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GRE Math Flashcards

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1
Q

triangle inequality theorem

A

The length of any side of a triangle is 1. less than the sum of the lengths of the other two sides 2. greater than the positive difference of the lengths of the other two sides

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2
Q

When to backsolve?

A

When answer choices have real values

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3
Q

When to pick numbers?

A

If the question is a multiple choice question, with undefined variables in Q, or has to do with number properties (multiples, factors, primes), or percentage (pick 100 for % questions)

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4
Q

even x even

A

even

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5
Q

even x odd

A

even

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6
Q

odd x odd

A

odd

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7
Q

even to power of positive integer

A

even

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8
Q

odd to power of positive integer

A

odd

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9
Q

even +/- even

A

even

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10
Q

odd +/- odd

A

even

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11
Q

odd +/- even

A

odd

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12
Q

multiply or divide two numbers with same signs

A

positive

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13
Q

multiply or divide two numbers with different signs

A

negative

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14
Q

negative number to the power of even number

A

positive

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15
Q

negative number to the power of odd number

A

negative

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16
Q

Prime numbers property

A
  1. positive integers (whole number) that are divisible by itself and 1 only 2. 0 and 1 are NOT prime 3. 2 is the smallest and ONLY even prime
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17
Q

First 10 prime numbers

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

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18
Q

Compare fractions

A

cross multiply: bottom gets multiplied to other side

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19
Q

Properties for 0

A
  1. 0 is a integer 2. 0 is even 3. 0 is neither positive or negative 4. 0 is always a multiple
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20
Q

Multiples properties

A

multiples could be both positive AND negative all integers are multiples of 1 0 is a multiple of all integers multiples do not need to be integer

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21
Q

When to consider negative root

A

IF x^2= 81, then consider both +9 and -9 IF √81=x, then consider only +9

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22
Q

Combination and Permutation, which gives more possible sets?

A

permutation does, because order matters, so you get a lot more combinations

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23
Q

Combination (order doesn’t matter)

A

If order doesn’t matter, you get a smaller number, so be sure to divide by the number of slots. E.g., 12 x 11 x 10 x 9 x 8 / 5! ; you get to pick from 12 things for 5 slots without replacement

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24
Q

Permutation (order matters)

A

If order matters, you get bigger number, so no need to divide by the number of slots

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25
Q

Prob of something AND something

A

X

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26
Q

Prob of something OR something

A

+

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27
Q

For probability questions…

A

keep in mind: 1. multiply for AND 2. add for OR 3. picture ALL the scenarios that match with prompt and then just add or multiply depending on prompt

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28
Q

Time management

A

Go slower on easy questions and straight up guess, mark, and skip harder/time-consuming ones

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29
Q

Percentage changes

A

As long as you stay in same pie chart or that the total amount does change, it is NOT necessary to calculate the actual numbers, just use %. E.g., 8% of 2800= 224 and 25% of 2800= 700, so together is 924; 32% of 2800= 896, so % increase is (924-896)/896 = 3.13% THIS IS SAME AS: ((8% + 25%) - 32%)/32%= 3.13%

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30
Q

Percent increase

A

diff/orig x 100% [i.e., Increase (100%) / Original] where original number is the SMALLER number

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31
Q

Percent decrease

A

diff/orig x 100% [i.e., Decrease (100%) / Original] where original number is the BIGGER number

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32
Q

Sum of interior angles for polygons with n sides

A

180 (n-2)

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33
Q

Sum of exterior angles for polygons

A

360

34
Q

Exterior angle of triangle

A

Sum of the other two interior angles

35
Q

integer

A

a number without fractional or decimal parts, including positive, negative whole numbers and zero. All integers are multiples of 1.

36
Q

PEMDAS

A

Parentheses Exponents Multiplication & Division (simultaneously from L to R) Addition & Subtraction (simultaneously from L to R)

37
Q

Divisibility by 2

A

if last digit is divisible by 2

38
Q

Divisibility by 3

A

if its digits add up to a multiple of 3

39
Q

divisibility by 4

A

if its last two digits are a multiple of 4

40
Q

divisibility by 5

A

if the last digit is 0 or 5

41
Q

divisibility by 6

A

if it is divisible by both 2 and 3 (if last digit is divisible by 2 AND if digits add up to a multiple of 3)

42
Q

divisibility by 9

A

if digits add up to a multiple of 9

43
Q

√ convention (when to consider + / -)

A

the radical symbol √ stands for the positive square root only, but if it’s asking x^2 = 9, then x can be both positive 3 or negative 3.

44
Q

Reciprocal of a fraction between 0 and 1

A

greater than both the original fraction and 1

45
Q

Reciprocal of a fraction between 0 and -1

A

smaller than both the original fraction and 1

46
Q

Square of a fraction between 0 and 1

A

smaller than the original fraction

47
Q

Square of a fraction between 0 and -1

A

greater than the original fraction

48
Q

%

A

means 1/100

49
Q

profit percentage

A

profit / original SELLING price x 100%

50
Q

simple interest

A

the interest payments received are kept SEPARATE from the principal (the amount contributed/invested)

51
Q

compound interest

A

the money earned as interest is reinvested, so the principal grows after every interest payment received. A= P (1 + r/n)^nt t must be times in year n is number of times per year

52
Q

Speed

A

speed = distance / time time = distance / speed distance = speed * time

53
Q

multiple rates

A

rates can be added

54
Q

If first person takes a units of time to complete the job, the second b units of time to complete, and the third c units of time. The time it takes for all 3 working together to complete the job is T, then what’s the rate of all of them working together?

A

1/a + 1/b + 1/c = 1/T

55
Q

Finding the missing number based on average and other numbers

A

Take each of the known number and subtract it from the average. Add up all the differences, then add that sum to the average to find the missing number. E.g., average= 26, known numbers are 19, 24, and 30 26-19= 7 26-24= 2 26-30= -4 7+2+(-4)= 5 26 (the mean) + 5= 31, the missing number is 31

56
Q

Combinations from multiple groups

A

multiply the potential combinations from each group

57
Q

ways/arrangements/orders/schedules

A

permutation (order matters)

58
Q

LCM of a lot of numbers

A

find the prime factorization of each one, then find the PRODUCT of the largest of each prime factorization e.g., 2^2 X 3 X 5^2 X 7^3

59
Q

Sum of consecutive numbers

A

use average formula: first find average using sum of smallest and largest number divide by 2. Then plug in this average in the average formula: AVERAGE= sum of all numbers / total number of numbers Total number of numbers inclusive is the largest number minus lowest plus 1

60
Q

Total number of numbers inclusive between a and b

A

if a > b a - b + 1

61
Q

Probability of A or B

A

If mutually exclusive: P(A or B)= P(A) + P(B) If independent: P(A or B)= P(A) + P(B) - P(A and B)

62
Q

mutually exclusive events

A

events that cannot both occur

63
Q

independent events

A

events that can both occur simultaneously

64
Q

Given prime factorization, find the number of distinct positive integer factors that number has. E.g., 2^7 * 3^4 * 7^3 * 23^5

A

Since the number 2*3 would give a factor of 6, which will then use up one 2, one 3, no 7, and no23, we can understand that we can use zero to seven 2s, zero to four 3s, zero to three 7s, and zero to five 23s, meaning there are 8 slots for 2, 5 slots for 3, 4 slots for 7, and 6 slots for 23. The combination of that is 8*5*4*6

65
Q

3!

A

6

66
Q

4!

A

24

67
Q

5!

A

120

68
Q

6!

A

720

69
Q

7!

A

5040

70
Q

Set Properties Total

A

Total = Group 1 + Group 2 - Both + Neither

71
Q

Sum of first n consecutive positive integers

A

Sum= n*(n+1)/2

72
Q

sum of consecutive positive even integers from 2 to n, where n is even

A

Sum=n*(n+2)/4

73
Q

sum of consecutive positive odd integers from 1 to n, where n is odd

A

Sum= [(n+1)^2]/4

74
Q

standard deviation

A

how spread out the data is

75
Q

normal distribution

A
76
Q

If range of data and spacing of data remains unchanged, what happens to standard deviation?

A

SD remains unchanged

77
Q

If range of data remains unchanged, but each data point is tripled, what happens to SD?

A

SD also triples, because spacing between consecutive data point also triples

78
Q

Measure of interior angle of regular polygon

A

180 (n-2)/n

79
Q

Sum of all interior angles of any polygons

A

180 (n-2)

80
Q

GCF of a lot of numbers

A

Do it the long way:

list all the factors for each number and find the greatest common factor

GRE Math (1 decks)

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