GRE Math Tips Flashcards Preview

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Flashcards in GRE Math Tips Deck (145):
1

an arrangement of items is a

an arrangement of items is a permutation of items

2

a distinct set of items is another way of saying

combination

3

differentiate between problems that ask you to determine standard deviations and those problems that ask you to determine x*standard deviation

x*standard deviation

4

to square both sides of an equality, make sure both are positive

make sure both are positive

5

taking the square root results in

2 solutions, a positive solution and a negative solution

6

answer QC questions involves

algebraic manipulation

7

mean (statistic)

= (number of entries)/N

8

median (statistic)

middle number on an ordered list

9

if a list has an even number of items, the median is the

average of the 2 middle numbers

10

mode (statistics)

the most often appearing number in list

11

regression line n.

best fit line

12

double matrix method

use for males and females when describing percentages

13

a negative base to an even power is

positive

14

b^s=b^t

s=t

15

x^2>x^6?

cannot be determined

16

when the square root sign is written, it means

the positive root only

17

x^2 means

the positive root and the negative root

18

if you yourself take the square root, them

you must include both signs

19

square root of 225

15

20

square root of 169

13

21

square root of 121

11

22

square root of 196

14

23

what produces extraneous roots

undoing the radical or squaring the radical

24

to determine numbers greater than a square root than is a prime factor

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