Quant - 1 Flashcards
1
Q
Reciprocal x
rɪˈsɪprəkəl
A
1/x
2
Q
Prime numbers less than 100
A
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51, 53, 59, 61, 67, 71, 73, 79, 89, 97
کلا ۲۵ تاس
۱۵ تا زیر ۵۰
۱۰ تا بالای ۵۰
3
Q
Finding number of factors in a particular number
A
Step 1: Find the prime factorization of the number
Step 2: Add 1 to the value of each exponent. Then multiply these results.
4
Q
Finding the LCM
Lowest Common Multiple
A
Step 1: Find the prime factorization of the number
Step 2: Of any repeated prime factors among the integers in the set, take only those with the largest exponents.
5
Q
Finding the GCF
Greatest Common Factor
A
Step 1: Find the prime factorization of the number
Step 2: Of any repeated prime factors among the integers in the set, take only those with the smallest exponents.
6
Q
LCM (x,y) * GCF (x,y)
A
x * y
7
Q
Perfect square 1 to 15
A
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
8
Q
Perfect cube 1 to 10
A
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
9
Q
Which one is bigger
X, X2, √X
0 < X < 1
A
X2 < X < √X
10
Q
Prime numbers less than 10
A
2, 3, 5, 7
11
Q
Prime numbers between 10 to 20
A
11, 13, 17, 19
12
Q
Prime numbers between 20 to 30
A
23, 29
13
Q
Prime numbers between 30 to 40
A
31, 37
14
Q
Prime numbers between 40 to 50
A
41, 43, 47
15
Q
Prime numbers between 50 to 60
A
53, 59
51 is divisible by 3, 17
16
Q
Prime numbers between 60 to 70
A
61, 67
17
Q
Prime numbers between 70 to 80
A
71, 73, 79
18
Q
Prime numbers between 80 to 90
A
83, 89
87 is divisible by 3, 29
19
Q
Prime numbers between 90 to 100
A
97
91 is divisible by 7 and 13
20
Q
Divisibility rule
2
A
if the ones digit is 0, 2, 4, 6, 8
21
Q
Divisibility rule
3
A
Sum of all digits must divisible by 3
22
Q
Divisibility rule
4
A
Last two digits must divisible by 4
23
Q
Divisibility rule
5
A
Last digit is 0 or 5
24
Q
Divisibility rule
6
A
It shoud both divisible by 2 and 3
25
Divisibility rule
8
Last three digits should divisible by 8
26
Divisibility rule
9
Sum of all digits should divisible by 9
27
Divisibility rule
11
A Number divisible by 11 if the sum of **odd-numbered** place digits minus the sum of **even-numbered** place digits is divisable by 11.
28
Trailing Zeros
Is the number of (2x5) pairs in prime factorization
29
Leading Zeros in a Decimal
| 1/X
If **X** is and integer with **k** digits, then **1/X** have **k-1** leading zeros
unless:
**X** is a perfect power of **10**, in which case there will be **k-2** leading zeros.
30
Terminating decimal
The decimal equivalent of a fraction will terminate if and only if the denominator of the reduced fraction has a prime factorization that contains only **2**s and **5**s, **or both**
##footnote
* 1/12=0.0833333...
* 1/20=0.05
31
Two consecutive integers
Will never share any prime factors. Thus, the GCF of two consecutive integers is 1.
32
Perfect square
11
121
33
Perfect square
12
144
34
Perfect square
13
169
35
Perfect square
14
196
36
Perfect square
15
225
37
Perfect cube
2
8
38
Perfect cube
3
27
39
Perfect cube
4
64
40
Perfect cube
5
125
41
Perfect cube
6
216
42
Perfect cube
7
343
43
Perfect cube
8
512
44
Perfect cube
9
729
45
√2
1.41
46
√3
1.73
47
√6
2.45
48
√7
2.65
49
√8
2.83
50
√10
3.16
51
√5
2.24
52
Bases of 2
53
Bases of 3
54
Bases of 4
55
Bases of 5
56
57
58
59
60
61
62
63
64
65
66
67
68
69
|a+b| relation with |a|+|b|
This is always true:
|a+b|≤|a|+|b|
## Footnote
When |a+b|=|a|+|b|, this means:
* One or both quantities are 0
Or
* Both quantities have the same sign.
70
|a-b| relation with |a|-|b|
This is always true:
|a-b|≥|a|-|b|
## Footnote
When |a-b|=|a|-|b|, this means:
* The **second quantity is 0**
Or
* Both quantities have the same sign **and the absolute value of |a-b| is greater than or equal to absolute value of |a|-|b|.**
71
# Translation
is
=
72
# Translation
was
=
73
# Translation
has been
=
74
# Translation
more
+
75
# Translation
years older
+
76
# Translation
years younger
-
77
# Translation
less
-
78
# Translation
times
x
79
# Translation
less than
-
80
# Translation
fewer
-
81
# Translation
as many
x
82
# Translation
factor
x
83
# Translation
of
x
84
Price per item
(Total cost)/(Number of items)
85
Profit
Total revenue - Total cost
or
Total revenue - [Total fix costs + Total variable costs]
86
Simple interest
Principale x Rate x Time
87
Compound Interest
## Footnote
A: Future value
P: Principale
r: rate of interest
n: number of times per year interest is compounded
t: times in years
88
Linear growth formula
## Footnote
Fn: Final growth
p: initial value
n: n (th) growth period
k: constant increase during each period
89
# Formula
Rate - Time - Distance
90
# Formula
Average rate
91
# Formula
Converging/Diverging Rate
92
# Formula
Round-Trip Rate
93
# Formula
Catch-Up Rate
94
# Formula
Catch-Up and Pass
95
# Formula
Combined worker
96
# Translation
Percent of
"Percent of" means to multiply a given percent by a given value
97
# Translation
What percent of
98
# Translation
Percent less than
99
# Translation
Percent greater than
100
# Translation
x is n percent of y
101
# Formula
Percent change
102
Number of members in either set
| A or B
#(A or B) = #(A) + #(B) - #(A and B)
103
Three circle venn diagram equations
104
# In three circle venn diagram
What is the total # of unique members?
| When the unique items is known
#[**A only**+**B only**+**C only**] + [#**(A and B) only**) + #**(B and C) only** + #**(A and C) only**] + #[**(A and B and C)**] + #[**Neither A nor B nor C**]
105
# In three circle venn diagram
What is the total # of unique elements?
| When the unique items is unknown
#in (**Group A**) + #in (**Group B**) +#in (**Group C**) ***-*** #in (**Groups of exactly two**) ***- 2*** #in (**Group of exactly three**) + #in (**Neither**)
106
# In three circle venn diagram
Where is only A
107
# In three circle venn diagram
Where is A and B and C only
108
# In three circle venn diagram
Where is neither A nor B nor C
109
# In three circle venn diagram
Where is intersection of Group B and Group C
110
# In three circle venn diagram
Where is A and B only
#(A and B) only = #(A and B) - #(A and B and C)
111
Defecit
| ˈdefəsət
an excess of expenditure or liabilities over income or assets in a given period
| کسری بودجه
112
Profit and Cost expression
%profit = 100 x (profit/cost)
113
Profit Margin
114
The Avg is 30, it would go up by 50
What is the new Avg?
30 + 50 = 80
115
Quadrupeled
| kwäˈdro͞opəld
x 4
116
If a ≤ x ≤ b and c ≤ y ≤ d what is the Max value of xy
will be largest amount amount among *_ac_*, *_ad_*, *_bc_* and *_bd_*
117
If a ≤ x ≤ b and c ≤ y ≤ d what is the Min value of xy
will be smallest amount among *_ac_*, *_ad_*, *_bc_* and *_bd_*
118
... we know the sign of the variable
119
Evently spaced sets
* {4, 5, 6, 7, 8, 9, 10, 11}
* {3, 5, 7, 9, 11}
* {5, 10, 15, 20, 25, 30}
120
Counting the number of integers in a set of consecutive integers (inclusive)
Highest number - Lowest numbers + 1
121
Counting the number of multiples in a set of consecutive integers (inclusive)
122
Average (Arithmatic mean) in a set of consecutive integers
123
Weighted Average Equation
124
Boundaries of a weighted average
The weighted average of two different data points will be closer to the data point with the greater number of observations or with the greater weighted percentage.
125
Median
When a set of numerically ordered, the median is the value in the middle of the arranged set.
126
Calculate the Median with. an Odd # of Terms
127
Calculate the Median with. an Even # of Terms
128
Mean = Median
In any evently spaced set, the mean of the set is equal to the median of the set.
***EXCEPT*** this situation: {1, 2, 4, 5}
129
Mode
The mode is the number that appears most frequently in a data set.
130
Range of sequence
= Highest number in a set - Lowest number in a set
131
Standard deviation range
**High value** = mean + x(sd)
**Low value** = mean - x(sd)
132
Two important Standard Deviation rules
133
Standard deviation = Zero
All data points are the same
134
Avoide your fucking careless mistakes
| Never tag it as mastered you idiot!
1. **Read carefully, word-by-word, slow down, in data sufficiency use the stem**
2. Place more **focus** when checking the **beginning** of your working!
3. **Estimate the accuracy** of your final answer!
4. Do not 🚫 get excited too soon! **Double-check** your work: After answering a question, go back and review your answer to make sure it makes sense and that you didn't make any mistakes.
5. **Correctly select** your final answer
6. Within the solving:
* Write **large, neat, and clear**.
* Write out the math you’re doing on **both sides of the equation every time** you simplify.
* Every time you **simplify or reduce**, think through exactly what you’re doing and **why it works**.
* **Don't try to do too much at once**. If you’re translating a word problem into math, you don’t have to translate the whole thing into a single, complex equation. It’s just as good to create two simpler equations, then combine them later.
* **Don't miss the units**.
* **One step at a time**.
## Footnote
If your answer shows that a boy runs 2.4km in 2mins or the price of a pencil is $2000 or the bank interest rate is 80% etc, you should guess that something is off. Time to check your work again!
135
Vowels
a, e, i, o, and u
| Total 26 (5 Vowels, 21 consonants)
136
Equilateral
| ˌiːkwɪəlætərəl
137
Acute triangle
| əˈkjuːt
All angels are less than 90º
## Footnote
مثلث حاده
138
Obtuse triangle
| əbˈtuːs
One angle is more than 90º
## Footnote
مثلث منفرجه
139
Quadrilateral
| ˌkwɒ:drɪəˈlætərəl◂
چهارضلعی
140
Rhombuse
لوزی
141
Decagon
ده وجهی
142
Unified border
143
# Data sufficiency
The length of a certain rectangular solid is 13. If the dimensions of the solid are all integers, what is its volume?
1. The area of one of the faces of the rectangular solid is 52.
2. The area of one of the faces of the rectangular solid is 12.
From statement two, we know that two of the edges of the rectangular solid must multiply together to equal 12.
This provides three different options for these two edges:
12 and 1, 6 and 2, and 3 and 4.
However, each of those options, along with the given length of 13, will give us the same volume of 156 (12 × 1 × 13 = 156, 6 × 2 × 13 = 156 and 3 × 4 × 13 = 156).
Statement two is sufficient to answer the question.
144
Pentagon
| penˈtægən
145
Octagon
| ˈɑːktəgɑːn
Octagon = 8 sides
146
Minimum perimeter of a rectangle ...
Given a rectangle with a fixed area, the rectangle with minimum perimeter is a Square
147
Maximum area of a rectangle .... (with constant perimeter)
Given a rectangle with a fixed perimiter, the rectangle with maximum area is a square
148
Area of a Hexagon with side “s”
Hexagon = 6 sides
149
Quant
Combination
| ˌkɒ:mbɪəˈneɪʃən
Order does **Not** matter
| ترکیب
150
The basic combination formula:
151
Permutation
| ˌpɜːrmjʊˈteɪʃən
Order **Does** matter.
| جایگشت
152
Basic permutation formula:
153
Permutation formula for indistinguishable items:
154
Number of ways to arrange a set of items in a circle:
155
The basic probability formula:
156
The probability of a sample space ...
**Must** sum to 1.
157
Probability of complementry events:
P(A) + P(Not A) = 1
158
Probability of A and B
159
Probability of A or B
## Footnote
Mutually exclusive: متقابلا منحصر بفرد
مثال: حیوانی که انتخاب می کنی یا سگ هست یا گربه
A and B cannot both occur
Not Exclusive: غیر منحصر بفرد
مثال: بیسکوییت برداریم یا بیسکوییت شکلاتی از بین بیسکوئیتا و آبنباتا
160
Probability of choosing at least one object:
1 - P(none of these items occur)
161
Acute angle
| əˈkjuːt
162
Right angle
163
Straight angle
| streɪt
164
Obtuse angle
| əbˈtuːs
165
360º angle
166
Supplementary angles
| ˌsʌplɪəˈmentəri◂
167
Exterior angle of a triangle ...
168
Parallel lines intersected by a Transversal
## Footnote
trænsˈvɝː.səl
169
Area of a triangle
170
Triangle inequality theorem
In **any** triangle, the sum of the length of two sides of a triangle is greater than the length of the third side.
* for each triangle with a, b, and x sides, **a-b < x < a+b**
171
Pythagorean theorem:
172
Pythagorean triples:
**3** - **4** - **5** Right triangle
**5** - **12** - **13** Right triangle
173
Isosceles Right triangle
| aɪˌsɒsəliːz ˈtraɪæŋgəl
174
The ratio of the sides of a 45-45-90 right triangle
175
The hypotenuse of a 45-45-90 right triangle is the diagonal of a square
176
The ratio of the sides of a 30-60-90 right triangle
177
The Area of an equilateral triangle
178
Cutting equilateral triangle in half
179
The Parallelogram
| ˌpærəˈleləgræm
180
Area and Perimeter of a rectangle
181
The longest side segment of a rectangle
182
Perimeter and Area of a Square
183
The Trapezoid
| ˈtræpɪəzɔɪd
184
Interior angles of a polygon ...
The sum of the interior angles of a polygon = (n-2) x 180, where n is the number of sides in the polygon.
185
Exterior angles of any polygon ...
186
Arc length and Sector Area
187
Inscribed angle in Circles
188
Right Triangle inscribed in a Circle
189
Regular Polygon inscribed in a Circle
When a regular polygon inscribed in a circle, the polygon devides the circle into arcs of equal length.
190
The Area of a Circle Ring
191
Surface Area and Volume of a Cylinder
192
Surface Area and Volume of a Cube
193
Surface Area and Volume of a Rectangular Solid
194
The Diognal of a Cube
| daɪˈægənəl
195
The Diagonal of Rectangle Solid
196
The coordinate plane
197
Slope of a line:
198
The Slop-Intercept equation:
199
Parallel lines ...
Parallel lines have the **same slope** but **different y-intercepts**, and as a result, the lines never intersect.
200
Perpendicular lines ...
| ˌpɜːrpənˈdɪkjʊələr◂
The slope of two perpendicular lines are negative reciprocals; negative reciprocals multiply to -1
201
# Coordinate Geometry
Distance formula:
202
# Coordinate Geometry
Midpoint formula:
203
# Functions and Sequences
Range
The set of all numbers a function generate (i.e. the set of all outputs) is called the range of function.
204
# Functions and Sequences
Domain
The set of all numbers a function use (i.e. the set of all inputs) is called the domain of function.
205
√8
2.83
