Memorize these for Math GRE
How would you calculate compound interest?
divide the percent by the number of times it is compounded per year to get the rate multiply the number of times it is compounded per year by the number of years to get the exponent
How do you find the Least common multiple of two or more big numbers
do the prime factorization of each element Line the values up so they each have their own column What is the highest power of 2? 2^4 Highest power of 3? 3^1 Highest power of 5? 5^2 Multiply each value 2^4 * 3^1 * 5^2
When asked to find the time where certain things occur at the same time during a given time frame what would you do?
find the LCM between the elements
Overlapping/combined ratios if the ratio to apples to oranges is 3:4 and the ratio of pears to oranges is 6:5 what is the ratio of apples to pears?
find the common term i.e oranges pick the LCM of the common item and multiply each ratio so the common term is the same you are left with a 3 part ratio of each item
What trick would you apply here? weighted average problem A group consists of both men and women. The average height of the women is 66 inches, and the average height of the men is 72 inches. If the average height of all the people in the group is 70 inches, what is the ratio of women to men in the group?
find the middle number W66______70_______72M 4. 2 2 : 4 W : M
What do you have to be careful of when doing the ratio switch trick?
if they are asking for the number at the start or the number after the changes. If they are asking for the number after the change, you must apply the change given in the word problem.
How would you find the simple interest rate?
interest = P*R*T
How do you find the rate of a single worker
multiply number of workers by time ex; 20 workers can build a house in 30 days one worker can build a house in 600 days
In a pie chart, the degree of the central angle of the sector is equal to...
n percent of 360 Ex: 10% of 360 is 36 degrees
What is the combination formula
n!/r!(n-r)! where n is the total and r is what you want
What is the sum of a list formula?
n(a1 + an) / 2 n = number of terms (be careful inclusive vs exclusive) an = last term
What should you be careful of in min/max inequalities?
negative * negative = positive two negative numbers multiplied together could give you a larger number than if you were to just assume x and y were positive
use the combination formula when
order does not matter. ie groups of students
What if they dont give you distance or time for average speed?
pick a distance that is a multiple of the speeds and solve for time.
if an integer is divisible by both 8 and 15 then the integer must also be divisible by which of the following?
prime factorize 8 and 15 to get the "ingredients" of said number. Prime factorize the answer choices until you find the one that has the same ingredients
How many factors does 999 have?
prime factorize 999 add 1 to the exponents multiply the exponents ONLY
if p= 5^6-3^4 what is the sum of the UNIQUE prime factors of p
recognize difference of squares do the multiplication of the squares you get 134 and 116 prime factorize these two numbers: 2,67,2,2,29 add the UNIQUE factors: 2+67+29
rt < 0 < -r Which is bigger? the value of t or 0 what is your thought process?
rt is < 0 so one of them has to be negative the only way for -r to be greater than 0 is if r is negative Thus we can conclude that t must be positive
What should be your first thought when presented with a double inequality?
simplify but doing the same thing to each value ex: -6 < 3x <9 divide by 3 -2 < x < 9
what must you do when given an absolute value equation or inequality?
solve for both the positive and negative number
When the gap is expanding you.. traveling in same direction overtaking -->
subtract the speeds to find the expansion rate
For any CONSECUTIVE LIST what is the median
the mean (median = mean)
How is the prime factorization related to perfect square
the prime factorization of a number must have all even exponents to be a perfect square
If danya paints takes 4 hours to paint 1 wall and grace takes 3/2 hours to paint one wall, what is each of their rates?
the reciprocal 1/4 and 2/3
What should you remember about standard deviation and the median?
they dont have anything to do with eachother
What should you remember about standard deviation and the range?
they dont have anything to do with eachother unless the range is 0. In this case, the SD is 0.
Tips for sequence questions aka find the nth term
translate to words x+1 = next term x-1 previous term x=current term you can pretend any term is the current term
Whenever you see a percent but no total, what should you do?
use 100
What are the side lengths of a 30-60-90 triangle?
x, x times squareroot of 3, and 2x
What are the side lengths of a 45-45-90 triangle?
x, x, x times squareroot of 2
The average of Kim's three tests is 500. Kim took a 4th test and her average is now 550. What is the score of kims 4th test?
For each average you are given: Multiply the average by the number of terms(tests) to get the sum. subtract the sums to get her 4th test score
When should use a double matrix?
For populations in which each member has two criteria associated with it How many toys are both green and blue? How many students are female and minorities?
What is the venn diagram formula?
Group 1 + Group 2 - Both + Neither = Total
If susan invests $1000 in an account that yields 5% annual, compounding quarterly, then how much does she have at the end of 6 years?
ID the quarterly percent: 5/4 = 1.25% ID the multiplier for the quarterly percent: 1.0125 How many times total does it get compounded? 4 times a year * 6 years = 24 times A = 1000(1.0125)²⁴
Given a chart, how do you find the median?
Order the percents from smallest to largest Lets say you have 9 percent values, the 5th largest percent will be your median
What is the probability of A and B occurring?
P(A and B) = P(A) * P(B)
What is the probability the spinner will land on pink OR red? Mutually Exclusive: cannot happen simultaneously
P(A or B) = P(A) + P(B) P(pink or red)=P(pink)+P(red)
What is the probability of drawing a black card OR a ten in a deck of cards? Mutually Inclusive: can happen simultaneously
P(A or B) = P(A) + P(B) - P(A and B) P(black or ten)= P(10)+P(black) − P(black and ten)
You are given a graph The amount of ____ is what percent less/greater than the amount of _____ What formula would you use?
Percent change = final - initial / initial
You drove 20 mph to work. You turned around and went back at 30 mph. What is your average speed?
Pick 60 as your common distance. Plug values into D=RT 60 = 20T 60 = 30T plug into total distance / total time 60+60 miles / 3+2 hours = 34mph
What is the formula for the amount of work that can be done when two machines/people work together?
RateA + RateB = Rate of A and B
When the gap is shrinking you... traveling towards eachother
add the speeds to find the shrink rate
If the signs are in the same direction you can ___ inequalities If they arent the same you must ____ them first a > d and b<c what is larger b+d or a+c?
add; rearrange rearrange: same as a > d and c > b add: a+c > d+b
how do you find the highest common factor of two or more big numbers
Do what you would do for LCM Line the values up in their own column Pick the SMALLEST values (if to the first power do not include) Multiply them together
A certain high school team has only sophomores, junior, and seniors. The ratio of sophomores to seniors is 2:3. The ratio of juniors to seniors is 5:6. How many sophomores are there? What approach would you take?
combine ratios using a common term
How do you find the area of an equilateral triangle?
cut it in half to form a 30 60 90 and apply the side rules
The average of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?
(10/3)_______70_______90 200/3 20 Average must be 10/3
What is the median of all the positive odd integers less than 75?
(73+1) / 2 = 37
length of arc
(angle / 360) x Circumference of circle
You are asked to find the median of a list or sequence and theres too many to do the cross off method. what should you do?
(biggest number + smallest number) / 2
How do you find the sum of all interior angles of a regular polygon?
(n-2)*180
How do you find the interior angle of a regular polygon?
(n-2)*180 / n
How to find vertex of parabola
-b/2a
2^5
32
In the smith house, the probability of one out of four children getting goal is 1/3. What is the probability that AT LEAST one child will get coal?
1 - (Probability of what you dont want)^number of children
How do you find the probability of neither A or B occuring?
1 - (probability of A or B)
Square root of 2 is approximately
1.4
The square root of 3 is approximately...
1.7
find the mean of all integers from 10-99
10+99/2 = 54.9 median = mean
how many edges does a cube have
12
5^3
125
2^4
16
Surface area of a rectangular solid
2(lw+lh+wh)
What are the percentages of the normal distribution curve? What to do they correspond to?
2, 14, 34 50 34 14 2 percentiles
Square root of 5 is approximately
2.2
What is the probability for you to choose two red cards in a deck of cards?
26/52 * 25/51
Surface Area of a Cylinder
2πr² + 2πrh
The numbers in a certain set have a SD of 5. If I add 3 to all the numbers in the set what is the SD?
5
if there are 3 red beads and 5 green beads in a bag, what is the probability of picking 2 green beads?
5/8 * 4/7
How many different ways can you arrange the word REDDIT?
6!/2! need to take into account the repeated letters using the factorial
5^4
625
Surface area of a cube formula
6s^2
Area of a sector
Area of a Sector = (angle/360) x Area of a circle
How do you calculate average speed?
Average velocity = total distance / total time
you are given a quadratic inequality, what should you do? x^2 + 3 < 10
DO NOT factor right away get zero on one side of the inequality Now you can factor Solve for X BUT this is not your answer REMEMBER the actual answer has to be between your x values to make the inequality true
How would you find the median of a frequency graph?
Divide the number of people surveyed by 2 and find what category that number falls in ex: if 24 people were surveyed then the median will be the average of the 12th/13th number
When positive integer N is divided by positive integer P, the quotient is 18 with a remainder of 7. When N is divided by (P+2), the quotient is 15 and the remainder is 1. What is the value of N? What formula should you use?
Dividend = Divisor*Quotient + remainder
If given percentiles and asked to compare, you cannot conclude anything unless the question states that it us under normal distribution
If given percentiles and asked to compare, you cannot conclude anything unless the question states that it us under normal distribution
You are given a word problem with a sequence of percent increases and decreases over a period of time. You are asked to find the percent change for the time period. What would you do?
Multiply the multipliers of the percent increases/decreases Subtract that number from 1 to get the percent change
You are given a word problem with a sequence of percent increases and decreases and the initial value. How would you find the final price?
Multiply the multipliers of the percent increases/decreases and the initial value
What could be the sum of 3 consecutive integers?
The answer must be a multiple of 3
If you are taking the square root of something to undo the exponent you need to consider
The negative option (esp in comparison)
Volume of a Cylinder Formula
V=πr²h
How do you identify a ratio switch question?
When the ratio changes from one thing to another when something is added or subtracted
What is the units digit of 57^123
Write out the powers of the units digit in the base. In this case it's 7. Keep writing then our til you see a pattern. Determine the period of the pattern (usually 4). Extend the pattern to 123 starting from 120 because it's a multiple of 4
What is the ratio switch trick Philip and Arif have sweets in a ratio of 6:11 if arif gives phillip 5 sweets the ratio is now 13:21. How many sweets does phillip have?
Write the first ratio in a fraction with x's 6x/11x apply the adjustments given in the problem 6x+5/11x-5 (remember giving/taking affects both parties) set this expression equal to the new ratio 6x+5/11x-5 = 13/21 cross multiply to find x sub in x to find the number they each have
Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon combines an amount of the two cereals in a single bowl of mixed cereal that is 65% fiber. If the bowl contains a total of 12 ounces of cereal, how much of the cereal, in ounces, is Fiber X?
X55______65______70M 10. 5 5. 10 X : M 5/15 * 12 = 4
