Gmat Math (Official Gmat Prep)

Front 1

Integer

Back 1

Number in the set {...-3,-2,-1,0,1,2,3...}

Front 2

Divisors, Factors, Multiples

Back 2

X is a DIVISOR or FACTOR of Y given Y=XN for some integer N. Assume X and Y are integers and X is not equal to zero. Y is thus a MULTIPLE of X and is divisible by X

Front 3

Quotients and Remainders

Back 3

For positive INTEGERS X and Y, there exist unique integers Q and R (called the quotient and remainder, respectively, such that Y=XQ+R and 0<=R<X.

Y divisible by X only if R=0.

When smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller integer.

Front 4

Prime numbers

Back 4

A POSITIVE INTEGER that has exactly two different positive divisors: 1 and itself

Front 5

Consecutive Integers Formulas

Back 5

N, N+1, N+2, N+3,... where N is an integer

Front 6

Consecutive Even Integers Formulas

Back 6

2N, 2N+2, 2N+4, 2N+6,... where N is an integer

Front 7

Consecutive Odd Integers Formulas

Back 7

2N+1, 2N+3, 2N+5,... where N is an integer

Front 8

Equivalent Fractions

Back 8

Represent the same number, one reduces to the other, or both reduce to the same fraction

Front 9

Greatest Common Factor/Divisor

Back 9

The largest number that evenly divides into each number within a set; to reduce a fraction to lowest terms, both numerator and denominator must be divided by their GCF/D

Front 10

Least Common Multiple

Back 10

The lowest number that all numbers in a set are a factor of. To simplify addition with fractions, choose the LCM of the denominators.

Front 11

Mixed Number

Back 11

A whole number added to a fraction; may be converted to a fraction by multiplying the whole number by the denominator, adding the result to the numerator, and then putting the total over the original denominator.

Front 12

Decimal Properties Examples

Back 12

0.321= (3/10) + (2/100) + (1/1000)= 321/1000
0.0321= (0/10) + (3/100) + (2/1000) + (1/10000)= 321/10000
1.56= 1 + (5/10) + (6/100)= 156/100

Front 13

Real Numbers

Back 13

Correspond to all points on the number line, includes both rational and irrational

Front 14

Absolute Value

Back 14

The distance between a number and zero on the number line

Front 15

Absolute Value Sum Property

Back 15

ABS(X + Y) <= ABS(X) + ABS(Y)

Front 16

Proportions

Back 16

A statement that two ratios are equal

Front 17

Percents greater than 100%

Back 17

Percents greater than 100% are represented by numbers greater than 1:
300%=300/100=3
250% of 80=2.50*80=200

Front 18

Exponents

Back 18

When a number k is to be used n times as a factor in a product, it can be expressed as k^n, which means the nth power of k

Front 19

Roots

Back 19

An nth root of a number k is a number that, when raised to the nth power is equal to k.

Front 20

Raising number to an exponent

Back 20

Squaring a number greater than 1 or raising it to a higher power results in a larger number; squaring a number between 0 and 1 or raising it to a number greater than 1 results in a smaller number

Front 21

Square Roots

Back 21

Every positive number has two square roots, one positive and one negative, but SQRT(N) denotes a positive number whose square is N

Front 22

Cube Roots

Back 22

Every real number has exactly one real cube root

Front 23

Unions and Intersections

Back 23

The union of A and B is the set of all elements that are in A or in B or in Both: A U B.

The intersection of A and B is the set of all elements that are in both A and B: A (UPSIDE DOWN U) B.

Two sets with no common elements are disjoint or mutually exclusive

Front 24

Total number of elements in a union

Back 24

ABS(S U T)= ABS(S) + ABS(T) - ABS(S "UPSIDE DOWN U" T)

Where S and T represent the numbers of elements in sets S and T. This formula removes the elements of the intersection so that these elements aren't counted twice

Front 25

Standard Deviation

Back 25

STND DEVO= SQRT((1/N)*EE((x-AVG)^2))

Front 26

0!

Back 26

0!=1!=1

Front 27

Principle of Multiplication in Counting Methods

Back 27

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

Front 28

Permutations

Back 28

A method of counting the number of ways that a set of objects can be ORDERED

If a set of N objects is to be ordered from 1st to Nth, there are N choices for the 1st object, N-1 for the 2nd object, N-2 for the 3rd object and so on.

Via the multiplication principle, the number of ways of ordering the n objects is :
n(n-1)(n-2)(n-3)...(3)(2)(1)= n!

The permutations of a set are the different orders of the sets

Front 29

Combinations

Back 29

Used when the order of selection is not relevant. This means that (A,K) is the same as (K,A).

The formula is:

(n choose k)= n!/((k!(n-k)!)

where n is a set of objects from which a complete selection of k objects is to be made without regard to order.

Front 30

Discrete Probability

Back 30

Concerned with experiments that have a finite number of outcomes. Given such an experiment, an event is a particular set of outcomes.

Discrete variables are either a finite number of values or an infinite sequence of values.

Front 31

Probability

Back 31

The probability that an event E occurs, denoted by P(E) is a number between 0 and 1 inclusive, If E has no outcomes, then E is impossible and P(E)=0; if E is the set of all possible outcomesof the experiment, then E is certain to occur and P(E)=1. Otherwise, E is possible but uncertain, and 0< P(E) <1. If F is a subset of E, then P(F) < P(E).

For experiments where all of the individual outcomes are equally likely, the probability of an event E is:

P(E) = (# of outcomes in E) / (# of possible outcomes)

Front 32

Probabilities for Combined Events

Back 32

Given an experiment with events E and F:
"not E" is the set of outcomes that are not outcomes in E
"E or F" is "E U F"
"E and F" is "E (upside down U) F"

The probability that E does not occur:
P(not E)=1-P(E)

The probability that E or F occurs:
P(E or F)= P(E) + P(F) - P(E and F)
<<See total number of elements in a union>>

Front 33

Mutually Exclusive Events and Probability

Back 33

P(E or F)= P(E) + P(F)

Mutually exclusive exists when there is no intersection of sets E and F

Front 34

Independent Events and Probability

Back 34

Two events are independent if the occurrence of either event does not alter the probability that the other event occurs

The following rule holds in this case:
P(E and F)= P(E)P(F)

Front 35

Domain of a Function

Back 35

The set of all allowable inputs for a function. If there is a variable in the denominator, and example of an "unallowable" variable would be a number that makes the denominator equal 0. The domain may be all real numbers.

Front 36

Triangle Properties

Back 36

The sum of any two sides of a triangle is greater than the length of the third side

Front 37

45-45-90 Triangles

Back 37

A right isosceles triangle with angle measurements 45, 45, and 90, and the lengths of the sides are in the ratio of 1:1:SQRT(2).

Front 38

30-60-90 Triangles

Back 38

A triangle with angle measurements of 30, 60, and 90, and the length of the sides are in the ratio of 1:SQRT(3):2

Front 39

Popular Pythagorean Triples

Back 39

( 3, 4, 5 ) ( 5, 12, 13) ( 8, 15, 17) ( 7, 24, 25)
(20, 21, 29) (12, 35, 37) ( 9, 40, 41) (28, 45, 53)
(11, 60, 61) (16, 63, 65) (33, 56, 65) (48, 55, 73)
(13, 84, 85) (36, 77, 85) (39, 80, 89) (65, 72, 97)

Front 40

Parallelogram

Back 40

A four-sided polygon (or quadrilateral) in which both pairs of opposite sides are parallel, the opposite sides are the same length, and the diagonals bisect each other. The area is (length of altitude) x (length of the base)

Front 41

Inscribed vs. Circumscribed and Triangles

Back 41

Inscribed: each vertex of a polygon lies on a circle, the polygon is inscribed in the circle (polygon inside)

Circumscribed: each side of a polygon is tangent to a circle, the polygon is circumscribed about the circle (polygon outside)

Inscribed: inside; Circumscribed: outside

If a triangle is inscribed in a circle so that one of its sides is a diameter of the circle, then then triangle is a right triangle

Front 42

X (Y) Intercept

Back 42

X (Y) intercept is found by setting Y (X) equal to 0 in the slope intercept formula

Front 43

Point Slope Formula

Back 43

y-y=m(x-x)

Front 44

Quadratic polynomial functions

Back 44

Graphed as a parabola; because the x variable is squared, there will be 2 x intercepts found by setting y=0.

For any function f, the x-intercepts are the solutions of the equation f(x)=0 and the y-int is the value of f(0).