GRE Formulas

a/b is greater than c/d if

ad is greater than bc

how do you square a fraction?

square the numerator and the denominator

complete this common quadratic identity: x²-y²

= (x-y)(x+y)

complete this common quadratic identity: (x+y)²

= x² + 2xy + y²

complete this common quadratic identity: (x-y)²

x² -2xy + y²

4x²-100=

(2x-10) (2x+10)

(odd) + (odd) =

even

(even) + (even)=

even

(odd) + (even) =

odd

(odd) - (odd)=

even

(even) - (even) =

even

even x even =

even

even x odd=

even

odd x odd =

odd

even / odd

even

odd / odd

odd

even / even

even or odd

if y divides evenly into x, we say y is a ______ of x

factor

a multiple of a number is the

product of that number and any integer

what is the quotient and remainder formula?

x/y = quotient + remainder / y

how do you find the LCM of a number?

find the prime factorization of each integer and take the highest power of any repeat prime factors and multiply it by all non-repeated prime factors

what is the LCM of 24 and 60?

24= 2³ x 3

60= 2² x 3 × 5

2³ x 3 × 5= 120

how do you find the GCF?

find the prime factorization of each number and of the repeated prime factors multiple those with the smallest exponent

√a x √b =

√ab

true or false: you can split up the radical when performing additional

FALSE

√(x+y)² =

|x+y|

(a^a)(a^b) =

a^a+b

x^a / x^b =

x^a-b

(x^a)^b

x^ab

2¹⁰ + 2¹¹ + 2¹²

2¹⁰ (1+2+2²)= 2¹⁰ (7)

(1/5)² ___ (1/5)

less than

(-1/5)² ____ (-1/5)

greater than

| a + b| ___ |a| + |b|

less than or equal to

|a-b| ___ |a| - |b|

greater than or equal to

what is the simple interest formula?

principal x rate x time

time is expressed in years

what is the compound interest formula?

A = P x (1+ r/n)^nt

what is the linear growth formula?

F= kn + p

what is the rate-time-distance formula?

distance = rate x time

time =

distance / rate

rate =

distance / time

average rate =

total distance / total time

what is the converging/diverging rate formula?

distance _{object 1} + distance _{object 2} = total distance _{objects 1 and 2}

what is the round-trip rate formula?

distance₁ = distance₂

what the is the catch-up rate formula?

distance₁ = distance₂

what is the catch up and pass formula?

time = change in distance / change in rate

what is the rate-time-work formula?

rate x time = work

how do you combine ratios?

find the least common multiple of the given values of the common variable

what is the percent less formula?

final = (1- % less than / 100) x initial

what is the percent greater than formula?

final = (1+ %greater than / 100) x initial

how would you set up this equation: x is n percent less than y

x= (100-n / 100) x y

what is the percent change formula?

(final value - initial value / initial value) x 100

what is the average formula?

average = sum of all terms / number of terms

what is the “formula” to find the number of integers in a set of consecutive integers?

highest number - lowest number + 1

what is the formula for counting the number of multiples of an integer in a set of consecutive integers (inclusive)

(highest multiple - lowest multiple / given number) + 1

how do you find the average (arithmetic mean) in a set of consecutive integers?

highest number + lowest number / 2

what is the equation for the weighted average?

(data point 1) (frequency 1) + (data point 2) (frequency 2) / total frequency of data poitns

how do you calculate the median with an odd number of terms?

n+1 / 2 position

how do you calculate the median with an even number of terms?

it is the average of the values at the n/2 and (n+2) / 2

when does the mean = median

in an evenly spaced set

what is the formula for the range?

highest number in set - lowest number in set

what is the standard deviation range?

high value = mean + x (sd)

low value = mean - x (sd)

what is the formula for the number of members in either set: (# A or #B)

= (#A) + (#B) = (#A and B)

how do you find the sum of a range of integers specified by being evenly divisible by a certain number?

first find the number of terms by finding the highest number and subtract the lowest number, divide by the number and add one

then find the average of highest and lowest term divisible by the number and divide by 2

multiply the results

what is the overlapping set formula when the number of unique items is known?

total # of unique members = #[A only + B only + C only] + #(A and B only) + # (A and C only) + (B and C only) + (# A and B and C) + #(Neither A nor B nor C)

what is the overlapping set formula when the number of unique items is unknown?

total # of unique elements = # in (Group A) + # (Group B) + # (Group C) - # in (Groups of exactly 2) - 2 (# in Groups of exactly three) + (# in neither)

what is the formula for combinations?

_nC_k = n! / (n-k)!k!

what is the formula for permutations?

_nP_k= n!/(n-k)!

what is the permutation formula for indistinguishable items?

P = n! / r₁! r_n!

what is the formula for circular arrangements?

(k-1)!

what is the basic probability formula?

favorable # of outcomes / total # of outcomes

the probability of a sample space must sum to

1

what is the formula for complementary events?

P(A) + P(not A) = 1

what is the probability of A and B if they are independent events?

P(A and B)= P(A) x P(B)

what is the probability of A and B if they are not independent events?

P(A and B) = P(A) x P(B|A)

what is the probability of A or B if they are mutually exclusive events?

P(A or B) = P(A) + P(B)

what is the probability of A or B if they are not mutually exclusive?

P(A or B) = P(A) + P(B) - P(A and B)

what is the probability of “choosing at least 1 object?”

P (at least 1 item occurs) = 1 - P(none of these items occur)

supplementary angles

angles that sum to 180 degrees

what is the formula for the are of a triangle?

A= ½ bh

what is the triangle inequality theorem?

in any triangle, the sum of the lengths of any two sides of the triangle is greater than the length of the third side

what is the formula for the pythagorean theorem?

a² + b² = c²

what is the ratio of the sides of a 45-45-90 triangle?

x: x: x√2

what is the ratio of the sides of a 30-60-90 triangle?

x: x√3: 2x

what is the area of of an equilateral triangle?

area= s²√3 /4

when you cut an equilateral triangle into two triangles, it creates two

30-60-90 triangles

what is the area of a parallelogram?

area = base x height

what is the formula for the perimeter of a rectangle?

2(length) x 2(width)

what is the formula for the diagonal of a rectangle?

diagonal = √l² +w²

what is the formula for the perimeter of a square?

4s²

what is the formula for the area of a trapezoid?

(base₁+base₂) x height / 2

what is the formula to find the sum of the interior angles of a polygon?

(n-2) x 180

what is the area of a hexagon?

(3√3)s²/2

what are the proportions we can use to find the arc length of a circle?

central angle / 360 = arc length / circumference

what is the formula for the circumference of a circle?

2πr or πd

what are the proportions we can use to find the sector area of a circle?

central angle / 360 = sector area / area of the circle

an inscribed angle is what proportion of the central angle?

half the measure of the central angle

what is the area of a circular ring (the outer portion)?

π[R₂²- R₁²]

what is the volume of a cylinder?

πr²h

what is the formula for the surface area of a cylinder?

2πrh + 2πr²