2h- a and b are parallel sides.
- Add a and b, divide by 2, and then multiply by the height (h).

**6. Laws of Exponents**

x 0 = 1x -1 =1x, x-2 =1x2, etc

xa xb = xa + bx axb = x(a-b)=1xb-axaya=(xy)a(xy)a=xaya(xa)b=xab

**7. Laws of Square Roots**

a square =aab=abab=ab

**8. Laws of Even and Odd Numbers**

even + even = even

odd + odd = even

even + odd = odd

even * even = even

odd * odd = odd

even * odd = even

**9. Distance**

D =rt

- Multiply the rate (r) by the time (t) to find the distance (D).
- You can also solve for the time or rate by rearranging this formula to equal either r or t: R =Dt or t=Dr

**10. Slope of a Line**

**Using the Equation of a Line**

y=mx+b

- A slope is the steepness of a line in a coordinate system.
- m is the slope.
- x and y are a pair of coordinates.
- b is the y-intercept, or where the line passes through the y-axis.
- You may occasionally see this equation written in a different way.
**Always convert it to the format above to ease calculations and avoid confusion.** - A line increasing as it moves left to right has a positive slope, whereas a decreasing line has a negative slope. A completely horizontal line has a slope of 0.
- If the y-intercept of a line is 0, the formula for it is y=mx+0 or y=mx. Here is an example:

**Using Two Sets of Coordinates**

m = (y2 – y1)/(x2- x1)*or*

slope=rise/run

- x1 and y1 are a corresponding pair of coordinates on a line. (x2 and y2 are a separate pair of coordinates on the same line).
- This equation is known as rise over run (the change in vertical distance over the change in horizontal distance).

**11. Average**

average = sum of n numbers/naverage speed = total distance/total time

- The average is also called the mean.
- Don’t confuse the average for other statistical terms. Common terms you may see on the GRE
^{®}test are:**Mode:**the most common number of a data set**Range:**the difference between the highest number and the lowest number of a data set.**Median:**the middle number of a data set.

**12. Probability**

Probability of an event occurring = number of successful outcomes/ total number of possible outcomes.

Probability of two independent events occurring = probability of event A * probability of event B

**Probabilities are usually written as fractions**, though you may see them written as decimals or ratios (e.g., 3:4).

**13. Percentages**

**Percent Basics**

**Solve for x percent of number n**

- Alternatively, a faster way to solve this is by moving the decimal point of the percent to the left two places and multiplying it by n. For example, what is 12 percent of 50? Answer: 50*(12/100) = 6.

**Solve for what number n is x percent of:**

100 nx

**Solve for what percent is number n of number m:**

100 nm

**Percent Change**

Percent Increase

Final amount – original amount/original amount *100.

The numerator is equivalent to the actual increase in the amount.

**Percent Decrease**

((Original amount –final amount)/(original amount)) *100

The numerator is equivalent to the actual decrease in the amount.

**Do you need to memorize GRE ^{®} Quant formulas?**

While the GRE^{®} is not a test of knowledge, you will need to show up on the test day with some basic math formula memorized. Though memorizing Quant formulas isn't the only way to study for the GRE^{®} Quant, memorizing certain frequently-tested math formulas will help you improve your speed on test day. Once you learn these GRE^{®} math formulas, be sure to practice using them! Timed practice will ensure you can answer all the questions giving you a higher chance to ace your test.

**Time allocated for the GRE ^{®} Quant section and knowing your GRE^{®} Quant formulas.**

The Quant section has 40 questions in total which are divided into 2 sections each containing 20 questions and the time allocated for each part is 35 minutes. In total, the GRE^{®} Quant sections take 1 hour 10 minutes. Therefore, knowing your quant formulas and keeping a handy math formula chart for your practice sessions is key.

#### Acing your GRE^{®} Quant Section:
**GRE**^{®} Quant study guide and Quant score range:

Prepping towards acing your GRE^{®} Quant section begins by understanding and breaking it down. You can't truly prepare overnight. It requires discipline, hard work, and focusing on concepts around the GRE^{®} Quant formulas. It is recommended to spend at least two months preparing for your exam.

- Quantitative Reasoning: The quantitative reasoning section of the GRE
^{®} takes into account the students basic mathematical reasoning skills, their understanding of simple math formula concepts, and their ability to apply those skills and GRE^{®} Quant formulas to get to real world solutions. - Composition: The quantitative reasoning section comprises four types of questions:
- Quantitative comparison questions.
- Multiple-choice questions with one answer.
- Multiple-choice questions with one or more answers.
- Numeric entry questions.

The quantitative reasoning section addresses math, with topics including prime numbers, percentages, and absolute value. The section also includes algebraic concepts, along with graphs of functions, quadratic equations, and word problems that must be translated to mathematical equations. The test also includes geometry, with subjects like the Pythagoras theorem, multi-dimensional figures, and parallel and perpendicular lines. Additionally questions on data analysis, ranging from basic descriptive statistics to scatter plots make up part of the GRE^{®} Quants. Each of the two quantitative reasoning sections contain 20 questions. In a nutshell, arithmetic, algebra, geometry, and "data analysis", which means statistics and probability are all being tested in the GRE^{®} Quants.

- Master the math concepts first through an in depth math review.
- Take lots of real GRE
^{®} practice tests-The more questions you successfully solve on your own, the better you get. - Keep a mistake journal and continue to do actual past GRE
^{®} test questions. - Memorize the required GRE
^{®} math formulas or GRE^{®} Quant formulas. - Download a GRE
^{®} calculator app on your phone during practice sessions. An on-screen calculator is available for use at any time during the GRE^{®} quantitative section. Your GRE^{®} calculator can add, subtract, multiply, divide, and square root.

The GRE^{®} Quant section is scored between 130–170, and an average score falls somewhere around 150-152.

**GRE**^{®} Quant study guide and Quant score range:

^{®}Quant study guide and Quant score range:

Prepping towards acing your GRE^{®} Quant section begins by understanding and breaking it down. You can't truly prepare overnight. It requires discipline, hard work, and focusing on concepts around the GRE^{®} Quant formulas. It is recommended to spend at least two months preparing for your exam.

- Quantitative Reasoning: The quantitative reasoning section of the GRE
^{®}takes into account the students basic mathematical reasoning skills, their understanding of simple math formula concepts, and their ability to apply those skills and GRE^{®}Quant formulas to get to real world solutions. - Composition: The quantitative reasoning section comprises four types of questions:
- Quantitative comparison questions.
- Multiple-choice questions with one answer.
- Multiple-choice questions with one or more answers.
- Numeric entry questions.

The quantitative reasoning section addresses math, with topics including prime numbers, percentages, and absolute value. The section also includes algebraic concepts, along with graphs of functions, quadratic equations, and word problems that must be translated to mathematical equations. The test also includes geometry, with subjects like the Pythagoras theorem, multi-dimensional figures, and parallel and perpendicular lines. Additionally questions on data analysis, ranging from basic descriptive statistics to scatter plots make up part of the GRE^{®}Quants. Each of the two quantitative reasoning sections contain 20 questions. In a nutshell, arithmetic, algebra, geometry, and "data analysis", which means statistics and probability are all being tested in the GRE^{®}Quants.

- Master the math concepts first through an in depth math review.
- Take lots of real GRE
^{®}practice tests-The more questions you successfully solve on your own, the better you get. - Keep a mistake journal and continue to do actual past GRE
^{®}test questions. - Memorize the required GRE
^{®}math formulas or GRE^{®}Quant formulas. - Download a GRE
^{®}calculator app on your phone during practice sessions. An on-screen calculator is available for use at any time during the GRE^{®}quantitative section. Your GRE^{®}calculator can add, subtract, multiply, divide, and square root.

The GRE^{®} Quant section is scored between 130–170, and an average score falls somewhere around 150-152.

#### Tips and Strategies on acing your GRE^{®} Quant Section:
It is best advised to take your GRE^{®} at least one year ahead of time. This allows you enough time to retake the exam if required. Listed below are a few tried and tested tips and strategies on how you can plan and study so as to have the best possible chances of acing your GRE^{®} Quant section.

**Know exactly what to expect:** memorize the structure of the exam and the subjects being examined.**Relearn any high school knowledge you forgot:** Many GRE^{®} questions are based on simple concepts you have learned through in high school. By now, you're probably rusty on the basic math formulas and those need to be revised and relearned.**Take practice tests:** It may be hard work and time consuming, but taking practice tests is one of the best ways to prepare you for the test day. It will help you familiarize yourself with the exam format, keeping you more focused on the test questions.**Stay consistent with your preparation:** Make a study plan and stick to it, even if it means simply carving out small chunks of time each day. If you're not taking GRE^{®} study classes, being disciplined about your study routine and knowing your Quant formulas is especially important. Being able to think out of the box and critically is a learned skill, and practice makes perfect.**Prepare for time restraints and learn to manage time:** It will be easier to ace the exam if you can learn to time manage your time and successfully complete the practice tests within the time frame, keeping a few extra minutes to recheck answers or spend more time on tricky questions on the actual test day. Having your GRE^{®} Quant formulas memorized cannot be overemphasized here.

It is best advised to take your GRE^{®} at least one year ahead of time. This allows you enough time to retake the exam if required. Listed below are a few tried and tested tips and strategies on how you can plan and study so as to have the best possible chances of acing your GRE^{®} Quant section.

**Know exactly what to expect:**memorize the structure of the exam and the subjects being examined.**Relearn any high school knowledge you forgot:**Many GRE^{®}questions are based on simple concepts you have learned through in high school. By now, you're probably rusty on the basic math formulas and those need to be revised and relearned.**Take practice tests:**It may be hard work and time consuming, but taking practice tests is one of the best ways to prepare you for the test day. It will help you familiarize yourself with the exam format, keeping you more focused on the test questions.**Stay consistent with your preparation:**Make a study plan and stick to it, even if it means simply carving out small chunks of time each day. If you're not taking GRE^{®}study classes, being disciplined about your study routine and knowing your Quant formulas is especially important. Being able to think out of the box and critically is a learned skill, and practice makes perfect.**Prepare for time restraints and learn to manage time:**It will be easier to ace the exam if you can learn to time manage your time and successfully complete the practice tests within the time frame, keeping a few extra minutes to recheck answers or spend more time on tricky questions on the actual test day. Having your GRE^{®}Quant formulas memorized cannot be overemphasized here.

#### FAQ's:
**Ques 1:** If I memorize all my GRE^{®} Quant formulas, will I get a perfect score?

**Ans 1:** While it is absolutely essential to memorize all the required GRE^{®} Quant formulas, it cannot guarantee a perfect score. These math formula have to be applied in the questions being asked. They can often be worded in a complicated way but can be solved by cutting through the words to figure out what the question's asking, or by using a logical shortcut. The GRE^{®} Quant section testing your ability to think with math skills and that is why the section is called "Quantitative Reasoning". This means that memorizing Quant formulas, reviewing notes, watching math videos are less important than practicing actual real past GRE^{®} test questions by yourself and keeping a math formula chart and then keeping a detailed mistake journal. This will allow you to learn from your previous mistakes and be well prepared for the GRE^{®} test.

**Ques 2:** How much time should I spend per question in the GRE^{®} quantitative section?

**Ans 2:** There are 2 Quant sections. 35 minutes per section is the time allocated and there are 20 questions per section. 1 un-scored section, which can either be Verbal or Quant, and can make up any stage of the GRE^{®} test. Sometimes, this un-scored section is even replaced by an identified “research” topic. It is advisable to attempt answering every question since there is no negative marking for wrong answers. If you don’t know how to answer a question at first it is best not to dwell on it for too long and to move on within the section and come back to it later. However once you have completed a section, you will not be allowed to backtrack. To break it down, in the Quant sections you have about 1 minute and 45 seconds per question.

**Ques 3:** Can I retake my GRE^{®} test if my GRE^{®} Quant score is low/below the standard range?

**Ans 3:** Yes! You can absolutely retake the entire GRE^{®} test up to 5 times in a given year. However, being even more well prepared than the previous time is key to getting a better score. Preparation entails rigorous hours of study practice, knowing your GRE^{®} Quant formulas well, keeping a math formula chart, and additionally consider the cost to retake the test. Retaking the test does not have any negative implications on your application and you can submit your best test score. Even though you may have scored well in other sections as compared to the Quant section, you would need to retake the entire GRE^{®} test again. It is therefore important to plan well ahead and take the first attempt at least one year before so you have enough time to retake the GRE^{®} test if required.

**Ques 1:** If I memorize all my GRE^{®} Quant formulas, will I get a perfect score?

**Ans 1:** While it is absolutely essential to memorize all the required GRE^{®} Quant formulas, it cannot guarantee a perfect score. These math formula have to be applied in the questions being asked. They can often be worded in a complicated way but can be solved by cutting through the words to figure out what the question's asking, or by using a logical shortcut. The GRE^{®} Quant section testing your ability to think with math skills and that is why the section is called "Quantitative Reasoning". This means that memorizing Quant formulas, reviewing notes, watching math videos are less important than practicing actual real past GRE^{®} test questions by yourself and keeping a math formula chart and then keeping a detailed mistake journal. This will allow you to learn from your previous mistakes and be well prepared for the GRE^{®} test.

**Ques 2:** How much time should I spend per question in the GRE^{®} quantitative section?

**Ans 2:** There are 2 Quant sections. 35 minutes per section is the time allocated and there are 20 questions per section. 1 un-scored section, which can either be Verbal or Quant, and can make up any stage of the GRE^{®} test. Sometimes, this un-scored section is even replaced by an identified “research” topic. It is advisable to attempt answering every question since there is no negative marking for wrong answers. If you don’t know how to answer a question at first it is best not to dwell on it for too long and to move on within the section and come back to it later. However once you have completed a section, you will not be allowed to backtrack. To break it down, in the Quant sections you have about 1 minute and 45 seconds per question.

**Ques 3:** Can I retake my GRE^{®} test if my GRE^{®} Quant score is low/below the standard range?

**Ans 3:** Yes! You can absolutely retake the entire GRE^{®} test up to 5 times in a given year. However, being even more well prepared than the previous time is key to getting a better score. Preparation entails rigorous hours of study practice, knowing your GRE^{®} Quant formulas well, keeping a math formula chart, and additionally consider the cost to retake the test. Retaking the test does not have any negative implications on your application and you can submit your best test score. Even though you may have scored well in other sections as compared to the Quant section, you would need to retake the entire GRE^{®} test again. It is therefore important to plan well ahead and take the first attempt at least one year before so you have enough time to retake the GRE^{®} test if required.

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