GRE Math Tips Flashcards
an arrangement of items is a
an arrangement of items is a permutation of items
a distinct set of items is another way of saying
combination
differentiate between problems that ask you to determine standard deviations and those problems that ask you to determine x*standard deviation
x*standard deviation
to square both sides of an equality, make sure both are positive
make sure both are positive
taking the square root results in
2 solutions, a positive solution and a negative solution
answer QC questions involves
algebraic manipulation
mean (statistic)
= (number of entries)/N
median (statistic)
middle number on an ordered list
if a list has an even number of items, the median is the
average of the 2 middle numbers
mode (statistics)
the most often appearing number in list
regression line n.
best fit line
double matrix method
use for males and females when describing percentages
a negative base to an even power is
positive
b^s=b^t
s=t
x^2>x^6?
cannot be determined
when the square root sign is written, it means
the positive root only
x^2 means
the positive root and the negative root
if you yourself take the square root, them
you must include both signs
square root of 225
15
square root of 169
13
square root of 121
11
square root of 196
14
what produces extraneous roots
undoing the radical or squaring the radical
to determine numbers greater than a square root than is a prime factor
take the square root of everything
mutually exclusive events in probability
means one doesn’t depend on the other, it means that it is impossible for both of them to happen together
P(A or B) mutually exclusive
P(A) + P(B)
generalized RULE for P(A or B)
P(A) + P(B)-P(A and B)
independent events (probability)
one event does not influence another even
two independent events A and B P(A and B)
simplified and rule P(A) * P(B)
independent events P(A and B)
use simple rule P(A) * P(B)
independent events are NOT mutually exclusive
TRUE: mutually exclusive influence one another
events A and B are not independent events, one happening changes the probability of the other happening
conditional probabilities: P(A | B)
P(A and B) when NOT INDEPENDENT
P(A and B)=P(B)*P(A|B) or
P(A and B)=P(A)*P(B|A)
complement solutions (probability)
if the math problem asks you “at least one”
determine the number of integers between x and y inclusive
y-x+1
when a probability questions states AT LEAST
determine the complement
“and” and “or” in combinatorics
“or” means add and “and” means multiply
for combinatorics, each slot can represent different groups
true
fundamental counting principle
nnn
alternative counting method
number of arrangements that obey rule versus number of arrangements that do not obey rule
counting problem that involves interaction with one another
divide by 2 to eliminate repetition
a problem that asks you to create different sets, meaning how many combinations
use combinations without repetition
for counting problems, “and” means and “or” means
multiply and add
use the FCP whenever possible starting with the most restrictive parts
count the most restrictive parts first
every 9 minutes beginning at 7:04 a train departs
first train leaves 7:04, next train leaves at 7:13
the absolute value is
the distance of the number from the origin
continuous probability distribution has a total area of
100% or 1
an isosceles triangle has equal sides
thus area can be calculated by taking the square root
if polygon is inscribed in circle, the area
is constant regardless of how you draw it as long as its inscribed
the largest possible rectangle inscribed inside a circle is a
square
2 chords in a triangle that form a triangle with the diameter form a
90 deg angle
standard deviation
square root ((1/N)*sum of difference squared)
triangle inequality
sum of any two sides must be bigger than the 3rd side
3,4,5
triangle
5,12,13
triangle
area of trapezoid
(b1+b2/2)h
a prime number
a number greater than 1 that has no positive divisors other than 1 and itself
to cancel two square roots, the inside
of each square root must be the same
a divisor is comprise of all the
prime numbers raised to powers
an odd divisor cannot contain any
2
1st quartile is
numbers lower than the median of the 1st half
to determine the larger of two fractions,
cross multiply
equation of a circle,
(x-h)^2 +(y-k)^2=r^2
K is a multiple of a
smaller number
dividend /divisor
quotient
divisibility by 11 if
difference of alternating is divisible by 11
the mean and mode are the same when
set is symmetric and even
add numbers from 1 to n
n(n+1)/2
in a right triangle, side in front of 90 angle is the biggest
this makes it easy to compare two triangles sharing a side
for math problems that ask you to select answer that can be true
use scenarios when it cannot be possibly true or use logic to rule things out (i.e. xy=0 or xy cannot equal 0)
The total number of people in honor society at Melpomene High School, regardless of other activities, is approximately
regardless mean it is okay to include honor society number + other activities
what percent higher than the total number of people in honor society at Thalia High School, regardless of other activities?
percent higher means calculate the percentage difference
compound interest
P(1+r/n)^nt
trillion
10^12
billion
10^9
million
10^6
in arithmetic
pay close attention to units when converting
logic-based QC problems have the following options unless EXPLICITlY stated
- variables can both be zero
- variables can be positive and/or negative decimals
- variables can be positive and/or negative integers
a,b,c, and d, a is half of b, which is third of c
the which is applies ONLY to the b
x^2-y^2=0
x=y is not necessarily the case, taking the square root of both sides x^2=y^2 yields |x|=|y|
QC problems that ask you to select the choices that MUST BE TRUE,
start with strategy ABC, then pick scenarios that are opposite to listed choices
how many positive divisors does a number have
- perform prime factorization
2. (n+1)(n+1)…
determine cost of tax plus price of item
price*1.tax
for a set of consecutive numbers, the mean BLANK the median
equals
5/6
.833
1/8
.125
when one section of a pie chart increases percentage while everything stays the same
new percentage/(100+difference between new percentage and old percentage)
triangle identity 5, 12, __
5, 12, 13
triangle identity 8, 15, __
8, 15, 17
measure of inscribed angle in circle
=0.5*chord
measure of central angle
=measure of chord
an inscribed angle inside a semicircle is a
right triangle
angle exscribed outside circle
bigger chord minus smaller chord
2 times any integer
equals an even number
if you have 3 ways to do one thing and 3 ways to do another thing,
multiply 3*3 to determine the number of possibilities of both groups together according to FCP
the range of a set
{a->c}
30-60-90
x,2x,x^1/3
equation of line
y-y=m(x-x)
the number zero is
even
the number zero is neither
positive or negative
triangle rule
A-B
select ALL POSSIBLE CHOICES
select answers that may work some of the time
range=
biggest - smallest
profit=
=revenue - cost
prime factorization
numbers when multiplied together give you the original number
rational expression
ratio of algebraic expressions
area of equilateral triangle
s^2(square root of 3 / 4)
number of odd divisors
select only odd prime factors
number of even prime numbers
total - odd
n consecutive integers always contains
one number divisible by n
if n is odd
the sum of set n consecutive numbers will always contain a number divisible by n
triangle identity 7,24,25
7,24,25
sum of numbers from 1 to n
n (n+1)/2
even numbers from 1 to n
n(n+2)/4
sum of odd numbers for 1 to n
(n+1)^2/4
squaring both sides of a solution may introduce
extraneous solutions
a natural number is a
positive integer
if a number is less than 100 and not divisible by 2,3,5,7,
than it is prime
counting strategy
- restrictions? (start with most restrictive item)
- alternative method?
- counting identical items?
- stages?
- define n
- repetition allowed?
- distinct sets desired?
SD decreases if you
add 2 symmetric numbers smaller than SD
SD increases if you
add 2 symmetric numbers larger than SD
bello curve left or right percentages
34% then 13.5%
min, 1st quartile, median, third quartile, max
5-number summary
interquartile range
Q3-Q1
if a score is in the xth percentile,
the score is larger than p% of the scores in the distribution
GCF
list the prime factors of each number, multiply those factors both have in common, if there are no common factors, the GCF is 1
greatest common divisor of two numbers
the smallest of two numbers
least common multiple of two numbers
the greatest of two numbers
for double x y-axis graphs
make sure you extrapolate using the correct y-axis
the product of 2 consecutive numbers equals
an even number
is the number 0 even or odd
even
(-1)^n
positive if n is even and negative if n is odd
slope-intercept form
y=mx+b
(divisor*quotient)+R=
dividend
x^2-y^2=
x^2-2xy+y^2
supplementary angles
sum is 180
probability = arrangements/arrangements
true sometimes
once the bases are the same you can
equate the exponents
when comparing ages at different points in time
equate the ages of a single person over time to solve
if a problem gives you the percentage or percentages,
make sure you can take the percentage of the number so you end up with an integer
if a math problem gives you 2 variables,
put one variable in terms of the other and solve
just because 2 triangles share the same angle
doesn’t mean the opposing sides are equal to each other
different committees means
combinations
sometimes, you may need to construct b^2+2bh+h^2
when given b^2+h^2
exception to the Mississippi rule
if the question doesn’t ask you to use all the spaces available and restricts you to using 3 spaces, them determine the number of combos with repeats then subtract the number of repeats from the word and calculate the number of permutations
