Quant - 1 Flashcards
Reciprocal x
rɪˈsɪprəkəl
1/x
Prime numbers less than 100
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
Finding number of factors in a particular number
Step 1: Find the prime factorization of the number
Step 2: Add 1 to the value of each exponent. Then multiply these results.
Finding the LCM
Lowest Common Multiple
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.
Finding the GCF
Greatest Common Factor
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.
LCM (x,y) * GCF (x,y)
x * y
Perfect square 1 to 15
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Perfect cube 1 to 10
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
Which one is bigger
X, X2, √X
0 < X < 1
X2 < X < √X
Prime numbers less than 10
2, 3, 5, 7
Prime numbers between 10 to 20
11, 13, 17, 19
Prime numbers between 20 to 30
23, 29
Prime numbers between 30 to 40
31, 37
Prime numbers between 40 to 50
41, 43, 47
Prime numbers between 50 to 60
53, 59
51 is divisible by 3, 17
Prime numbers between 60 to 70
61, 67
Prime numbers between 70 to 80
71, 73, 79
Prime numbers between 80 to 90
83, 89
87 is divisible by 3, 29
Prime numbers between 90 to 100
97
91 is divisible by 7 and 13
Divisibility rule
2
if the ones digit is 0, 2, 4, 6, 8
Divisibility rule
3
Sum of all digits must divisible by 3
Divisibility rule
4
Last two digits must divisible by 4
Divisibility rule
5
Last digit is 0 or 5
Divisibility rule
6
It shoud both divisible by 2 and 3
Divisibility rule
8
Last three digits should divisible by 8
Divisibility rule
9
Sum of all digits should divisible by 9
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.
Trailing Zeros
Is the number of (2x5) pairs in prime factorization
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.
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 2s and 5s, or both
- 1/12=0.0833333…
- 1/20=0.05
Two consecutive integers
Will never share any prime factors. Thus, the GCF of two consecutive integers is 1.
Perfect square
11
121
Perfect square
12
144
Perfect square
13
169
Perfect square
14
196
Perfect square
15
225
Perfect cube
2
8
Perfect cube
3
27
Perfect cube
4
64
Perfect cube
5
125
Perfect cube
6
216
Perfect cube
7
343
Perfect cube
8
512
Perfect cube
9
729
√2
1.41
√3
1.73
√6
2.45
√7
2.65
√8
2.83
√10
3.16
√5
2.24
Bases of 2
Bases of 3
Bases of 4
Bases of 5
|a+b| relation with |a|+|b|
This is always true:
|a+b|≤|a|+|b|
When |a+b|=|a|+|b|, this means:
- One or both quantities are 0
Or - Both quantities have the same sign.
|a-b| relation with |a|-|b|
This is always true:
|a-b|≥|a|-|b|
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|.
Translation
is
=
Translation
was
=
Translation
has been
=
Translation
more
+
Translation
years older
+
Translation
years younger
-
Translation
less
-
Translation
times
x
Translation
less than
-
Translation
fewer
-
Translation
as many
x
Translation
factor
x
Translation
of
x
Price per item
(Total cost)/(Number of items)
Profit
Total revenue - Total cost
or
Total revenue - [Total fix costs + Total variable costs]
Simple interest
Principale x Rate x Time
Compound Interest
A: Future value
P: Principale
r: rate of interest
n: number of times per year interest is compounded
t: times in years
Linear growth formula
Fn: Final growth
p: initial value
n: n (th) growth period
k: constant increase during each period
Formula
Rate - Time - Distance
Formula
Average rate
Formula
Converging/Diverging Rate
Formula
Round-Trip Rate
Formula
Catch-Up Rate
Formula
Catch-Up and Pass
Formula
Combined worker
Translation
Percent of
“Percent of” means to multiply a given percent by a given value
Translation
What percent of
Translation
Percent less than
Translation
Percent greater than
Translation
x is n percent of y
Formula
Percent change
Number of members in either set
A or B
(A or B) = #(A) + #(B) - #(A and B)
Three circle venn diagram equations
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]
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)
In three circle venn diagram
Where is only A
In three circle venn diagram
Where is A and B and C only
In three circle venn diagram
Where is neither A nor B nor C
In three circle venn diagram
Where is intersection of Group B and Group C
In three circle venn diagram
Where is A and B only
(A and B) only = #(A and B) - #(A and B and C)
Defecit
ˈdefəsət
an excess of expenditure or liabilities over income or assets in a given period
کسری بودجه
Profit and Cost expression
%profit = 100 x (profit/cost)
Profit Margin
The Avg is 30, it would go up by 50
What is the new Avg?
30 + 50 = 80
Quadrupeled
kwäˈdro͞opəld
x 4
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
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
… we know the sign of the variable
Evently spaced sets
- {4, 5, 6, 7, 8, 9, 10, 11}
- {3, 5, 7, 9, 11}
- {5, 10, 15, 20, 25, 30}
Counting the number of integers in a set of consecutive integers (inclusive)
Highest number - Lowest numbers + 1
Counting the number of multiples in a set of consecutive integers (inclusive)
Average (Arithmatic mean) in a set of consecutive integers
Weighted Average Equation
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.
Median
When a set of numerically ordered, the median is the value in the middle of the arranged set.
Calculate the Median with. an Odd # of Terms
Calculate the Median with. an Even # of Terms
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}
Mode
The mode is the number that appears most frequently in a data set.
Range of sequence
= Highest number in a set - Lowest number in a set
Standard deviation range
High value = mean + x(sd)
Low value = mean - x(sd)
Two important Standard Deviation rules
Standard deviation = Zero
All data points are the same
Avoide your fucking careless mistakes
Never tag it as mastered you idiot!
- Read carefully, word-by-word, slow down, in data sufficiency use the stem
- Place more focus when checking the beginning of your working!
- Estimate the accuracy of your final answer!
- 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.
- Correctly select your final answer
- 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.
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!
Vowels
a, e, i, o, and u
Total 26 (5 Vowels, 21 consonants)
Equilateral
ˌiːkwɪəlætərəl
Acute triangle
əˈkjuːt
All angels are less than 90º
مثلث حاده
Obtuse triangle
əbˈtuːs
One angle is more than 90º
مثلث منفرجه
Quadrilateral
ˌkwɒ:drɪəˈlætərəl◂
چهارضلعی
Rhombuse
لوزی
Decagon
ده وجهی
Unified border
Data sufficiency
The length of a certain rectangular solid is 13. If the dimensions of the solid are all integers, what is its volume?
- The area of one of the faces of the rectangular solid is 52.
- 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.
Pentagon
penˈtægən
Octagon
ˈɑːktəgɑːn
Octagon = 8 sides
Minimum perimeter of a rectangle …
Given a rectangle with a fixed area, the rectangle with minimum perimeter is a Square
Maximum area of a rectangle …. (with constant perimeter)
Given a rectangle with a fixed perimiter, the rectangle with maximum area is a square
Area of a Hexagon with side “s”
Hexagon = 6 sides
Quant
Combination
ˌkɒ:mbɪəˈneɪʃən
Order does Not matter
ترکیب
The basic combination formula:
Permutation
ˌpɜːrmjʊˈteɪʃən
Order Does matter.
جایگشت
Basic permutation formula:
Permutation formula for indistinguishable items:
Number of ways to arrange a set of items in a circle:
The basic probability formula:
The probability of a sample space …
Must sum to 1.
Probability of complementry events:
P(A) + P(Not A) = 1
Probability of A and B
Probability of A or B
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
Probability of choosing at least one object:
1 - P(none of these items occur)
Acute angle
əˈkjuːt
Right angle
Straight angle
streɪt
Obtuse angle
əbˈtuːs
360º angle
Supplementary angles
ˌsʌplɪəˈmentəri◂
Exterior angle of a triangle …
Parallel lines intersected by a Transversal
trænsˈvɝː.səl
Area of a triangle
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
Pythagorean theorem:
Pythagorean triples:
3 - 4 - 5 Right triangle
5 - 12 - 13 Right triangle
Isosceles Right triangle
aɪˌsɒsəliːz ˈtraɪæŋgəl
The ratio of the sides of a 45-45-90 right triangle
The hypotenuse of a 45-45-90 right triangle is the diagonal of a square
The ratio of the sides of a 30-60-90 right triangle
The Area of an equilateral triangle
Cutting equilateral triangle in half
The Parallelogram
ˌpærəˈleləgræm
Area and Perimeter of a rectangle
The longest side segment of a rectangle
Perimeter and Area of a Square
The Trapezoid
ˈtræpɪəzɔɪd
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.
Exterior angles of any polygon …
Arc length and Sector Area
Inscribed angle in Circles
Right Triangle inscribed in a Circle
Regular Polygon inscribed in a Circle
When a regular polygon inscribed in a circle, the polygon devides the circle into arcs of equal length.
The Area of a Circle Ring
Surface Area and Volume of a Cylinder
Surface Area and Volume of a Cube
Surface Area and Volume of a Rectangular Solid
The Diognal of a Cube
daɪˈægənəl
The Diagonal of Rectangle Solid
The coordinate plane
Slope of a line:
The Slop-Intercept equation:
Parallel lines …
Parallel lines have the same slope but different y-intercepts, and as a result, the lines never intersect.
Perpendicular lines …
ˌpɜːrpənˈdɪkjʊələr◂
The slope of two perpendicular lines are negative reciprocals; negative reciprocals multiply to -1
Coordinate Geometry
Distance formula:
Coordinate Geometry
Midpoint formula:
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.
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.
√8
2.83
