GMAT Quant Flashcards
Rule for length of triangle sides (all triangle)
The length of a third side will always be between the sum and difference of the other two sides
Pythagorean theorem
For right triangles - a^2 + b^2 = c^2
Common right triangles
3-4-5
6-12-13
8-15-17
Icosoles right triangle
Degree angles: 45-45-90
Side length: 1 - 1 - SR2
30 -60 - 90 triangle
1/2 of an equilateral triangle
Side length: 1 - SR3 - 2 (short, long, hypot)
Diagonal of a square
D=side length x SR2
Main diagonal of a cube
D = side length x SR3
Similar triangles
Have same angles, therefore have same side ratios
Area of an equilateral triangle
(side length^2 x SR3)/4
Circumference
C=Dπ or C=2rπ
Diameter
D=2π
Area of a circle
A=πr^2
Area of a cylinder
A=2πr^2+ 2πrh
Volume of a cylinder
V=πr^2h
Divisibility properties (1-9)
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
Prime numbers under 50
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Remainders
Dividend = quotient x divisor + remainder
Find GCF
Multiply common primes (use prime columns if numbers are large)
Find LCM
Multiply non-common primes (use prime columns if numbers are large)
odd ± even
odd
odd ± odd
even
even ± even
even
odd x odd
odd
even x even
even
odd x even
even
even / even
even, odd, or non-int
even / odd
even or non-int
odd / even
non- int
odd / odd
odd or non-int
Sum of two primes
Always even unless one of the primes is 2
3!`
6
4!
24
5!
120
6!
720
7!
5040
8!
40320
Perfect squares
Have an odd number of total factors
Adding, multiplying, and subtracting remainders
Can be done, just correct for excess at the end
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
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
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)
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
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
Reciprocals
If 2 numbers are reciprocals, when multiplied by each other they equal 1
Percent change
Change in value / original value
New percent
New value / original value
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
Solving ratios with 2+ parts
Use unknown multiplier OR create a common term
FDP 1/8
.125, 12.5%
FDP 1/6
.166666 , 16.7%
FDP 3/8
.375, 37.5%
FDP 5/8
.625, 62.5%
FDP 5/6
.833333, 83.3%
FDP 7/8
.875, 85.7%
FDP 7/4
1.75, 175%
Fraction form preferred for…
Multiplication
Decimal or percent form preferred for…
Addition
Subtraction
Estimating numbers
Comparing numbers
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
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
Repeating decimals
Solve through long division OR if the denominator can be multiplied to be only “9s” then the numerator is the repeating decimal
Deluxe pythagorean theorem
Used to find diagonal in a 3D shape: l^2 + w^2 + h^2 = d^2
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
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
Exterior angles of a triangle
Sum of non-adjascent angles
Slope of a line
y1-y2 / x1-x2
Find distance between 2 points on a coordinate plane by…
Creating an invisible triangle and using the pythagorean theorem
Prime factoring large numbers
Add all digits, and find the prime factors of the sum of the digits
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
When multiplying terms with exponents…
Add the exponents if the bases are the same
When dividing terms with exponents…
Subtract the exponents if the bases are the same
Negative exponents…
Are fractions (ex: a^-2 = 1/a^2)
Raising an exponent to another power…
Multiply the exponents
Difference of squares
x2 - y2
Multiply or divide ineqaulity by a negative…
Flip the sign
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
Sum of interior angles of a polygon
180 (n-2)
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)
If an exponent is outside parentheses…
Apply it to everything inside the parens
When finding the maximum area of a polygon…
Squares usually give max area
When finding the minimum perimeter of a polygon..
Squares usually have minimum primeter
Finding max. area when given two sides of a parallelogram or triangle…
Make the two sides be perpendicular to each other, and calculate area
To find how many times a parabola touches the X axis…
Set y=0 and solve by factoring or solving the quadratic equation
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
Negative exponents
(1/n^x)
Anything raised to a power of 0
1
Negative rules for exponents
Unless - is in ( ), the exponent doesn’t distrubute to the - sign
Fractional exponents
Numerator = power to raise base to
Denominator= which root to take
Ex: 25^3/2 = square root of 25^3
If 2+ exponents with the same base are added or subtracted….
Can factor out a common term
Even exponents _____ the sign of the base
Hide the sign, as they usually have 2 answers
Odd exponents _____ the sign of the base
Keep the sign, and only have one solution
If exponents are on both sides of an exponential equation….
Rewrite the equation so bases or exponents are the same, and then eliminate
Fraction raised to a negative exponent
Take reciprocal of fraction and raise to a positive exponent
Can only simplify roots via combination and separation using…
Multiplication and division NOT addition and subtraction
First step in quadratic equations
Set to 0 before solving
Components of quadratic equations
Variable raised to 2nd power, variable raised to first power, 2 solutions
Square root of quadratic equations
Can be done if one side is a perfect square, but must consider both positive and negative solutions
x^2-y^2
(x+y)(x-y)
Sum of squares: x^2+2xy+y^2
(x+y)^2
Difference of squared: x^2-2xy+y^2
(x-y)^2
Making an equation not a fraction
Multiple whole side by LCD
Can’t multiply or divide inequalities with variables unless…
know the sign of the # the variable stands for
In compound inequalities, you must apply all actions to…
All parts of the inequality
Can add inequalities as long as sign is facing the same way, but…
Must add 2nd inequality twice???
Combination problems with variables
Combine equations to isolate the combination first, don’t try to solve for each variable
If a variable combination problem results in quadratics…
Answer in DC problems is E because there could be two answers
Raising any fraction to a power…
Brings it closer to 0 on the number line
Any positive proper fraction raised to a power >1 wil…
Result in a number smaller than the original fraction
Any positive proper fraction raised to a power between 0-1 will…
Result in a number larger than the original fraction
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
2+ variable in 2+ absolute value expressions (usually lack constants)….
Use conceptual approach, not easy to solve with algebra
One variable, at least one constant, and 1+ absolute value expressions…
Solve with algebra
