GMAT Quant Flashcards
(111 cards)
1
Q
Rule for length of triangle sides (all triangle)
A
The length of a third side will always be between the sum and difference of the other two sides
2
Q
Pythagorean theorem
A
For right triangles - a^2 + b^2 = c^2
3
Q
Common right triangles
A
3-4-5
6-12-13
8-15-17
4
Q
Icosoles right triangle
A
Degree angles: 45-45-90
Side length: 1 - 1 - SR2
5
Q
30 -60 - 90 triangle
A
1/2 of an equilateral triangle
Side length: 1 - SR3 - 2 (short, long, hypot)
6
Q
Diagonal of a square
A
D=side length x SR2
7
Q
Main diagonal of a cube
A
D = side length x SR3
8
Q
Similar triangles
A
Have same angles, therefore have same side ratios
9
Q
Area of an equilateral triangle
A
(side length^2 x SR3)/4
10
Q
Circumference
A
C=Dπ or C=2rπ
11
Q
Diameter
A
D=2π
12
Q
Area of a circle
A
A=πr^2
13
Q
Area of a cylinder
A
A=2πr^2+ 2πrh
14
Q
Volume of a cylinder
A
V=πr^2h
15
Q
Divisibility properties (1-9)
A
2 = ends in 2 or 0 3= sum of digits is divisible by 3 (ex. 72) 4 = divisible by 2 twice OR last 2 digits divisible by 4 6 = divisible 2 and three 8 = divisible by 2 three times OR the last three digits divisible by 8 9 = sum of digits divisible by 9
16
Q
Prime numbers under 50
A
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
17
Q
Remainders
A
Dividend = quotient x divisor + remainder
18
Q
Find GCF
A
Multiply common primes (use prime columns if numbers are large)
19
Q
Find LCM
A
Multiply non-common primes (use prime columns if numbers are large)
20
Q
odd ± even
A
odd
21
Q
odd ± odd
A
even
22
Q
even ± even
A
even
23
Q
odd x odd
A
odd
24
Q
even x even
A
even
25
odd x even
even
26
even / even
even, odd, or non-int
27
even / odd
even or non-int
28
odd / even
non- int
29
odd / odd
odd or non-int
30
Sum of two primes
Always even unless one of the primes is 2
31
3!`
6
32
4!
24
33
5!
120
34
6!
720
35
7!
5040
36
8!
40320
37
Perfect squares
Have an odd number of total factors
38
Adding, multiplying, and subtracting remainders
Can be done, just correct for excess at the end
39
Factoring large numbers (finding number of factors)
Count total occurrences of each prime factor, including 0, add 1 to each of them, and then multiply together
40
Glue method
For combinatorics, when things can't happen (e.g., people won't sit next to each other)
1) calculate normal probability w/o constraints
2) imagine constrainers are glued (i.e., 1 person not 2), then calculate new number of total possibilities
3) double number in #2 because they could be "glued" either way
4) subtract step #1 from #1
41
Multiplying decimals
Ignore decimals at first, and multiply normally. Then add decimals back in OR move decimals same number of spaces in opposite directions (if multiplying very large and very small number)
42
Dividing decimals
If decimal is only in the dividend, bring it straight up to the answer and divide normally BUT if the decimal is in divisor, shift the decimal in both dividend and divisor until divisor is a whole number, then bring the decimal up
43
Decimal raised to a power or the root of a decimal
Rewrite as an integer times 10 to a power, and then distribute the exponent to the integer and the power of 10
Number of decimal points on a squared decimal is 2x the number of decimals in the original
44
Reciprocals
If 2 numbers are reciprocals, when multiplied by each other they equal 1
45
Percent change
Change in value / original value
46
New percent
New value / original value
47
Compound interest formula
CI = P (1+ (r/n))^nt
```
r= rate in decimalr form
n= number of times per year
t = number of years
```
But more useful to think of these as successive percents problems instead of applying formulas
48
Solving ratios with 2+ parts
Use unknown multiplier OR create a common term
49
FDP 1/8
.125, 12.5%
50
FDP 1/6
.166666 , 16.7%
51
FDP 3/8
.375, 37.5%
52
FDP 5/8
.625, 62.5%
53
FDP 5/6
.833333, 83.3%
54
FDP 7/8
.875, 85.7%
55
FDP 7/4
1.75, 175%
56
Fraction form preferred for...
Multiplication
57
Decimal or percent form preferred for...
Addition
Subtraction
Estimating numbers
Comparing numbers
58
DS question asks for relative value of 2 pieces of any ratio, then you need...
Any statement that give the relative value of either of the pieces of the ratio
59
DS question asks for concrete vale of one element of a ratio, then you need...
Both concrete and relative value of at least 1 element
60
Repeating decimals
Solve through long division OR if the denominator can be multiplied to be only "9s" then the numerator is the repeating decimal
61
Deluxe pythagorean theorem
Used to find diagonal in a 3D shape: l^2 + w^2 + h^2 = d^2
62
If given an inequality with more than two parts...
Break down into multiple inequalities, each with just one inequality sign, and solve for potential values, then plug potential answers back into original equation
63
If given equation where one side is an absolute value...
Make two different equations, and set one positive and one negative. Then plug solutions into original equation to test it
64
Exterior angles of a triangle
Sum of non-adjascent angles
65
Slope of a line
y1-y2 / x1-x2
66
Find distance between 2 points on a coordinate plane by...
Creating an invisible triangle and using the pythagorean theorem
67
Prime factoring large numbers
Add all digits, and find the prime factors of the sum of the digits
68
Applying exponents to negative numbers...
If negative is not in parentheses: apply exponent, then negative sign (number will always be negative)
If negative is in parens: then include it in the calculation
69
When multiplying terms with exponents...
Add the exponents if the bases are the same
70
When dividing terms with exponents...
Subtract the exponents if the bases are the same
71
Negative exponents...
Are fractions (ex: a^-2 = 1/a^2)
72
Raising an exponent to another power...
Multiply the exponents
73
Difference of squares
x2 - y2
74
Multiply or divide ineqaulity by a negative...
Flip the sign
75
Standard deviation
1) Find difference between each measurement and the mean
2) Square differences
3) Add squared differences
4) Divide sum by the number of measurements - this quotient will equal the variance
5) Find the positive square root of the variance
76
Sum of interior angles of a polygon
180 (n-2)
77
Fractional exponents are the same as...
Roots equal to the value of the fraction (e.x. 1/2 exponent is same as taking square root)
78
If an exponent is outside parentheses...
Apply it to everything inside the parens
79
When finding the maximum area of a polygon...
Squares usually give max area
80
When finding the minimum perimeter of a polygon..
Squares usually have minimum primeter
81
Finding max. area when given two sides of a parallelogram or triangle...
Make the two sides be perpendicular to each other, and calculate area
82
To find how many times a parabola touches the X axis...
Set y=0 and solve by factoring or solving the quadratic equation
83
Steps to find information about perpendicular lines...
1) Find slope of line 1
2) Find slope of line 2 (negative recip)
3) Find midpoint on given line (use coordinates given, or find midpoint and then figure out missing)
4) Substitute midpoint coordinates into y=mx+b formula to find y-intercept
84
Negative exponents
(1/n^x)
85
Anything raised to a power of 0
1
86
Negative rules for exponents
Unless - is in ( ), the exponent doesn't distrubute to the - sign
87
Fractional exponents
Numerator = power to raise base to
Denominator= which root to take
Ex: 25^3/2 = square root of 25^3
88
If 2+ exponents with the same base are added or subtracted....
Can factor out a common term
89
Even exponents _____ the sign of the base
Hide the sign, as they usually have 2 answers
90
Odd exponents _____ the sign of the base
Keep the sign, and only have one solution
91
If exponents are on both sides of an exponential equation....
Rewrite the equation so bases or exponents are the same, and then eliminate
92
Fraction raised to a negative exponent
Take reciprocal of fraction and raise to a positive exponent
93
Can only simplify roots via combination and separation using...
Multiplication and division NOT addition and subtraction
94
First step in quadratic equations
Set to 0 before solving
95
Components of quadratic equations
Variable raised to 2nd power, variable raised to first power, 2 solutions
96
Square root of quadratic equations
Can be done if one side is a perfect square, but must consider both positive and negative solutions
97
x^2-y^2
(x+y)(x-y)
98
Sum of squares: x^2+2xy+y^2
(x+y)^2
99
Difference of squared: x^2-2xy+y^2
(x-y)^2
100
Making an equation not a fraction
Multiple whole side by LCD
101
Can't multiply or divide inequalities with variables unless...
know the sign of the # the variable stands for
102
In compound inequalities, you must apply all actions to...
All parts of the inequality
103
Can add inequalities as long as sign is facing the same way, but...
Must add 2nd inequality twice???
104
Combination problems with variables
Combine equations to isolate the combination first, don't try to solve for each variable
105
If a variable combination problem results in quadratics...
Answer in DC problems is E because there could be two answers
106
Raising any fraction to a power...
Brings it closer to 0 on the number line
107
Any positive proper fraction raised to a power >1 wil...
Result in a number smaller than the original fraction
108
Any positive proper fraction raised to a power between 0-1 will...
Result in a number larger than the original fraction
109
VIC problems
1) Replace variables in question with numbers (small primes are good choices), 2) Calculate answer using chosen numbers, 3) Plug same numbers into answer choices to get matching answers
110
2+ variable in 2+ absolute value expressions (usually lack constants)....
Use conceptual approach, not easy to solve with algebra
111
One variable, at least one constant, and 1+ absolute value expressions...
Solve with algebra
