GMAT Math Memorize Number Properties & Formulas

=7^3

343

Pythagorean Triples (lengths)?

3:4:5 -- 5:12:13 -- 7:24:25

Another way to write cube root 5

5^(1/3)

Probability that A and B will both happen?

A*B (Multiply both probabilities)

Probability that A or B will happen?

A+B (Add both probabilities)

Adding or subtracting fractions with the same denominator

Add or subtract the numbers on top and keep the same denominator

Area of a parallelogram?

Base * Height

What is the difference between a permutation or a combination?

Combinations don't care about the order of the problems

Two fractions that equal each other with one variable how do you solve for x?

Cross multiply

How do you find the slope of a line?

Difference in the y-coordinates over the difference in the x coodinates

How do you unfactor a quadratic equation? (x+2)(x+5)

FOIL X^2+7x+10

Dividing Fractions

Invert (reciprocal) the second fraction and multiply

If you raise a negative number to an even power, what happens to the number?

It becomes positive

If you raise a negative number to an odd power, what happens to the number?

It gets smaller

If you raise a positive fraction that is less than 1 to a power, what happens to the fraction?

It gets smaller

Adding and Subtracting Decimals

Line up the decimal points and proceed as usual

Dividing Decimals

Move the decimal to the right on both numbers until there is nothing to the right of the decimal

Adding or subtracting fractions with different denominators

Multiply both fractions to get a common denominator add or subtract as usual

Problem that asks you to choose a # of items to fill specific spots, when each spot is filled from a different source?

Multiply the # of choices for each of the spots

Permutations: single source, order matters

Multiply the # of choices for each of the spots--but the number of choices keeps getting smaller

Permutations: single source, order matters BUT only for a selection

Multiply the # of choices for each of the spots--but the number of choices keeps getting smaller, stop when all the places are taken

Exponents - Raising a power to a power

Multiply the exponents (4^3)^2 = 4^(3*2) = 4^6

Multiplying Fractions

Multiply the numerators and put the product over the product of the denominators

Does (x^2 + y^2 + z^2)/(x^2 + y^2) = z^2?

NO

Does x^2 + x^3 = x^5?

NO

Does x^6 - x^2 = x^4?

NO

Order of operations

PEMDAS (parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)

How do you tell if it's a permutation or combination?

Permutations ask for "arraingements" Combinations ask for "Groups"

How do you find the mode of a set of numbers?

Pick the # that occurs most frequently

Distance Formula?

Rate * Time = Distance (Hint: Draw a chart)

Right Isosceles triangle (lengths)?

Side, Side, Side^2

Combinations: single source, order doesn't matter

Start with the number of permutations, that is the numerator(top). The Denominator is the number of combinations (eg 4*3*2*1)

What happens if you multiply or divide both sides of an inequality by a negative number?

The direction of the inequality symbol changes

Any number to the negative power (y) is equal to?

The reciprocal of the same number to the positive power (y). (eg 3^-2 = 1/(3^2) = 1/9)

4/0 =

Undefined

Distributing Exponents

When several #s are inside parenthesis, the exponent outside the parentheses must be distributed to all the #s within (4y)^2 = ((4)^2)((y)^2) = (4^2) * (y^2) = 16y^2

Odds that at least one thing will happen?

Will = 1 - Won't

Odds that something doesn't happen?

Won't = 1 - Will

The solvability rule

You must have at least as many distinct equations as you have variables

Exponents - Multiplying numbers with same base

add their exponents (6^2 *6^3 = 6^5)

Key to percent increase/decrease

amount of increase/original amount = x/100 (Then cross multiply to find x)

How do you find the median of a set of numbers?

arrainge #s from least to greatest and take the middle number or the average of the two middle #s

even + even =

even

even x even =

even

even x odd =

even

odd + odd =

even

When is a number divisible by 6?

if it is divisible by both 2 and 3 (318 is because it is even and the sum of 3+1+8 is divisible by 3)

When is a number divisible by 4?

if the number formed by it's last 2 digits is divisible by 4 (3,028 is because 28 is divisible by 4)

When is a number divisible by 3?

if the sum of its can be divided evenly by 3 (216, is because 2+1+6 is divisible by 3)

0/1 =

0 (any fraction with 0 on top is 0)

Area of a triangle?

(b*h)/2

Factor x^2-y^2

(x+y)(x-y)

Factor x^2+2xy+y^2

(x+y)^2

Factor x^2-2xy+y^2

(x-y)^2

Rules for "Plugging in" for cosmic problems

1)Pick numbers that make sense for the variable in the problem 2)Find an answer using those numbers to get the "target answer" 3)plug your #s into the answer choices to see which choice equals the target answer

Rules for "Plugging in" the answer choices

1)Start with choice "c" plug that into the problem to see if it works 2)If "c" is to small go larger 3) if "c" is too big try smaller 4)If you don't know try them all

Circumference of a circle?

2pr

multiplying decimals

ignor decimal points and multiply the two numbers, then count the digits to the right of the decimal points in the original numbers and place the decimal so there are the same number of digits to the right of the decimal

Any number to the first power is?

itself

Basic probability formula?

number of outcomes you want/total number of possible outcomes

even + odd =

odd

odd x odd =

odd

Any number to the 0 power is?

one (1)

Area of a circle?

pr^2

Work Problems?

simmilar to distance but ... Think how much of the job can be done in one hour (as a fration of the whole).

Exponents - Dividing numbers with same base

subtract the bottom exponents from the top exponents (3^6 / 3^2 = 3^4)

how do you find the range of a set of numbers?

subtract the smallest number from the greatest number

30:60:90 Right Triangle (Lenghts)

x:x^(1/3):2x

Unfactor (x+y)^2

x^2+2xy+y^2

Unfactor (x-y)^2

x^2-2xy+y^2

Unfactor (x+y)(x-y)

x^2-y^2

Equation for a line?

y=mx+b where b is the y-intercept (the point which crosses the y-axis) m is the slope of the line, and x & y are the coordinates of some point on that line