GRE Math

How do you test if a large number is prime?

Divide this large number by 2,3,5,7. If it is not divisible by these numbers, then it is a prime number.

even divided by even

Even or odd integer or not an integer

X^7-4x^5

Factor out X^5. Example: X^5(X^2-4) and now factor as difference of two squares.

X^2=-5 is

Impossible since you can't square a number and get a negative.

compound interest

Interest paid on interest previously earned; credited daily, monthly, quarterly or semiannually

odd divided by even

Is never an integer

What kind of prime is 2?

It's the only even and it's the lowest prime.

Hotdogs are sold 12 to a pack and buns are sold 8 to a pack what is the least number you can buy to have perfect amount is what type of question?

LCM

Find GCF

Multiply the HIGHEST POWER OF EACH factor share by both factor trees

Percent Change Formula

Percent Change =(final value−initial value)/initial value×100

Circumference/diameter equals

Pi

real numbers

Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers.

When there is addition or subtraction in the numerator, we can

Separate it into more than one fraction: a+b/c = a/c +b/c and d-e/f = d/f - e/f. We can even do a+b/c+d = a/c+d + b/c+d

x/2+5/4 divided by x/3+3/2 (How do I simplify)

Simply by multiplying both sets of fractions by 12. It becomes 6x+15 divided by 4x +18

Algebraic simplification rule

We can combine like terms by adding and subtracting. Like terms must have same variable part. Only coefficient can be different.

56 is what percent of 800?

X= 56/800

$1,000 investment yields 5% annual compounded quarterly for six years.

You don't get 5% every quarter. You divide 5% by 4 to get .0125. Follow Compound interest formula: 1000 (1.0125)^4*6 = 1000 (1.0125)^24

a times b divided by c equals (ab/c)

a * b/c or b * a/c

When you factor out an x with no coefficient,

a 1 is still present. Ex: (X^9-X) with X factored out becomes X(X^8-1)

1 is not

a prime number

Every number not a prime is

a product of prime numbers

difference of squares

a^2 -b^2 = (a+b)(a-b)

In a proportion if a/b = c/d then

ad=bc

If a task can be completed in K minutes/hours/days/etc. then,

after 1 minute/hour/day/etc., 1/k of the job will be completed.

0 is

an even integer

quadratic expression

an expression in one variable with a degree of 2 written in the form ax^2+bx+c

Monomial

an expression with only one term

even divided by odd

can be even, can never be ODD or can be not an integer

Clearing fractions in a proportion

cross multiple Ex: a/b = c/d becomes ad=bc

A set of n consecutive integer will always contain one number

divisible by n Ex: (4,5,6) There are three numbers and 6 is divisible by 3.

Add or subtract likes (odd+odd or even + even) equals

even

even times even

even

Even times odd

even (factor of 2 will be in product)

If there is a single even number in a multiplication problem then the answer must be

even. Only ALL odd gives you an odd answer.

Any elements that are equally far from the median of an evenly spaced list...

have the mean value of the entire list.

Zero Product Property

if ab=0, then a=0 or b=0 or both equal 0

simple interest

interest paid on the principal alone

Adding the same number to the numerator and denominator

moves the fraction closer to 1. 3/5 + 6/6 = 9/11 which is closer to 1 7/4 + 1/1 = 8/5 which is also closer to 1. This means smaller than one moves right on the timeline and larger moves left on the timeline. 147/200 is smaller than 150/203 because 150/203 is now closer to 1. If we subtract same number from both then the effect is opposite.

odd divided by odd

never even, but can be ODD or a NON INTEGER

Add or subtract unlikes (odd+even) equals

odd

odd times odd

odd

A perfect square always has an _______ number of factors.

odd. For example, 6 is a factor of 36, but 6 is it's own factor pair, so there is only 1 six not two.

Any single digit repeating is that digit

over 9. Ex: .6666666... is 6/9

A negative squared is

positive

Primes are always

positive

Integers are

positive and negative whole numbers and zero

fraction = fraction

proportion

Rates are

ratios. ratio = ratio is a proportion

When adding two expressions with parentheses

removed the parentheses. (3x+4) + (5x-4) becomes 3x+4+5x-4

Bigger denominators make

small fractions

Two strategies for solving equations with two unknowns

substitution and elimination

quotient rule for exponents

subtract the exponents

If numerator gets bigger and denominator gets smaller

than the fraction gets bigger.

If x/y of a task can be completed in 1 minute/hour/day/etc. then,

the entire task will take y/x minutes/days/hours/etc. to complete. Ex: Pump A take 1/3 and Pump B take 1/2. Add them together by changing to 2/6+3/6=5/6. 6/5 equal hours to complete.

The GCF of a variable is

the lowest amount of the exponents. GCF of X to the 8th and X to the 12 is X to the 8th.

If we add a different number to the numerator and a different number to the denominator,

the new fraction will be closer to the fraction that was added to it. Ex: 1/8 + 2.5 = 3/13 which is closer to 2/5. 37/60 vs. 43/69. We added 6/9 which means the new fraction is closer to 2/3. Since 37/60 is less than 40/60 then 43/69 is bigger.

If a divisor is larger than a dividend, then...

the quotient = 0 and the remained equals the dividend. 5/12 = 0 r 5

One divided by any fraction equals

the reciprocal of that fraction. 1 divided by 3/7 equals 7/3

If you have a set of n consecutive integers and n is odd, then

the sum of the set of n consecutive integers will always be divisible by n. Ex. (4,5,6) have a sum of 15 which is divisible by 3. The quotient 5 is also the median of the set.

Legal Cancellation in Proportions.

vertical or horizontal. NO diagonal.

When subtracting two expressions with parentheses

you remove the parentheses but change the signs in the second ( ). (3x+4) - (5x-4) becomes 3x+4-5x+4

25x2-64y2

(25x-8y)(25x+8y)

9x2-16

(3x+4) (3x-4)

a2-b2

(a+b)(a-b)

x2 - 49

(x+7)(x-7)

x^6 - 16

(x3+4)(x3-4) Why? X^6 = (X^3)^2, so square root of X^6 is X^3

x2y2-1

(xy-1)(yx+1)

0 squared

0

1/9

0.111

1/8

0.125

1/7

0.142857 i.e. 0.143

1/6

0.1666...

1/3

0.3 repeating

3/8

0.375

5/8

0.625

2/3

0.666...

7/9

0.777...

5/6

0.8333 repeating

7/8

0.875

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

QC strategies

1. Add same # to both quantities 2. Subtract same # from both quantities. 3. Multiply or divide by the same positive #

Find LCM

1. Find GCF 2. GCF times what equals first number? 3. GCF times what equals second number? 4. Multiple GCF and the multipliers from steps 2 and 3.

Simplify a rational expression

1. First, the factors of the numerator and denominator must be found. Take a GCF out of the binomial in the numerator and break the denominator down into its factors as well. 2. Look at the the numerator and the denominator. Any factors that appear in both places can be cancelled out. 3. And there it is! The simplified rational expression.

Combining Ratios Ex: S:J=2:3 and J:SR = 5/6. S is what fraction of the whole?

1. Identify common element 2. Find equivalents of both. 3. List sharing common element. 4. Add list Ex: S:J=2:3 and J:SR = 5/6. The common element is j. J is 3 in one ratio and 5 in the other. The equivalent is 15. List: 10:15:18 Sum: 43 Answer: 10/43

How many factors in a number?

1. Prime factorization 2. List exponents of the factors (no exponent equals 1 in the list) 3. Add one to every number on the list 4. multiply the numbers together.

How many odd factors in a number?

1. Prime factorization 2. List exponents of the factors (no exponent equals 1 in the list) 3. Add one to every number on the list 4. multiply the numbers together. But ignore factors of 2.

How many even factors in a number?

1. Prime factorization 2. List exponents of the factors (no exponent equals 1 in the list) 3. Add one to every number on the list 4. multiply the numbers together. 5. Find the number of odd factors by redoing 1-4 but without factors of 2. 6. Subtract answer to step 5 from step 4.

Most quadratic equations will have

2 solutions, and the coefficient of x2 will equal 1 unless the numerical GCF can be factored from all terms.

Primes over 20 (There are 9 of them)

23, 29, 31, 37, 41, 43, 47, 53, 59

240 is 30% of what number?

240 = .3 * X

Why can't 15 be a factor of 96?

5 is a factor of 15, but it's not of 96. Any factor X must be composed of prime factors of the X.

1 squared

=1

Compound Interest Formula

A = p(r^y) P is principal, r is multiplier and y is years. If you invest 4,000 at 6% interest is compounded annually for 8 years: 4,000 (1.06)^8 It's 1.06 because you have to combine the initial investment with the interest amount.

Trinomial

A polynomial with three terms

Binomial

A polynomial with two terms

linear expression

An algebraic expression in which the variable is raised to the first power.

cubic expression

An expression with a degree (highest exponent) of 3.

Polynomial

An expression with multiple terms but only one variable.

When there is addition or subtraction in the denominator, we

CANNOT separate into more than one fraction. a/b+c cannot be turned into a/b + b/c