Let’s be honest—when you hear the words Arithmetic, Algebra or Geometry, you might feel like you’ve been thrown back into high school math class. But here’s the deal: the GMAT Quant section isn’t about complex math. It’s about logic, speed, and strategy. If you’ve got the basics down and a game plan in hand, this section can actually be kind of fun.
So grab your mental calculator (and maybe a snack), because we’re breaking down GMAT Quant—focusing on its three core areas: Arithmetic, Algebra, and Geometry—in the chillest way possible.
Arithmetic
Number Terminology and Properties
Integers are the numbers that you see on a number line. Positive integers are integers that are larger than zero. Negative integers are smaller than zero.
The result in an addition problem is called the sum. The result in a subtraction problem is called the difference.
Adding integers often involves the use of certain properties. The associative property of addition states that when you add a series of numbers, you can regroup the numbers any way you’d like:
The commutative property of addition states that when you add numbers, order doesn’t matter:
The result in a multiplication problem is called a product. The result in a division problem is called a quotient.
The product of two integers with the same sign (+ and + or – and –) is always positive. The product of two integers with different signs (+ and –) is always negative. For example:
Likewise, the quotient of two integers with the same sign (+ and + or – and –) is always positive. The quotient of two integers with different signs (+ and –) is always negative. For example:
When multiplying integers, you will often use the same properties you used with the addition of integers. The associative property of multiplication states that when you are multiplying a series of numbers, you can regroup the numbers any way you’d like:
The commutative property of multiplication states that when you multiply integers, order doesn’t matter:
The Order of Operations
To remember the order of operations with numerical expressions, you can use a mnemonic, the word PEMDAS.
P Do operations inside parentheses.
E Evaluate terms with exponents.
M/D Do multiplication and division in order from left to right.
A/S Add and subtract terms in order from left to right.
Absolute Value
If you look at a point on a number line, measure its distance from zero, and consider that value as positive, you have just found the number’s absolute value. The absolute value of 3, written as |3|, is 3. The absolute value of –3, written as |–3|, is also 3.
When using the order of operations, the absolute value symbol is treated at the same level as parentheses. Try this out:
First, evaluate the expression inside the absolute value symbol:
Now, evaluate the absolute value:
Factoring Numbers
A number is a factor of a second number if it can be divided into the second number without leaving a remainder. Let’s look at the factors of 12: 1, 2, 3, 4, 6, and 12. The number 12 can be divided by each of these numbers without leaving a remainder. 
If a number is a factor of a given number, the given number is divisible by the factor. A few simple rules will help you quickly determine divisibility and factor problems.
■ An integer is divisible by 2 if its ones digit is divisible by 2.
■ An integer is divisible by 3 if the sum of its digits is divisible by 3.
■ An integer is divisible by 4 if its last two digits form a number divisible by 4.
■ An integer is divisible by 5 if its ones digit is either 0 or 5.
■ An integer is divisible by 6 if it is divisible by both 2 and 3.
■ An integer is divisible by 9 if the sum of its digits is divisible by 9.
■ An integer is divisible by 10 if its ones digit is 0.
When an integer greater than 1 has exactly two factors (1 and itself), it is a prime number. Examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Note that the opposite (negative version) of these numbers are also prime. For example, the factors of –23 are 1, –23, –1, and 23. Thus, –23 is prime because it has exactly two positive factors: 1 and 23.
When an integer greater than 1 has more than two factors, it is called a composite number. The numbers 0 and 1 are neither prime nor composite. Zero has an infinite number of factors. The number 1, on the other hand, has one factor— itself. When a number is expressed as a product of factors that are all prime, that expression is called the prime factorization of the number.
The greatest of all the factors common to two or more numbers is called the greatest common factor (GCF). A multiple of a number is the product of that number and any whole number. The least of the common multiples of two or more numbers, excluding 0, is called the least common multiple (LCM)
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Fractions
A proper fraction has a numerator that is smaller than its denominator:
Improper fractions have numerators that are bigger than their denominators:
A mixed number is a number that is represented as a whole number and a proper fraction. The following are all mixed numbers:
To change a mixed number into an improper fraction, follow these steps:
1. Multiply the denominator of the fraction by the whole number.
2. Add that sum to the numerator.
3. Put that amount over the original denominator.
A fraction can be considered negative if either its numerator or denominator is negative. When a fraction receives any type of sign, particularly the negative sign, it can appear in three different places—in the numerator, denominator, or right before the fraction.
To add or subtract fractions, the denominators have to match. To add fractions with like denominators, just add the numerators. To subtract fractions with like denominators, just subtract the numerators.
To find the sum or difference of two fractions with unlike denominators, rename the fractions with a common denominator. Then, add or subtract and simplify your answer.
To multiply fractions, multiply the numerators, then multiply the denominators, and finally simplify if possible and necessary.
To divide one fraction by another, you need to flip the second fraction and then multiply the fractions. This flip of the second fraction is called the multiplicative inverse of a number or the reciprocal.
Sometimes, you may need to find the greatest fractions or put fractions in order from least to greatest or from greatest to least. To do this, you should first give all the fractions a common denominator.
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Decimals
The decimal system is a way to name numbers based on the powers of 10. The numbers to the right of the decimal point are fractional equivalents with denominators that are powers of ten. For example,
Decimal numbers are easy to compare and order, when you remember that the place value has meaning. In mathematics, 2.4 is the same number as 2.400 because both numbers represent two and four tenths. A whole number is understood to have a decimal point to the right of the number. For example, 12 = 12. = 12.0 = 12.000. Each expression represents twelve with no remainder. To compare decimals, it is best to change each decimal into an equivalent decimal with the same number of decimal places.
To add or subtract decimal values, line up the decimal points and add or subtract.
When you are multiplying decimals, first you multiply in the usual fashion, and then count over the proper number of places. This is done by counting how many places are to the right of the decimal point in each number you are multiplying.
When you are dividing decimals, you move the decimal point of the dividend and divisor the same number of places
Mean, Median, Mode, and Range
When you are dealing with sets of numbers, there are certain measures used to describe the set as a whole. These are called measures of central tendency, and they include mean, median, mode, and range.
Mean is another way of saying average. To find the average, you total up all the values and then divide by the number of values.
When you are considering a list of values in order (from smallest to largest), the median is the middle value. If there are two middle values, you just take their average.
In a list of values, the mode is the number that occurs most often. If two numbers occur most often, you have two modes. This is called bimodal.
The range indicates how close together the given values are to one another in a set of data. To find the range, determine the difference between the largest and the smallest values in the set of data. Subtract the smallest value from the largest value in the set.
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Probability
Probability is the mathematics of chance. It is a way of calculating how likely it is that something will happen. It is expressed as the following ratio:
The term favorable outcomes refers to the events you want to occur. Total outcomes refers to all the possible events that could occur.
A probability of zero (0) means that the event cannot occur. A probability of 50% is said to be random or chance. A probability of 100% or 1.00 means it is certain to occur. Probabilities can be written in different ways:
Percents
When you see a number followed by the percent symbol, think of the percent as a ratio comparing that number to 100. Percents can be expressed in two different ways:
Recall that the word of tells you to multiply. When you take the percent of a number, you should multiply.
When you take the percent of a percent, all you need to do is multiply:
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Algebra
Sequences
Arithmetic sequences grow by adding or subtracting a constant number to each term. For example, look at the following series: 
Notice that each term is four more than the term that comes before it. This is an example of an arithmetic series with a common difference of 4. What will the next term be? To solve, add 4 to 21: 21 + 4 = 25
Thus, the next term will be 25. Geometric sequences grow by multiplying each term by a constant number to get the next term. For example, look at the following series:
Note that each term is five times the prior term. This is an example of a geometric series with a common ratio of 5. What will the next term be? Multiply 625 by 5:
Thus, the next term will be 3,125.
Exponents
An exponent tells you how many times the base is used as a factor. In the expression 43, the three is the exponent and the four is the base. The expression 43 shows that four is a factor of three times. That means four times four times four.
When you are multiplying two identical bases, you add the exponents instead of multiplying them. For example: 
Roots
You know you need to take the square root of a number when you see a radical sign, which looks like following.
To find the square root of a number, ask yourself: What number when squared will equal the number under the radical sign?
Expressions
In algebra, letters are often used to represent numbers. These letters are called variables. The numbers in front of the variable or variables are called coefficients. Remember:
■ A coefficient is a factor in an algebraic term, as are the variable or variables in the term.
■ Like terms can have different coefficients, but the configuration of the variables must be the same for the terms to be alike. For example, 3x and –4x are like terms, but they are different from 7ax.
Mathematical expressions, like numbers, can be named in different ways. For example, here are three ways to write the same expression:
x + –3
x + (–3)
x – 3
For purposes of combining like terms, a variable by itself is understood to mean one of that terms:
n = +1n
A term without a sign in front of it is considered to be positive. To simplify expressions, clear any parentheses, combine like terms by adding coefficients, and then combine the constants. When you are asked to evaluate an algebraic expression, you substitute a number in place of a variable (letter) and then simplify the expression.
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Equations
An equation is a mathematical tool that helps people solve many real-life problems. The word equation means two equal expressions. These expressions could be numbers, such as 6 = 5 + 1, or variables, such as D = rt.
What does it mean to solve an equation? When you find the value of the variable, you have solved the equation. For example, you have solved the equation 2x = 10 once you know the value of x.
Here’s the basic rule for solving equations: When you do something to one side of an equation, you must do the same thing to the other side of the equation. You’ll know you have solved an equation once the variable is alone (isolated) on one side of the equation and the variable is positive. In the example –x = 5, 5 is not the answer because the x variable is negative. Remember that –x is the same as –1x. To make the variable positive, divide both sides by –1. Therefore, x = –5
Formulas
Formulas are special equations that show relationships between quantities. For example, you have probably worked with the formula A = lw. This formula tells you to multiply the length times the width of a rectangle to find its area. The formula D = rt tells you to multiply the rate by the time to find the distance traveled.
When you substitute the information you know into a formula, you can use that to find the information you don’t know. For example, if you travel 55 miles per hour (mph) for 3 hours, how far would you travel? Substitute what you know into the equation. Then, solve the equation for the variable you don’t know.
This technique works for any formula, even if the formula is very complex.
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Inequalities
An inequality is two numbers or expressions that are connected with an inequality symbol. The inequality symbols are
Here are some examples of inequalities: 
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