gmat

sum of 1st n terms in arithmetic sequence

n/2(asub1 + asubn)

arithmetic sequence

asubn = asub1 + (n-1)d

geometric sequence

asubn = asub1 * r^(n-1)

trick for sum of consecutive terms in a non arithmetic or geometric sequence

look for cancelling terms out

cases where a number is not in the domain

numbers that make denom of fraction = 0 or negative numbers with even index root

rules for range

sqrtx + b or x^n + b where n is positive even int : >= b

x^n + b where n is positive odd int or ax + b: all real numbers

otherwise find min, max, out of bounds. does min or max approach zero?

max and min of a quadratic equation

if a > 0 there is no max, min is -b/2a

if a < 0 no min, max is -b/2a

perpendicular slopes

negative reciprocals

distance between points formula

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

midpoint formula

M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

must/can’t choose in combinatorics word problem

can’t pick - remove from big group

must pick - remove from big and small group

how to solve for total number of items if you have probability of choosing some of them

set up a quadratic ex. prob choosing 1 red = r/4, second red = (r-1)/3

counting triangles

combination of ways to pick 3, if there are colinear points subtract the number of ways to pick 3 on a line

permutation

n!/(n-k)!

arranging indistinguishable items

n!/factorial of amount of each in each group

circular arrangement

(n-1)! - there are n! ways to arrange them in a line

formula for combination problem where you are arranging people but g people are stuck together

(n-g+1)! * g!

pathway checkpoint question

multiply number of ways to pass through each checkpoint

how many ways to get from corner to corner in a grid

how many ways can you reorder the letters

handshake formula n = total entities each connected to k other entities

n*k/2

how does SD change if you multiply all numbers by x

SD*x

finding min and max value of a var given an average between it and another number. ex. p over 5 q over 7, avg is 20 find max of p

(p+q)/2 = 20. minimize q. (5+p)/2 = 20. solve for p

medians odd and even amount of terms

odd = n+1/2 term even is average of n/2 and n+2/2 terms

sum of the reciprocals of consecutive ints

within a range of smallest number * # of fractions to largest

sum of N numbers given the average

N * avg

avg of evenly spaced set

high + low / 2

number of ints in evenly spaced set inclusive: consecutive, consec even/odd numbers, consecutive multiples

high-low + 1, (high - low )/ 2 + 1, (high - low)/number they are a multiple of + 1

number of multiples of a or b in a set

a: (highest multiple - lowest multiple)/a + 1 - this is just the way of counting how many consecutive multiples in a set. do same with b. then subtract answer for LCM of a and b

a is what percent greater than 50?

a = 50 + \left(50\times\frac{x}{100}\right)

percent profit

profit/cost * 100

50 reduced by x percent

50 * (1-x/100)