Gmat Math (Arithmetic)

Front 1

integer

Back 1

any number in the set {. . . −3, −2, −1, 0, 1, 2, 3, . . .}

Front 2

divisor (factor)

Back 2

If x and y are integers and x ≠ 0, x is a divisor (factor) of y provided that y = xn for some integer n. In this case y is also said to be divisible by x or to be a multiple of x. For example, 7 is a divisor or factor of 28 since 28 = 7 × 4, but 8 is not a divisor of 28 since there is no integer n such that 28 = 8n.

Front 3

fraction

Back 3

In a fraction n/d , n is the numerator and d is the denominator. The denominator of a fraction can never be 0, because division by 0 is not defined.

Front 4

equivalent

Back 4

Two fractions are said to be equivalent if they represent the same number. For example, 8/36 and 14/63 are equivalent since they both represent the number 2/9.

Front 5

greatest common divisor

Back 5

In each case, the fraction is reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor (gcd). The gcd of 8 and 36 is 4 and the gcd of 14 and 63 is 7.

Front 6

decimal point

Back 6

In the decimal system, the position of the period or decimal point determines the place value of the digits. For example, the digits in the number 7,654.321 have the following place values: thousands, hundreds, tens, ones or units, tenths, hundredths, thousandths

Front 7

real numbers

Back 7

All real numbers correspond to points on the number line and all points on the number line correspond to real numbers.

Front 8

ratio

Back 8

The ratio of the number a to the number b (b does not equal 0) is a/b. A ratio may be expressed in several ways. For example, the ratio of 2 to 3 can be written as 2 to 3, 2:3, or 2/3.

Front 9

proportion

Back 9

a statement that two ratios are equal ex. 2/3= 4/6=8/12

Front 10

solving proportions

Back 10

One way to solve a proportion involving an unknown is to cross multiply, obtaining a new equality.

Front 11

percent

Back 11

Percent means per hundred or number out of 100. A percent can be represented as a fraction with a denominator of 100, or as a decimal. To find a certain percent of a number, multiply the number by the percent expressed as a decimal or fraction.

Front 12

powers and roots

Back 12

When a number k is to be used n times as a factor in a product, it can be expressed as , which means the nth power of k. An nth root of a number k is a number that, when raised to the nth power, is equal to k.

Front 13

Average or (arithmetic) mean

Back 13

One of the most common statistical measures of the center of a list of data is the average, or (arithmetic) mean. The average of n numbers is defined as the sum of the n numbers divided by n.

Front 14

Median

Back 14

To calculate the median of n numbers, first order the numbers from least to greatest; if n is odd, the median is defined as the middle number, while if n is even, the median is defined as the average of the two middle numbers. For the data 6, 4, 7, 10, 4, the numbers, in order, are 4, 4, 6, 7, 10, and the median is 6, the middle number. The median of a set of data can be less than, equal to, or greater than the mean. Note that for a large set of data (for example, the salaries of 800 company employees), it is often true that about half of the data are less than the median and about half of the data are greater than the median; but this is not always the case.

Front 15

Mode

Back 15

The mode of a list of numbers is the number that occurs most frequently in the list. For example, the mode of 1, 3, 6, 4, 3, 5 is 3. A list of numbers may have more than one mode. For example, the list 1, 2, 3, 3, 3, 5, 7, 10, 10, 10, 20 has two modes, 3 and 10.

Front 16

Range

Back 16

The simplest measure of dispersion is the range, which is defined as the greatest value in the numerical data minus the least value. For example, the range of 11, 10, 5, 13, 21 is 21 − 5 = 16. Note how the range depends on only two values in the data.

Front 17

Standard deviation

Back 17

One of the most common measures of dispersion is the standard deviation. Generally speaking, the greater the data are spread away from the mean, the greater the standard deviation. The standard deviation of n numbers can be calculated as follows: (1) find the arithmetic mean; (2) find the differences between the mean and each of the n numbers; (3) square each of the differences; (4) find the average of the squared differences; and (5) take the nonnegative square root of this average.

Front 18

Frequency Distribution

Back 18

useful for data that have values occurring with varying frequencies. For example, the 20 numbers shown on the left below are displayed on the right in a frequency distribution by listing each different value x and the frequency f with which x occurs.

Front 19

set

Back 19

In mathematics a set is a collection of numbers or other objects. The objects are called the elements of the set.

Front 20

counting methods

Back 20

If a first object may be chosen in m ways and a second object may be chosen in n ways, then there are mn ways of choosing both objects.

As an example, suppose the objects are items on a menu. If a meal consists of one entree and one dessert and there are 5 entrees and 3 desserts on the menu, then 5 x 3 = 15 different meals can be ordered from the menu.

Front 21

discrete probability

Back 21

Discrete probability is concerned with experiments that have a finite number of outcomes. Given such an experiment, an event is a particular set of outcomes. For example, rolling a number cube with faces numbered 1 through 6 (similar to a 6-sided die) is an experiment with 6 possible outcomes: 1, 2, 3, 4, 5, or 6. One event in this experiment is that the outcome is 4, denoted {4}; another event is that the outcome is an odd number: {1, 3, 5}.