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GMAT > 001 FOM- Arithmetic > Flashcards

001 FOM- Arithmetic Flashcards

1
Q

Define: integer

A

A whole number

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2
Q

Express x as a factor of y for some integer n

A

y=xn

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3
Q

What is another name for factor?

A

Divisor

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4
Q

What are the quotient and remainder for the following equation?

=28/8

A

Quotient is 3

Remainder is 4

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5
Q

Express quotient and remainder as a formula. What are the bounds of r?

A

y = xq+r

0

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6
Q

What are the quotient and remainder when a smaller integer is divided by a larger one?

A 
Q= 0
R = the smaller integer

Y=xq+r
5=7*0+5

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7
Q

Define prime numbers

A

A positive integer with two different positive divisors, 1 and itself.

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8
Q

What is the smallest prime number?

A

2

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9
Q

Express consecutive integers as an equation

A

N, n+1, n+2, n+3…where n is an integer

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10
Q

Express consecutive even integers as an equation

A

2n, 2n+2, 2n+4…

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11
Q

Define least common multiple

A

The smallest common multiple of two numbers

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12
Q

How do you divide by a fraction?

A

Invert the divisor (ie take the reciprocal of the fraction) and multiply

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13
Q

Define a mixed number.

A

A number consisting of a whole number and a fraction

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14
Q

How to change a mixed number into a fraction?

A

Multiple the whole number by the denominator and add to the numerator

7 2/3 = 23/3

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15
Q

Express 0.0321 as a fraction

A

0/10 + 3/100+2/1000+1/10,000
= 321/10,000

lcm is 10,000

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16
Q

How to multiply decimals?

A

Multiply the numbers as whole numbers. Insert the decimal so that the number of digits to the right is equal to the sum of the numbers of digits to the right of the decimal points in the numbers being multiplied.

2.09 x 1.3 = 627+2090= 2.717

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17
Q

How to divide decimals?

A

Move the decimal point of the divisor to the right until it’s a whole number. Move the decimal of the dividend the same number. Divide. Put the decimal in the quotient directly above the decimal in the new dividend.

12.4[698.12
=124[6981.2
=56.3

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18
Q

Express xy+xz alternatively

A

X(y+z)

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19
Q

Define proportion re ratios

A

Statement that two ratios are equal

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20
Q

How can you find the % increase?

A

1) find amount of increase
2) divide increase by original amount
3) express as a %

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21
Q

How does the % increase from x to y compare to a % decrease from y to x?

A

Decrease will be a smaller %, as it is the same amount of change, but the comparable is a larger number

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22
Q

What happens when you square a number between 0 and 1?

A

It gets smaller

1/3 squared = 1/9

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23
Q

How many square roots does a positive number have?

A

Two: one positive and the other negative

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24
Q

How many cube roots does a real number have

A

One

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25
Define mean
The average
26
Define median
Center for a list of numbers (which are in order from least to greatest). If there are an even amount of numbers, the median is the average of the two middle numbers
27
What is the relationship between median and mean?
None. Median can be less, equal or more.
28
Define mode
The number occurring most frequently in a lost. Can be multiple modes for a given list.
29
What values influence standard deviation most?
Those farthest from the mean. The closer data is grouped around the mean, the smaller the SD
30
How to calculate standard deviation?
1) calculate mean of x numbers 2) calc each diff from mean (x-mean) 3) square each diff 4) calc mean of squared diff 5) find positive square root of this mean
31
How to determine mean using frequency distribution?
1) multiply each data value by its frequency 2) sum the results 3) divide by the number of data values
32
What is union of any two sets A and B?
The set of all elements that are in set A or B or both. represented by a capital U
33
What is the intersection of sets A and B?
The set of all elements that are both in A and B. Represented by the shaded part of a Venn diagram or an inverted U
34
Express the Union of two sets mathematically
s U t = set s + set t - Intersection s and t
35
What is the factorial of n?
n! Defined as the product of all integers from 1 to n. 4! = 1*2*3*4=24
36
Define permutation and express as a formula
A selection process in which objects are selected one by one in a certain order. Represents all the ways the objects can be ordered. For a set of n objects: n(n-1)(n-2) =n!
37
Formula for a set of n objects from which a complete selection of k objects is to be made without regard to order, where 0
N K = N!/k!(n-k)!
38
Probabilities are between what range?
0 (impossible) to 1 (certain)
39
Express probability as a formula
Number of outcomes in E/total number of possible outcomes. Where E represents a possible event
40
What is the probability of event E and event F happening, where E and F are independent events? What is this called?
P(E)*P(F) Intersection
41
What is the probability of E or F happening, where E and F are independent? What is this called?
= P(E)+P(F)-P(E and F) Called the union
42
What are alternative ways of saying 15 is divisible by 3?
1) 15 is a multiple of 3 2) 3 is a factor of 15 3) 3 goes into 15 4) 3 divides 15
43
Is zero even or odd? Why?
Even, because it is divisible by 2 (0/2 = 0)
44
What is the number underneath an exponent?
The base
45
What does a root do to an exponent?
Undoes it
46
What is a perfect square?
The square of an integer (the square root of a perfect square therefore is always an integer).
47
What is the order of arithmetic?
PEMDAS (Parantheses, exponents, multiply, divide, add, subtract).
48
How do you state (3+2)*2?
The quantity 3 plus 2, all times 2. Quantity refers to parantheses.
49
Name the first 8 prime numbers.
2,3,5,7,11,13,17,19
50
If a/b and b/c, then...?
a/c
51
If d is divisible by two primes e and f, then what is true?
d is also divisible by e*f. ex: 20 is divisible by 5*2=10
52
Define a prime factor
The unique set of prime numbers multiplied to arrive at a given integer.
53
If x is divisible by a and b, what is true about the LCM of a and b?
x is also divisible by that
54
What is true re LCM when two numbers share no prime factors?
The LCM is the product of the two numbers.
55
What is true about LCM when numbers x and y share prime factors?
The LCM of x and y is less than x*y.
56
What is 11^2?
121
57
What is 12^2?
144
58
What is 13^2?
169
59
What is 14^2?
196
60
What is 15^2?
225
61
What is 4^3?
64
62
What is 5^3?
125
63
What is 2^5?
32
64
What is 2^4?
16
65
What is 2^6?
64
66
What is 2^7?
128
67
What is 2^8?
256
68
What is 2^9?
512
69
What is 2^10?
1024
70
What is 3^3?
27
71
What is 3^4?
81
72
What is true about even exponents?
They can hide the sign of the base. (-2)^2 = (2)^2
73
x^3 * x*4 =?
x^7
74
x^4 / x^3?
x^1
75
What is 0^0?
Undefined
76
4^0 = ?
1
77
a^-2 =?
1/a^2
78
What is (a^3)^2?
a^6
79
What is true about the square root symbol?
It only gives a positive result.
80
Simplify sq root{3^2 + 4^2}
sq root {25} = 5
81
Simplify sq root{3^2 * 4^2}
sq root {3^2} * sq root {4^2} = 3*4 = 12
82
What is an improper fraction?
Where the numerator exceeds the denominator (ie the number is more than 1).
83
What is the easiest way to see which of two fractions is larger?
Cross multiply - the side with the bigger number is the larger one (generates the numerators of the fractions were you to re-express them using the common denominator)
84
What is a shortcut way to convert an improper fraction to a mixed number?
Express the number as a sum, then split the fraction and simplify. ie 13/4 = (12+1)/4 = 12/4 +1/4 = 3 1/4
85
How do you convert a decimal to a fraction?
Put a power of 10 in the denominator of the fraction. The power depends how many places to the right of the decimal there are. ie 0.007 = 7/1000
86
When converting a fraction to a decimal, how do you know when the decimal will end?
If the denominator contains only 2's and/or 5's as factors.
87
If you know a fraction converted to a decimal will end, what's a shortcut way to convert it?
Make the denominator a power of 10 by multiplication. ie 1/4 * 25/25 = 25/100 = 0.25
88
How do you convert a fraction to a percent?
Convert is to a decimal, then convert to a percentage.
89
Convert to a percent: 1/8
12.5%
90
Convert to a percent: 3/8
37.5%
91
Convert to a percent: 2/5
40%
92
Convert to a percent: 3/5
60%
93
Convert to a percent: 5/8
62.5%
94
Convert to a percent: 7/8
87.5%
95
Convert to a percent: 5/4
125%
96
Translate "what percent"
= x/100
97
How do you find the percent change?
Change in value / original value
98
What is another way to state "percent increase"?
Percent more than
99
What's the difference between an expression and an equation?
Expressions represent a number, and does not contain an equals sign. You may simplify an expression, but you never change that expression's value. You determine the expression's value by evaluating it. An equation is a complete sentence: subject equals object.
100
What is true re simplification of expressions and equations?
You can simplify one side of an expression, but you must do the same thing to both sides of an equation.
101
For an equation involving exponents, what is true about the bases?
Once the bases are the same, the exponents must be the same (except for bases 1, 0 and -1).
102
What are two strategies to solve a system of equations?
1) Isolate, then substitute | 2) Combine equations to eliminate a variable
103
In solving a system of equations, which variable should you isolate?
The variable you ultimately don't want (ie if the problem asks x=? the isolate and sub the variable y).
104
How many solutions does a quadratic equation usually have?
2
105
What does x^3 in an equation indicate?
There could be 3 solutions.
106
What is the square of a sum?
(x+y)^2 = x^+2xy+y^2
107
What is the square of a difference?
(x-y)^2 = x^2-2xy+y^2
108
What is a difference of squares?
(x+y)(x-y) = x^2-y^2 middle terms cancel
109
What should you do if you see a special product or something close to it?
Convert a special product to its other form, especially for a difference of squares. If it's close to a special product, rearrange the equation to get there.
110
What is true about solutions to inequality expressions?
They have a range of solutions.
111
What happens when you multiply or divide both sides of an inequality by a negative number?
You must flip the inequality sign.
112
What is true about a variable inside of an absolute value expression?
It generally has two values.
113
What is the formula for Total Cost?
Fixed Cost + Price x Additional Quantity
114
What is the process to solve a "work" word problem?
Use Rate x Time = Work, choosing work units and often adding rates. Invent widgets (small units of work) to avoid dealing with fractions (i.e. half a 100 box warehouse a day is 50 boxes per day).

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