GRE Math
nearest .1 percent
means rounded to tenths .1578 = 15.8%
(34x)(98x) > (274x)(3280)
remember to add exponents when multiplying numbers with the same base
5 less than a number
x - 5
Solve for what is 12 percent of 25
(12/100) x 25 = 3
Exponent Rules
(X^b)(Y^b) = (XY)^b (X^b/Y^b) = (X/Y)^b (X^n)(X^m) = X^n+m X^n/X^m = X^n-m MA DS PM i.e. 15^15 - 15^14 = 15^14 (15) -1 (lower number, then subtract higher exponent) -A fraction raised to a higher exponent results in a lesser number
"Causal"
- look at premise and conclusion -Only cause, no other cause, not reversed
"at least one" Q's?
1 - P(zero) EX. What's the Probability of getting at least one 6 in 6 tosses of s die 1 - no 6's (all numbers besides 6) 1 - (5/6)^6
"at least one" Q's?
1 - P(zero) i.e. Prob of at least one 6 in 6 tosses = 1 - zero 6's. 1 - (5/6)^6
mile to feet
1 mile = 5280 feet
Triangle Properties
1) the sum of any two side lengths will ALWAYS be greater than the third side length 2) if 90 degree angle inside circle then diameter 3) sides correspond to their opp angles if right angle then isosceles triangle
30:60:90 45:45:90 Proportions
1, root 3, 2 1, 1, root 2 - think as Half of equilateral
30:60:90 triangles
1, root 3, 2 think as Half of equilateral
Plug in numbers when
1. "How much" "how many" "What is the value of" - And answer choices in ascending/descending order 2. list answers and start trial spreadsheet with choice C
A fair die with sides numbered 1, 2, 3, 4, 5, and 6 is to be rolled until a number greater than 4 first appears. What is the probability that a number greater than 4 will first appear on the third or fourth roll?
1. 1 - 2/6 = 2/3 Probability of not landing above 4 2. 2/3×2/3×1/3 + 2/3×2/3×2/3x1/3 (P3) or (P4) 20/81
How many numbers between 1 and 100 (inclusive) are divisible by 10 or 7?
1. 100/10 = 10 100/7= 14.3 = 14 2. 24 - 1 (because 70 overlaps)= 23 **Dont forget about overlap
How many numbers between 1 and 100 (inclusive) are divisible by 3 or 2?
1. 100/3 = 33 100/2= 50 2. 83 - 16 = 67 -Multiply 2x3= 6/100 to get numbers that are divisible by both 2 and 3
It's ok to multiply bases of common exponent
2^6 x 3^6 = 6^6
Surface Area of a Cylinder
2πr² + 2πrh
Common right triangle proportions
3:4:5 6:8:10 5:12:13 The length of one side of triangle must be less than the sum of other sides and greater than the difference of other sides -instead of Pie just approximate to 3
original whole before percent increase/decrease
After decreasing 5 percent, the population is now 57,000. What was the original population? .95x=57000
The only people in an auditorium are sophomores, juniors, and seniors. The ratio of the number of sophomores to the number of juniors in the auditorium is 4 to 3. The ratio of the number of juniors to the number of seniors in the auditorium is 5 to 7. The total number of people in the auditorium is 448. How many juniors are in the auditorium?
find common multiple in proportion 147 set up eqn w/ variables
hour to seconds
1 hour = 3600 seconds
At least one
1-P(none)
How many different positive integer factors does (64)(81)(125) have?.
1. 64 = 2^6 81 = 3^4 125 = 5^3 2. Take exponent!! and add one so..... (6+1)(4+1)(3+1) 3. Then multiply (6+1)(4+1)(3+1) = 7x5x4 7 x 5 x 4 = 140 - remember 0 is an integer
Area of a sector
Area of a Sector = (central angle/360) x πr²
Laws of Even and Odd Numbers
Ex. If m is even and n is odd, is the product of mn odd or even? even + even = even odd + odd = even even + odd = odd even * even = even odd * odd = odd even * odd = even
45 is what percent of 9?
45 = (n/100) x 9
Quantity A Quantity B 518 + 100(5^16)/5^16 5^19
A 1. divide by 5^16 2. 5^2 + 100 = 25 + 100 B 1. 5^19/5^16 - keep an eye out for ways to simplify by pausing before answering and thinking about the best approach
box and whisker plot
A graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median
Standard Deviation (SD)
A measure of variability that indicates the average difference between the scores and their mean.
prime number
A whole number that has exactly two factors, 1 and itself. 2,3,5,7,11, 13, 17, 19, 23 and 29. - 1 is not prime!!!!
Trapezoid formula
A=1/2h(b1+b2) or half the average of bases
Compound Interest Formula
A=P(1+(r/n))^nt p=principle amount r=rate n=times componded t=years i.e If 10,000 is invested at 8 percent annual interest, compounded semiannually, what was the balance after one year? (10,000)x(1+(.08/2))^(1x2) = 10,816
Probability problems where probabilities are multiplied
Ex. If two students are chosen at random to run an errand from a class with 5 girls and 5 boys, what is the probability that both students chosen will be girls? (5/10)(4/9) = (2/9
Quantitive comparison
FROZEN F=fractions R= repeats O= one Z= zero E= extremes N= negatives -use these numbers to plug in
Numbers to test
FROZEN FR: fractions (both positive and negative) O: one and negative none ZE: zero N: negatives
How many unique ways are there to arrange the letters in the word CANNON?
For these divide out repeats because 3 n's 6!/3!
Formula for solving a GROUP problem involving BOTH/NEITHER
Group 1 + Group 2 + Neither - Both = Total
How to find the NEW AVERAGE when a number is added or deleted
I.e. Nike's avg score after 4 tests is 80. If he scores 100 on the fifth tests what's the new avg?
How to find the COMMON multiple of two numbers?
I.e. What is the least common multiple of 28 and 42? 28= 2x2x7 42=2x3x7 LCM=2x2x3x7= 84
How to find average of consecutive numbers?
I.e. average of all integers from 13 to 77? same as avg of 13 and 77
How to use the ORIGINAL AVERAGE and NEW AVERAGE to figure out WHAT WAS ADDED OR DELETED
I.e. the average of 5 numbers is 2. After one number is deleted the new average is -3. What number was deleted? Original sum: 5x2= 10 New sum: 4x(-3)= -12 Number deleted: 10-(-12)= 22 difference of averages
Simple Interest Formula
Interest = Principal X Rate X Time A = P(1+rt) i.e. If 12,000 is invested at 6 percent simple annual interest, how much interest is earned after 9 months? (12,000)x(.06)x(9/12)=$540
Factor
Include 1, number itself, and and positive and neg negative
P(A or B)
P(A) + P(B) - P(A and B)
Probability of A or B
P(A) + P(B) - both
Probability A and B
P(A) x P(B)
Given Event A
P(a) + P( not A) = 1
then the area of field N is greater than the area of field M by what amount?
Pay attn to language!! If factor then 4 If amount then 4-1 = 3
How to find the SUM OF CONSECUTIVE NUMBERS
Sum = (average) x (number of terms) i.e. What is the sum of the integers from 10 through 50, inclusive? average: 10 + 50 / 2 = 30 number of terms: 50 - 10 + 1 = 41 sum: 30 x 41 = 1230
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
How to count consecutive numbers
The number of integers from A to B inclusive is B-A+1.
percent increase/decrease
When computing a percent increase, the base is the smaller number. When computing a percent decrease, the base is the larger number. In either case, the base is the initial number, before the change. amount of increase/ base
A lab technician needs a 40% solution of a certain chemical for an experiment, but the lab that she works in only has a 20% solution and a 50% solution in stock. In what ratio should she mix the 20% solution with the 50% solution in order to obtain the 40% solution that she needs?
Work backwards with answer options - If the lab technician used 100 ml of 20% (20 ml of chemical) and 200 ml of 50% (100 ml of chemical), she would have a solution that contained 20 ml + 100 ml = 120 ml of chemical out of a total 100 ml + 200 ml = 300 ml of solution. 120 ml is indeed 40% of 300 ml, so this is the correct choice.
Toni makes apple pies for the local bakery. When Toni works with an assistant, she produces 60% more apple pies and works 20% fewer hours. Having an assistant increases Toni's output of apple pies per hour by what percent?
insert numbers to work with -100%
If x^2 + 25y^2 = 274 and y=21/x, then what is the value of (x - 5y)^2 ?
look for relations/ substitutions b/w equations 64
Permutation Formula
nPr = n!/(n-r)! - How many ordered samples of 5 cards can be drawn from a deck of 52 cards without replacement? ex. number of 4 member subsets of s ex. How many three-digit integers can be created using only 5 distinct digits? -often schedules, lists, arrangements, orders
Lines u and v form 4 angles that each measure 90 degrees. The points (−4, 7) and (8, 23) are on line u. The points (−68, −16) and (−40, t) are on line v. What is the value of t ?
perpendicular lines, plug into point slope form
At Deb's Deli, a customer may choose either a sandwich and a salad or a sandwich and a soup for the lunch special. There are 5 choices of sandwich, 4 choices of salad, and 3 choices of soup. How many possible lunch special combinations can be ordered?
so a customer can choose 5 × 4 = 20 different sandwich/salad specials and 5 × 3 = 15 different sandwich/soup specials, for a total of 20 + 15 = 35 lunch specials. The correct answer is 35.
random selection
subjects are selected randomly from a larger group (1/10)(/9....
Combination Formula
{10/1}*{9/2}*{8/3}*{7/4}={5040/24}=210 nCr = n!/r!(n-r)! - Imagine the social club has 10 different members and you're asked, "How many groups of 3 members can you choose from the social club to make a party committee?" - usually groups, teams, comittees i.e. from a group of 4 men and 6 women, 2 people are randomly selected. What is the probability that the committee members will be women? - numbers on bottom How many different committees of 7 people can be formed from a group of 10 people?
The number of square units in the area of circle O is equal to 16 times the number of units in its circumference. Which of the following are diameters of circles that could fit completely inside circle O ?
πr2=16(2πr)
