GRE Math Tips Flashcards
1
Q
an arrangement of items is a
A
an arrangement of items is a permutation of items
2
Q
a distinct set of items is another way of saying
A
combination
3
Q
differentiate between problems that ask you to determine standard deviations and those problems that ask you to determine x*standard deviation
A
x*standard deviation
4
Q
to square both sides of an equality, make sure both are positive
A
make sure both are positive
5
Q
taking the square root results in
A
2 solutions, a positive solution and a negative solution
6
Q
answer QC questions involves
A
algebraic manipulation
7
Q
mean (statistic)
A
= (number of entries)/N
8
Q
median (statistic)
A
middle number on an ordered list
9
Q
if a list has an even number of items, the median is the
A
average of the 2 middle numbers
10
Q
mode (statistics)
A
the most often appearing number in list
11
Q
regression line n.
A
best fit line
12
Q
double matrix method
A
use for males and females when describing percentages
13
Q
a negative base to an even power is
A
positive
14
Q
b^s=b^t
A
s=t
15
Q
x^2>x^6?
A
cannot be determined
16
Q
when the square root sign is written, it means
A
the positive root only
17
Q
x^2 means
A
the positive root and the negative root
18
Q
if you yourself take the square root, them
A
you must include both signs
19
Q
square root of 225
A
15
20
Q
square root of 169
A
13
21
Q
square root of 121
A
11
22
Q
square root of 196
A
14
23
Q
what produces extraneous roots
A
undoing the radical or squaring the radical
24
Q
to determine numbers greater than a square root than is a prime factor
A
take the square root of everything
25
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
26
P(A or B) mutually exclusive
P(A) + P(B)
27
generalized RULE for P(A or B)
P(A) + P(B)-P(A and B)
28
independent events (probability)
one event does not influence another even
29
two independent events A and B P(A and B)
simplified and rule P(A) * P(B)
30
independent events P(A and B)
use simple rule P(A) * P(B)
31
independent events are NOT mutually exclusive
TRUE: mutually exclusive influence one another
32
events A and B are not independent events, one happening changes the probability of the other happening
conditional probabilities: P(A | B)
33
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)
34
complement solutions (probability)
if the math problem asks you "at least one"
35
determine the number of integers between x and y inclusive
y-x+1
36
when a probability questions states AT LEAST
determine the complement
37
"and" and "or" in combinatorics
"or" means add and "and" means multiply
38
for combinatorics, each slot can represent different groups
true
39
fundamental counting principle
n*n*n
40
alternative counting method
number of arrangements that obey rule versus number of arrangements that do not obey rule
41
counting problem that involves interaction with one another
divide by 2 to eliminate repetition
42
a problem that asks you to create different sets, meaning how many combinations
use combinations without repetition
43
for counting problems, "and" means and "or" means
multiply and add
44
use the FCP whenever possible starting with the most restrictive parts
count the most restrictive parts first
45
every 9 minutes beginning at 7:04 a train departs
first train leaves 7:04, next train leaves at 7:13
46
the absolute value is
the distance of the number from the origin
47
continuous probability distribution has a total area of
100% or 1
48
an isosceles triangle has equal sides
thus area can be calculated by taking the square root
49
if polygon is inscribed in circle, the area
is constant regardless of how you draw it as long as its inscribed
50
the largest possible rectangle inscribed inside a circle is a
square
51
2 chords in a triangle that form a triangle with the diameter form a
90 deg angle
52
standard deviation
square root ((1/N)*sum of difference squared)
53
triangle inequality
sum of any two sides must be bigger than the 3rd side
54
3,4,5
triangle
55
5,12,13
triangle
56
area of trapezoid
(b1+b2/2)h
57
a prime number
a number greater than 1 that has no positive divisors other than 1 and itself
58
to cancel two square roots, the inside
of each square root must be the same
59
a divisor is comprise of all the
prime numbers raised to powers
60
an odd divisor cannot contain any
2
61
1st quartile is
numbers lower than the median of the 1st half
62
to determine the larger of two fractions,
cross multiply
63
equation of a circle,
(x-h)^2 +(y-k)^2=r^2
64
K is a multiple of a
smaller number
65
dividend /divisor
quotient
66
divisibility by 11 if
difference of alternating is divisible by 11
67
the mean and mode are the same when
set is symmetric and even
68
add numbers from 1 to n
n(n+1)/2
69
in a right triangle, side in front of 90 angle is the biggest
this makes it easy to compare two triangles sharing a side
70
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)
71
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
72
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
73
compound interest
P(1+r/n)^nt
74
trillion
10^12
75
billion
10^9
76
million
10^6
77
in arithmetic
pay close attention to units when converting
78
logic-based QC problems have the following options unless EXPLICITlY stated
1. variables can both be zero
2. variables can be positive and/or negative decimals
3. variables can be positive and/or negative integers
79
a,b,c, and d, a is half of b, which is third of c
the which is applies ONLY to the b
80
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|
81
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
82
how many positive divisors does a number have
1. perform prime factorization
| 2. (n+1)*(n+1)*...
83
determine cost of tax plus price of item
price*1.tax
84
for a set of consecutive numbers, the mean BLANK the median
equals
85
5/6
.833
86
1/8
.125
87
when one section of a pie chart increases percentage while everything stays the same
new percentage/(100+difference between new percentage and old percentage)
88
triangle identity 5, 12, __
5, 12, 13
89
triangle identity 8, 15, __
8, 15, 17
90
measure of inscribed angle in circle
=0.5*chord
91
measure of central angle
=measure of chord
92
an inscribed angle inside a semicircle is a
right triangle
93
angle exscribed outside circle
bigger chord minus smaller chord
94
2 times any integer
equals an even number
95
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
96
the range of a set
{a->c}
97
30-60-90
x,2x,x^1/3
98
equation of line
y-y=m(x-x)
99
the number zero is
even
100
the number zero is neither
positive or negative
101
triangle rule
A-B
102
select ALL POSSIBLE CHOICES
select answers that may work some of the time
103
range=
biggest - smallest
104
profit=
=revenue - cost
105
prime factorization
numbers when multiplied together give you the original number
106
rational expression
ratio of algebraic expressions
107
area of equilateral triangle
s^2(square root of 3 / 4)
108
number of odd divisors
select only odd prime factors
109
number of even prime numbers
total - odd
110
n consecutive integers always contains
one number divisible by n
111
if n is odd
the sum of set n consecutive numbers will always contain a number divisible by n
112
triangle identity 7,24,25
7,24,25
113
sum of numbers from 1 to n
n (n+1)/2
114
even numbers from 1 to n
n(n+2)/4
115
sum of odd numbers for 1 to n
(n+1)^2/4
116
squaring both sides of a solution may introduce
extraneous solutions
117
a natural number is a
positive integer
118
if a number is less than 100 and not divisible by 2,3,5,7,
than it is prime
119
counting strategy
1. restrictions? (start with most restrictive item)
2. alternative method?
3. counting identical items?
4. stages?
5. define n
6. repetition allowed?
7. distinct sets desired?
120
SD decreases if you
add 2 symmetric numbers smaller than SD
121
SD increases if you
add 2 symmetric numbers larger than SD
122
bello curve left or right percentages
34% then 13.5%
123
min, 1st quartile, median, third quartile, max
5-number summary
124
interquartile range
Q3-Q1
125
if a score is in the xth percentile,
the score is larger than p% of the scores in the distribution
126
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
127
greatest common divisor of two numbers
the smallest of two numbers
128
least common multiple of two numbers
the greatest of two numbers
129
for double x y-axis graphs
make sure you extrapolate using the correct y-axis
130
the product of 2 consecutive numbers equals
an even number
131
is the number 0 even or odd
even
132
(-1)^n
positive if n is even and negative if n is odd
133
slope-intercept form
y=mx+b
134
(divisor*quotient)+R=
dividend
135
x^2-y^2=
x^2-2xy+y^2
136
supplementary angles
sum is 180
137
probability = arrangements/arrangements
true sometimes
138
once the bases are the same you can
equate the exponents
139
when comparing ages at different points in time
equate the ages of a single person over time to solve
140
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
141
if a math problem gives you 2 variables,
put one variable in terms of the other and solve
142
just because 2 triangles share the same angle
doesn't mean the opposing sides are equal to each other
143
different committees means
combinations
144
sometimes, you may need to construct b^2+2bh+h^2
when given b^2+h^2
145
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
