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