GMAT Math
If you are planning on applying to and attending a graduate business school, you are probably familiar with the vast majority of the math concepts that you will see on the Quantitative section of the GMAT. In fact, if you went to junior high school in the United States, you have probably studied this kind of math at some time in the past. The Quantitative section of the GMAT largely tests your knowledge of arithmetic (approx. 50 percent of all questions), algebra (25 percent or so), and geometry (generally less than 15 percent). There are a few more specialized concepts that make up the final 10 percent or so but you can prepare for them as well with targeted study on specific topics. Mastering the less-difficult questions for mastery will take you a long way toward acing the GMAT.
In short - the math content of the GMAT is not as difficult as you may think. You’ll probably find that a review of the main question topics and formats will go a long way toward increasing your comfort level with these sections. Certain types of questions come up on every test. Since the makers of the GMAT strive to standardize scoring from one test to the next, you’ll see the same question types expressed the same way each time. Becoming familiar with the predictable wording and phrasing of these question types will put you at a significant advantage over those who have to figure everything out during the test.
Here are some question topics that you can expect from the Quantitative section of the GMAT, as well as some brief reminders that should help you brush up on the basic math skills that you’ll see on test day:
• Adding, subtracting, multiplying, and dividing
- Whole numbers
- Fractions
- Positive/negative numbers
• Converting fractions to decimals and decimals to fractions
• Forming and solving basic algebraic expressions
• Calculating a percentage value using the percentage formula (Part = percent × whole).
- Example: What is 50 percent of 40?
- Setup: Part = × 40 = 20
• Calculating percent change. × 100. If a question asks by what percent a value increased, put the positive difference of the two values in the numerator, and the smaller of the two values in the denominator. If a question asks by what percent a value decreased, put the positive difference of the two values in the numerator, and the larger of the two values in the denominator.
• Calculating a simple average. Average = sum of terms / number of terms
• Calculating certain measures for shapes:
- Rectangles/squares
area = length × width
perimeter = 2 × (length + width)
- Triangles
area = ½ × (base × height)
perimeter = side A + side B + side C
- Circles
area = πr²
circumference = πd = 2πr
• The remainder will consist of more difficult questions on topics such as simple probabilities and standard deviations. (Review these topics only if you have extra time – remember: these make up less than 10 percent of the total questions)
Let’s look at some of the most effective tools used to handle the types of math questions that you will encounter on the GMAT.
You probably learned these concepts back in school, but hey, that was a long time ago! The following is a quick recap of the terms you need to know for GMAT Math. If you have trouble with any of these terms, write them down in your notebook so you can review them right before your test.
Integer - also known as a whole number. It may be positive or negative but it must be whole. 0 is considered an even integer.
A Prime Number (or a Prime) is a number that can only be divided by itself and the number 1. The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Note that 1 is not prime.
A multiple is the result of multiplication. 12 is a multiple of 3. Every number is a multiple of itself.
A factor is any number that can be divided into another and will give an integer result. 3 is a factor of 12. Every number is a factor of itself.
An Exponent is also known as an index or power. It is written as a small number to the right and above the base number, and it tells you how many times the base number is to be multiplied by itself. For example 52 = 5 × 5 = 25.
A Numerator is the number in a fraction that lies above the divide line.
A Denominator is the number in a fraction that lies below the divide line.
To Reduce a Fraction means to reduce it to its lowest terms by factoring both the numerator and denominator with their common factors. For example 6/63 can be reduced to its lowest term by dividing both the numerator and denominator by their common factor, 3. So 6 divided by 3 = 2 and 63 divided by 3 = 21. The fraction is reduced to 2/21 .
To Cancel is to eliminate a number, quantity, or term from both the numerator and denominator of a fraction, or from opposite sides of an equation, because they are common and equal.
A Variable is a lettered term. Commonly expressed as x, y and z. A variable can change while a numbered term is constant. (In the example of 3x, x is a variable but 3 must remain constant).
Reciprocals are two numbers that when multiplied together equal 1. Most reciprocals on the GMAT can be found by inverting the fraction (switching the numerator and the denominator upside down). 3/4 is the reciprocal of 4/3 .
The Mean, also known as average, of a set of numbers is calculated by adding up the set, and dividing that sum by the number of members in the set. With the set 4, 10, 16, the mean would be calculated with the equation (4+10+16)/3 = 10.
The Median of a set is the middle value for the set. If the numbers are placed in order, the middle number represents the median. If there two middle numbers (in an even number of data points), taking the average of the two middle numbers represents a median value.
The Mode is the number that occurs most often in a set of data. It is possible to have more than one mode in a set of data, although bimodal sets are generally not seen on the GMAT.
The Standard Deviation is a statistic that tells you how tightly, in a set of data, various examples are clustered around the mean. A small standard deviation would mean that the examples are closely bunched together. If they are spread out, then the standard deviation is large.
A Polynomial expression is made up of constants (numbers), variables (letters) and exponents, which are combined using addition, subtraction and multiplication signs. It has one or more summed terms. An example would be 2x -7x + 3, or 4yz + xy - 3.
A Binomial is an expression that consists of two terms, such as 2x + 2z
A Vertex is a corner or a point where lines meet. The plural form of vertex is Vertices. Triangles have 3 vertices and quadrilaterals have 4.
An Isosceles Triangle is a triangle which has two sides of equal length.
A Hypotenuse is the longest side of any right angled triangle and faces opposite the right angle.
The Pythagorean Theorem (also known as Pythagoras' Theorem)
In any right angled triangle, the length of the sides follow the following equation:
a2 + b2 = c2
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
An Operation is an action or procedure that changes the value or create a new value from one or more values. Addition, Subtraction, Multiplication, Division are basic operations.
A Product is the result of a multiplication.
A Quotient is the answer to a division problem or equation. The quotient of 20 ÷ 5 is 4.
A Rational number is a number that can be written as a simple fraction (i.e. as a ratio). It can be an integer, a terminating decimal, or a repeating decimal.
An Irrational number is a number that cannot be written as a ratio or fraction. An example of this is Pi. π = 3.1415926535897932 (etc). Pi cannot be written as a simple (accurate) fraction or ratio. Rational and irrational numbers are not generally tested on the GMAT.
A Real number is a number between positive and negative infinity without imaginary component, and it is either a Rational number or an Irrational number. The GMAT does not test imaginary numbers.