GRE Quant Section
how to find the points of intersection between two functions in the coordinate plane
set them equal to each other and solve
how to factor a polynomial
(x ) (x ) fill in the missing term - product of the missing terms is the last term in the original polynomial, the sum will be the coefficient of the second term
midpoint formula
(x1 + x2/2, y1+y2/2)
how to find least common multiple
1. determine prime factorization of each integer 2. write out each prime number the maximum number of times that it appears in any one of the prime factorizations 3. multiply those prime numbers together to get the least common multiple of the original integers ex: 6 and 8 6 = (2)(3) 8 = (2)(2)(2) LCM = (2)(2)(2)(3) = 24
"if digits of an integer are reversed and the resulting number is added to the original x the sum is 7777. what is the smallest possible value of x?"
1. must be four digit number bc no two three digits add up to the answer 2. find a small and a large - smallest must begin with 1 1BCD+DCB1 = 7777 3. for the sum to end in 7, D must be 6 1BC6+6CB1 = 7777 4. smallest possible value of B would be zero 10C6+6C01=7777 5. do the math, C must be 7 ---> 1076 is the smallest possible value of x
how to answer a question like "what is the largest 4 digit multiple of 71"
1. start with largest 4 digit number (9999) 2. divide it by 71 3. 9999 - remainder of that division = the largest 4 digit multiple (also it's just the answer to the division - 1)
first ten prime numbers
2 3 5 7 11 13 17 19 23 29
two common pythagorean triples
3 4 5 5 12 13
what are the side engths of a 30 60 90 triangle
30 --> x 60 --> x*sqrt(3) 90 --> 2x
if there is a 5:7 ratio of two things, what is the fractional amount of things in the 5 category
5/12
how to find the number of elements in the union of two sets
A U B = A + B - A upside down U b so you dont count the ones that show up in both sets twice
compound interest formula
A=P(1+r/n)^nt money is reinvested - principal grows after every interest payment is received, so if money is compounded annually its every year
(sqrt(3)+3sqrt(27))(2sqrt(3)-sqrt(27)) what method do you use for this multiplication
FOIL
simple interest formula
I=prt (interest = principal x rate x time) principal of 100 yields 20% interest per year. because 20% of 100 is 20, after three years the investor will have 3 years of interest (60) plus the principal --> 160
how to convert quartile to percentile
Q1 is same value as 25th percentile Q2 is same value as 50th percentile Q3 is the same value as 75th percentile
difference of two squares
Two perfect squares separated by a subtraction sign ex: 9x^2 - 1
when you have two different rates and want to find the ultimate amount that the combined rates will accomplish what do you do
add the rates (300/hr + 200/hr = 500/hr)
for finding the largest prime factor of something divisible by 10...
always divide by 10 to 2 and 5 and go from there
area of a sector formula
angle/360 * (area of circle)
arc length formula
angle/360 * circumference
how to determine quartiles
arrange terms in data set in numberical order from least to greatest subdivide the set into two halves with an equal number of terms median of lower half is the first quartile (Q1) median of the upper half is the third quartile(Q3) median of entire set is Q2
how to find greatest common factor
break down both integers into their prime factorizations multiply all of the prime factors they have in common ex: 36 and 48 36 = (2)(2)(3)(3) 48 = (2)(2)(2)(2)(3) GCF = 2*2*3 = 12
permutations
combination but order matters
Ratio of X to Y is 5:4. Ratio of Y to Z is 1:2. What is the ratio of x to z?
combine x:y and y:z ratio --> x:y:z ratio --> multiply the second ratio by 4 so y to z ratio is 4:8 5:4:8 --> ratio x to z is 5:8
what to do in a problem that has a mixture of exponents and radicals
convert each radical into an exponential term, then factor out using the lowest number to find a common base
what to do when you have a decimal and a radical or decimal and exponent?
convert the decimal to a fraction !!!
interquartile range
difference between third and first quartile values Q3-Q1
range
distance between the greatest and least values in a group of data point
how to find total numbers of combinations from multiple groups
do the combination formula and then multiply he results together
how to calculate standard deviation
find mean determine difference between mean and each value in the group square each difference find the mean of the squared differences take non negative sqrt of this mean
the reciprocal of a fraction between 0 and 1 is ____ than both the original fraction and 1
greater
how tto interpret a normal distribution
greater spread of data around average, wider curve more tightly values are clustered around the mean, more narrow curve mean median and mode are always equal normal distributions are more dense in the center, less dense at tails prob of random selected value falling somewhere under the curve of a normal distribution is 100% (1) 68% is within one SD, 95% is within 2 SDs of the mean
the square of any fraction between 0 an -1 is ____ than the original fraction
greater than
how to determine if an integer is divisible by 6
if it is divisible by both 2 and 3
how to determine if an integer is divisible by 3
if its digits add up to a multiple of 3
how to determine if an integer is divisible by 9
if its digits add up to a multiple of 9
how to determine if an integer is divisible by 2
if its last digit is divisible by 2
how to determine if an integer is divisible by 4
if the last 2 digits are a multiple of 4
how to determine if an integer is divisible by 5
if the last digit is a zero or a 5
difference between sets and lists
in sets, there are no repeats in lists, the order of the elements matters and duplicate members can be include
the reciprocal of a fraction between -1 and 0 is ___ than both the original fraction and -1
less than
the square of a fraction between 0 and 1 is _____ than the original fraction
less than
median of a list of terms with an even number of values
median is the average of the two middle
median of a list of terms with an odd number of values
median is the middle number
how to do prime factorization
method 1: work way up through prime numbers starting with two method 2: figure out one pair of factors, determine their factors, continuing until you only have prime numbers (these will be the prime fctorization) - tree method
probability of multiple independent events
multiply probabilities
negative fractions raised to an odd power are ____
negative
combination formula
number items in whole group = n number of items in subgroup = k n!/k!(n-k)!
rules for odds and evens
odd + odd = even even + even = even odd + even = odd odd x odd = odd even x even = even odd x even = even
triangle inequality theorem
one side is greater than the positive difference of the two other sides, and it is less than the sum of the other two sides ex: 11-5<y-4<11+5
what is a discount in percent word problems
original price minus reduced price percent discount = discount / original price * 100%
how to determine the percentage from the part and the whole
part/whole * 100%
formula for when the GRE tests percent decrease
percent decrease = decrease`(100%)/original
formula for when the GRE tests percent increase
percent increase = increase(100%)/original
if a question just has percents and you have to determine an increase or decrease, what do you do
pick a number value for the original price of the stock - pick $100 or something 100 because this makes percents easier
negative fractions raised to an even power are _____
positive
if you multiply or divide an inequality by a negative number, you have to _______
reverse the direction of the inequality sign
union of two sets
riht side up u all the elements that are elements of either or both sets
what is profit in percent word problems
sellers price minus cost to seller percent of selling price that is profit = profit/selling price (100%)
example of a disguised remainder problem
slats of a fence are three colors in a fixed order, then asked "first slat is red, what color is the 301st" --> 3 goes into 300 evenly, the whole pattern finishes on 300th and the 301st must be red also
what is the principal in interest problems
sum of money invested
mode
term that appears most frequently in a set of numbers
intersection of two sets
the upside down u all elements that are contained in bot sets
how to answer a question like "how many two digit multiples of 6 are multiples of 15"
this is an LCM problem 1. find the LCM 2. any multiples of the LCM are also common multiples, find all of the ones that are two digit
what are the side lengths of a 45 45 90 triangle
x x x*sqrt(2)
when a hypothetical is given about remainders, what do you do?
you use real numbers - plug them in and determine an answer that way
