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Quant Formulas > Arithmetic > Flashcards

Arithmetic Flashcards

1
Q

Number of Factors of an Integer

A

Every integer N is the product of powers of prime numbers:

N = p^αq^β· … · r^γ.

Number of integers :(α + 1)(β + 1) … (γ + 1)

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2
Q

Is zero an integer?

A

yes

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3
Q

name integers

A

-3,-2,-1,0,1,2,3…

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4
Q

even integer and formula

A

any integer divisible by 2 | can be expressed as 2N (N integer). -4, -2,0,2,4,6,8

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5
Q

Is Zero an even integer?

A

yes

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6
Q

odd integer and formula

A

not divisible by 2 | -3,-1,1,5,… | can be expressed by formula 2N+1 (N is an integer)

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7
Q

even X even = ?

A

even 2x4=8

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8
Q

even x odd = ?

A

even 2*3=6

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9
Q

odd x odd = ?

A

odd 3 x 5 = 15

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10
Q

even +/- even = ?

A

even 3+4=6

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11
Q

even +/- odd = ?

A

odd 2+3=5

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12
Q

odd +/- odd

A

even 3+5 =8

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13
Q

consecutive integers (provide examples)

A

are two or more integer written in sequence in which each integer is 1 more than the preceding one

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14
Q

prime number

A

positive integer that has exactly two different positive divisors: 1 and itself

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15
Q

first fifteen prime numbers

A

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47

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16
Q

what is digit?

A

digit refers to just one symbol, 9674 ; 9 - thousands digit, 6 - hundreds digit, tens digit, units digit

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17
Q

quotient

A

the result of division is quitient

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18
Q

square root of 2

A

1.4

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19
Q

square root of 3

A

1.7

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20
Q

a number is divisible

A

if the first number divided by the second number resulting in an integer

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21
Q

N/M=q what is N,M,q

A

m is a divisor of n, m is a factor of n, n is divisible by m, n is a multiple of m

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22
Q

a number is divisible by 2 IF

A

if the last digit is even! 2376 is div by 2

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23
Q

a number is div by 5 if

A

if the last digit is 0 or 5! 8745 or 8740

24
Q

a number is div by 10 if

A

if the last digit is 0! 4500

25
Q

a number is div by 4 if

A

if the number formed by last two digits is divisible by 4! 2376 -> 76 is div by 4

26
Q

a number is divisible by 8 if

A

if the number formed by last three digits is divisible by 8!

2376 -> 376 is divisible by 8

27
Q

a number is div by 3 if

A

the sum of all digits is div by 3

28
Q

a number is div by 9 if

A

if the sum of all digits is div by 9 ! 2376 = 2+3+7+6=18 div by 9

29
Q

a number is div by 12 if

A

if the number is div by both 3 and 4 ! 2376 div by 4, 2376 is div by 3

30
Q

a number is div by 11 if

A

число делится на 11, если знакочередующаяся сумма его цифр делится на 11. 1234321. Знакочередующаяся сумма цифр этого числа равна 1 − 2 + 3 − 4 + 3 − 2 + 1 = 0. Так как 0 делится на 11, то и число 1234321 делится на 11

31
Q

when a small number is div by large number integer then /?

A

the quotient is 0 and the reminder is the smaller integer: 5=7X0 + 5

32
Q

Prime factors

A

positive integers are the prime numbers that divide that integer

33
Q

prime factorization

A

every integer greater than 1 either is prime or can be uniquely expressed as a product of prime factors
14=27, 81 = 3333

34
Q

Least Common Multiple (LCM) - наименьшее общее кратное

A

Is the smaller positive integer that is a multiple of each of them
LCM of 14363 and 1950: use simple prime factorizaition
1. 14364 = 2^2 x 3^2 x 7 x 19
2. 1950 = 2 x 3 x 5^2 x 13

LCM = 2^2 x 3^3 x 5^2 x 7 x 13 x 19

35
Q

Greates Common Factor, Divisor(GCF) - наибольший общий делитель

A 
is the largest positive integer that is a factor of each of them. 
GCF 14363 and 1950
-prime factorization
1. 14364 = 2^2 x 3^2 x 7 x 19 
2. 1950 = 2 x 3 x 5^2 x 13

GCF = 2 x 3
берем наименьшие степени чисел, которые есть в двух числах

36
Q

Factorial of 0 = 0!

A

1

37
Q

fractions

A

5/11 5 - numerator, 11 - denominator

38
Q

reciprocal

A

means flip over a fraction: 2/5 -> 5/2

39
Q

improper fraction

A

numerator is larger than or equal to their denominator 11/4

40
Q

mixed fraction

A

have a whole number part and a fraction part

41
Q

decimal fraction

A

fraction whose denominator is a power of ten 0.21

42
Q

decimal point determines

A

determines the place value of the digits

98765.432: 9 - ten thousands, 8 - thousands, 7 - hundreds, 6 - tens, 5 - units. 4 - tenths, 3 - hundreds, 2-thousandths

43
Q

ratio

A

shows the relationship between two o more numbers, but it does not tell you the actual values of those numbers

44
Q

proportion and how to solve?

A

statement that two ratios are equal
Example: 2/3=8/12 in general X/Y=A/B
One way to solve is to cross multiply

45
Q

Ratio and Proportions.
X+Y= 180
X : Y = 3: 7

A

Easies way:
x:y = 3:7 -> 10 parts
180/10 = 18 - value of 1 part
X=3*18

46
Q

Percent; Whole 100% , part = p%. What percent?

A

p% = part/whole * 100. Example: 40 is what percent of 250? % = 40/250100=16%
250 is what percent of 40?
250/40100=625%

47
Q

Percent; Whole 100% , part = p%. What is the value?

A

Part = p%/100% X Whole. Example:
What is 25% of 36?
25/100*36=9

48
Q

Percent. What percent greater or less?

A 
delta=Difference/whole * 100%
Example:
150 is what percent greater than 120?
(150-120)/120*100=25%
120 is what percent less than 150?
(150-120)/150 * 100 = 20%
49
Q

Percent. What percent increase or decrease?

A

Percent Increase = Amount of increase/original whole * 100
Percent decrease = Amount of decrease/original whole * 100
Example
If the price increases from $24 to $30, what is the percent increase in price?
(30-24)/24 X 100=25%

When dealing with percent decrease and increase always be careful ti put the amount of increase or decrease over the original whole. not the new whole!!!

50
Q

Percent. What is the value …? Increase or decrease a number by certain percent.

A

To increase a number by r% multiply it by 100% + r%/100%
or (1+ r%/100)

Example: Increase a number by 15% ->
multiple (1+15%/100%) or 1.15

To decrease : multiply by (1+r/100)
Decrease a number by 15%
multiple by 0.85

51
Q

Percent. An increase of a% followed by an increase of b%

A

always results in a larger increase than a single increase of (a+b)%
Example: An increase of 10% followed by an increase of 15%.
X * 1.1 * 1.15
Decrease the same but: X0.90.85

52
Q

Average, arithemetic mean

A

Average = Sum of Values/Number of Values

53
Q

Median

A

To calculate the median of n numbers. The list of numbers from the least to the greatest; if number of numbers is odd, the median is defined as the middle number. if n is even - average of the two middle numbers

54
Q

mode

A

is the number that occurs most frequently in the list
{1,3,3,4,5,6} mode =6
{1,2,3,3,3,5,5,7,10,10,10,20} two modes = 3 and 10

55
Q

range

A

difference between the largest and the smallest values

56
Q

Standard Deviation

A

The more data are spread away from the mean the greater the standard deviation.

How to find the SD of n numbers:

  • find the arithmetic mean
  • find the difference between the mean and each of the n numbers
  • square each of the differences
  • find the average of the squared difference
  • take nonnegative square root of this average
Example
{ 1, ,2,3,3,5,8,27}
1) mean = 7
2)difference:6,5,4,4,2,1,20
3)squares: 36,25,16,16,4,1,400
4) avg of squared = 71.7
5)square root(71.7) = 8.4

Quant Formulas (6 decks)

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