Quant Flashcards
(x + y)2 =
x2 + y2 + 2xy
(x - y)2 =
x2 + y2 - 2xy
(x + y)(x - y) =
x2 - y2
(x - y)
/
(y - x) = ?
and x =/ y
-1
List the prime numbers under 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
LCM (x,y) * GCF (x,y) =
LCM = Least Common Multiple
GCF = Greatest Common Factor
LCM (x,y) * GCF (x,y) = xy
LCM (x,y) = xy / GCF (x,y)
GCF (x,y) = xy / LCM (x,y)
How to tell if a number is divisible by 4:
If the last 2 digits are divisible by 4
How to tell if a number is divisible by 6:
If the number’s digits add up to 3, AND it’s an even number
How to tell if a number is divisible by 8:
If the last 3 digits are divisible by 8 (has to be even)
How to tell if a number is divisible by 9:
If the sum of the number’s digits is divisible by 9
How to tell if a number is divisible by 11:
If the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is divisible by 11
How to tell if a number is divisible by 12:
If it’s divisible by both 3 and 4
Formula for division
x/y =
x/y = Quotient + remainder/y
Prime numbers from 10 to 19:
11, 13, 17, 19
0! =
0! = 1
3! =
6
4! =
24
5! =
120
6! =
720
7! =
5,040
8! =
40,320
9! =
362,880
10! =
3,628,800
In decimals, 1/6 =
0.166666
In decimals, 1/7 =
0.142857 142857 etc.
In decimals, 1/8 =
0.125
In decimals, 1/9 =
0.11111111 etc.
In decimals, 1/11 =
0.0909090909 etc.
Prime numbers from 0 to 10:
2, 3, 5, 7
Prime numbers from 20 to 29:
23, 29
Prime numbers from 30 to 39:
31, 37
Prime numbers from 40 to 49:
41, 43, 47
Prime numbers from 50 to 59:
53, 59
Prime numbers from 60 to 69:
61, 67
Prime numbers from 70 to 79:
71, 73, 79
Prime numbers from 80 to 89:
83, 89
Prime numbers from 90 to 99:
97
Square root of 2?
1.41
Square root of 3?
1.73
Square root of 5?
2.24
Square root of 6?
2.45
Square root of 7?
2.65
Square root of 8?
2.83
Square root of 10?
3.16
14 times 14 =
196
15 times 15 =
225
16 times 16 =
256
17 times 17 =
289
18 times 18 =
324
19 times 19 =
361
3^4 =
81
3^5 =
243
3^6 =
729
5^4 =
625
6^3 =
216
6^4 =
1296
7^3 =
343
7^4 =
2401
8^3 =
512
9^3 =
729
If |x + y| = |x| + |y| then…
x and y must have the same sign (positive or negative)
Why do you have to be careful about multiplying both sides of an inequality by an unknown variable?
If it is negative, the inequality sign will have to be reversed.
Which sign does this phrase translate to:
“up to”
<= (less than or equal to)
Which sign does this phrase translate to:
“at least”
>= (greater than or equal to)
Which sign does this phrase translate to:
“no more”
<= (less than or equal to)
Which sign does this phrase translate to:
“at most”
<= (less than or equal to)
Which sign does this phrase translate to:
“as few as”
>= (greater than or equal to)
Formula for calculating number of positive integers that will divide evenly into a number?
N = (e1 + 1)(e2 + 1)(e3 + 1)
e1 is the exponent of first prime number etc
Any product of three consecutive integers is divisible by…
3! = 6
If a 2 digit integer x has a tens digit of a and a units digit of b, then the formula for x in the terms of a and b is x = :
x = 10a + b
Formula for the sum of consecutive numbers:
(n/2) * (first number + last number)
Surface Area of a cube formula:
Surface Area = 2(Length * Width) + 2(Length * Height) + 2(Height * Width)
13 * 3 =
39
13 * 4 =
52
13 * 5 =
65
13 * 6 =
78
13 * 7 =
91
13 * 8 =
104
13 * 9 =
117
13 * 11 =
143
13 * 12 =
156
13 * 14 =
182
13 * 15 =
195
14 * 6 =
84
14 * 7 =
98
14 * 8 =
112
14 * 9 =
126
14 * 11 =
154
14 * 12 =
168
16 * 7 =
112
Units digit pattern for exponents of numbers ending in 2:
2, 4, 8, 6 repeated
- 2
- 4
- 8
- 6
- 2
- 4
etc
Units digit pattern for exponents of numbers ending in 3:
3, 9, 7, 1 repeated
List the perfect squares up to 225:
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
List the perfect cubes up to 1000:
0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
Permutation formula?
nPk = n! / (n−k)!
or
Box and fill method (just multiply the boxes)
Formula for the area of an equilateral triangle:
area = (a² * √3)/ 4
Area of a trapezoid?
Area = ((base1 + base 2) * height) / 2
The sum of the interior angles of a polygon =
(n - 2) * 180
where n = the number of sides of a polygon
So triangle = 180
rectangle = 360
pentagon = 540
etc.
The measure of any one interior angle in a regular polygon =
180 * (n - 2)
/
n
where n is the number of sides of the polygon
The interior angles of a hexagon sum to:
720 degrees
One interior angle of a regular hexagon measures:
120 degrees
The area of a regular hexagon =
(3√3 * s2)
/
2
or 2.6s2
The exterior angles of any polygon sum to:
360 degrees
Three-part circle ratio:
central angle / 360
=
arc length / circumfrence
=
area of sector / area of circle
Extended Pythagoras Theorem:
(for finding diagonals in 3D shapes, e.g. a room)
a2 = b2 + c2 + d2
A central angle (of a circle) is always ____ the inscribed angle
A central angle (of a circle) is always twice the inscribed angle
The slopes of two perpendicular lines are negative reciprocals and therefore multiply to:
The slopes of two perpendicular lines are negative reciprocals and therefore multiply to -1.
When point (3, 2) is reflected over line y = x, it becomes:
(2, 3)
(x, y) becomes (y, x)
When point (x, y) is reflected over line y = -x, it becomes:
(-y, -x)
When point (x, y) is reflected over line y = b, it becomes:
(x, 2b - y)
E.g. (5, -2) becomes (5, 4) when it’s reflected over the line y = 1
When point (x, y) is reflected over line x = a, it becomes:
(2a - x, y)
E.g. when reflected over line x = 2, (5, -2) becomes (-1,-2)
When (x, y) is reflected over some point (a, b), it becomes:
(2a - x, 2b - y)
E.g. when reflected over point (2, 1), (5, -2) becomes (-1, 4).
Distance between two points =
Distance between two points =
[(x2 - x1)2 + (y2 - y1)2 ] 0.5
Midpoint of a line segment =
( (x1 + x2) / 2 , (y1 + y2) / 2 )
The 2 major concerns fo the domain of a function are:
1) we can’t take the square root of a negative number
2) we aren’t allowed to divide by zero
What is the vertical line test?
If a graph is the graph of a function, then any vertical line drawn can only intersect the graph at exactly one point or at no points.
Arithmetic sequence formula:
an = a1 + (n - 1)d
d = is the common difference
The sum of the first n terms of an arithmetic sequence is:
Sn = (n/2) * (a1 + an)
Geometric sequence formula:
an = a1 * rn-1
r = the common ratio
Addition rule for Mutually Exclusive Events:
P(A or B) =
P(A or B) = P(A) + P(B)
Addition Rule for Events That Are Not Mutually Exclusive
P(A or B) =
P(A or B) = P(A) + P(B) - P(A and B)
2n + 2n =
2n + 2n = 2n+1
3n + 3n + 3n =
3n + 3n + 3n = 3n+1
4n + 4n + 4n + 4n =
4n + 4n + 4n + 4n = 4n+1
When |a + b| = |a| + |b|, this means:
One or both quantities are 0; or
Both quantities (a and b) have the same sign
When |a - b| = |a| - |b|, this means:
b is zero; or
Both quantities have the same sign and the absolute value of |a - b| is greater than or equal to the absolute value of |a| - |b|
Profit Equation:
Profit =
Profit = Total Revenue - (Total Fixed Costs + Total Variable Costs)
a is what percent of b?
Formula:
(a/b) * 100
“x is n percent less than y”
Formula:
x = [(100 - n) / 100] * y
(A or B) =
Overlapping Sets:
Number of Members in Either Set
(A or B) = #(A) + #(B) - #(A and B)
Overlapping Sets
When the number of unique items is known
Total # of unique members =
[A only + B only + C only] +
Total # of unique members =
+ #[Neither A nor B nor C]
Overlapping Sets
When the number of unique items is Unknown
Total # of unique members =
Total # of unique elements =
in (Group A) + # in (Group B) + # in (Group C) -
in (Groups of exactly two) -
2[# in (group of exactly three)] +
in (Neither)
Number of ways to arrange a set of items in a circle:
(k - 1)!
k = number of objects to be arranged in circle
