# GRE math

7 sequence after 3 terms 1/3, 2/3, 3/3 150/3= a whole number 150 starts at 4

1, -3, 4, 1,-3,4,1,-3,4,1,-3,4... In the sequence above the first 3 terms repeat without end. what is the sum of the terms in the sequence from the 150th to the 154th?

1993-1994

1991-1992 1992-1993 1993-1994 1995-1996 1997-1998

Practice test 3 question 18 (section 2) how many factors of 3 is 18^10 equal to 20

6 9 12 20 40

C

Among the 9,000 people attending a football game at College C, there were x students from College C and y students who were not from college C Quantity A: the number of people attending the game who were not students Quantity B: 9,000- x- y

C 5*60=300 minutes 300*60= 18,000 seconds 18,000/ 3= 6,000 6,000*2= 12,000 pages

For 5 hours, a photo copied at a constant rate of 2 pages every 3 seconds Quantity A the number of pages the photo copier copied in 5 hours Quantity B 12,000

E increase by the same amount in #'s (could not work this problem out with percents) find the sum of the current locations whichever is lowest is the one with the greatest % increase

If all five companies increase their number of foreign locations by 200 and decrease their number of U.S. locations by 50, which company will see the greatest overall percentage increase in its number of locations? A B C D E

white book pg 150 #3 c

QA the sum of the first 7 positive integers QB 7 times the median of the first 7 positive integers

11.12 q3 #1 inclusive 8-18 is 11

Quantity A The number of perfect squares between 50 and 350 Quantity B 10

1. √x2+y2 2. y-3

Simplify 1. √x^2+y^2 2. √(y-3)^2

D. difficulty (medium) plug in numbers

The line y = -3x + 4 passes through all of the following points EXCEPT: (0, 4) (1, 1) (2, -2) (3, -6) (4, -8)

E Number Properties Difficulty: medium * find lowest common multiple of 24 and 50 by prime factorization, then plug in that number for x once you find x you should be able to guess the answer

The positive integer x is divisible by 24 and 50. Each of the following must be an integer EXCEPT A. x/200 B. x/100 C. x/25 D. x/20 E. x/16

11.12 q3 #4 1-.7=.3 1-.9= .1 1-.8=.2 .3(.2)(.1)= .006 1-.006=.994

The probability that machine A operates properly is 0.7, the probability that machine B operates properly is 0.8, and the probability that machine C operates properly is 0.9. The operations of the machines are independent of one another. What is the probability that at least one of the machines operates properly? 0.8 0.85 0.94 0.952 0.994

a. substitute area of circle for a and circumference for C pier^2=k(2pier)^2- have to square pie divide r^2 by each side pie= k(4pie^2 )

The relationship between the area A of the circle and its circumference C is given by the formula A=kC^2, where k is constant. What is the value of K? a. 1/4pie b.1/2pie c. 1/4 d. 2pie e. 4pie^2

B 1/1 and 1/2 never cancel out 1/21 and 1/22 never cancel out

The sequence of numbers a1, a2, a3, ..., an is defined by an=(1/n)-(1/n+2) for each integer n >= 1. What is the sum of the first 20 terms of the sequence? a. (1+1/2)-1/20 b. (1+1/2)-(1/21+1/22) c. 1-(1/20+1/22) d. 1-1/22 e 1/20-1/22

Practice test 3 #10 165/3= 55 n-1+n+n+1=165 2n=165 three consecutive integers are 55-1, 55, 55+1 previous THREE 51+52+56

The sum of three consecutive integers is 165. What is the sum of the previous three consecutive integers? a. 153 b. 156 c. 159 d. 162 e. 164

practice test 6 number 19 (1/2)(1/2)(1/2)= (1/8) 1- (1/8)= (7/8 )

Three fair coins are tossed. What is the probability that at least one head is tossed? Give your answer as a fraction.

C prime factorization

all roots are cubed Quantity A 3^√270−3^√10 Quantity B 3^√80

B&C example of fraction:1/2 +2 gives you (3/4) *5 gives you 5/10= 1/2 divided by 100 gives you (1/100)/(2/100); multiply reciprocal= 1/2

options are in squares which of the following operations carried out on both the numerator and the denominator of a fraction will always produce an equivalent fraction. adding 2 multiplying by 5 dividing by 100

1.29 44/34

the table above shows the frequency distribution of the values of a variable Y. What is the mean of the distribution? give your answer to the nearest 0.01

(9x^2)/7

three times x is squared, and the result is divided by 7

question 20 pg. 157 in whitebook b

which of the following is closest to the mean of the prices of the 700 homes sold in 2012 and 2013 combined? a. 265,000 b. 270,000 c.275,000 d.280,000 e.285,000

B the equation simplified is 4x^2-y^2 which =3; which is less than 6

(4x-2y)(6x+3y)=18 Quantity A 4x^2-y^2 Quantity B 6

Practive test 3 question 17 (section 2) 15 minutes is 1/4 an hour 1/4*40mph= 10 miles last 25 minutes mph is unknown 40 minutes is 2/3 and hour 2/3*40= 20 miles total therefore the last 25 minutes was 10 miles 10miles/ 5/12= 10*12/5= 24

A car traveled at an average speed of 40 miles per hour for the first 15 minutes of a 40-minute trip, and the car traveled at an average speed of 30 miles per hour for the entire 40-minute trip. What was the car's average speed, in miles per hour, for the final 25 minutes of the trip? 20 24 35 36 70

C solve this by back solving

A certain machine can produce 37 units in 2 hours. If all such machines produce these units at the same rate, what is the minimum number of machines that would be needed to produce at least 100 units per hour? a. 3 b. 5 c. 6 d. 7 e. 8

11.17 qr #1 if two combination formulas are needed there would have to be two different groups only one combination formula is needed here B

A certain travel agency organizes a 5-city sightseeing package from a selection of 10 cities total. Each client selects 3 of the cities to visit. The travel agent then selects the 2 remaining cities to complete the 5-city package. Disregarding the order in which the cities might be visited, how many different groups of 5 cities might be selected? a. 60 b. 252 c. 420 d. 2,520 e. 5,400

11.15 q3 4,200

A gallery owner is selecting pieces for an exhibit. The artist submitted 10 sculptures and 6 prints, and the owner will select 4 sculptures and 3 prints to show. How many different groups of 4 sculptures and 3 prints can the gallery owner select?

OTDE question 19 origin is point of the graph equal to (0,0) bisector is the part of line that divides it into 2 (midpoint) midpoint is (4,4) y intercept is 0 because of origin (4-0)/(4-0)=1 y=1x-0 otr y=x so any point that has the same x or y values is on the line

A line segment has the endpoints A (0,8) and B (8,0). Which of the following points fall on the line that passes through the origin and bisects the line segment? Indicate all such points. (−6,14) (−2,6) (0,−8) (−1,−1) (1,−1) (4,4) (6,2) (8,8)

Question 4 11.12 n!k!/(n−k)!: 6!/2!(6−2)!=6×5×4×3×2×1/2×1×4×3×2×1=6×5/2×1=15. Thus, there are 15 possible 2-color combinations from a group of 6 colors. To find the number of test subjects, add 5 to this number: 15 + 5 = 20. That's (E)

A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.) 7 10 15 17 20

frequency distribution quiz (liters sizes *frequency)/ (frequency))

A zoologist studying a local marmot population recorded the number of pups in each of this year's litters, as shown in the frequency distribution table above. The zoologist found that the average (arithmetic mean) litter size was 4 pups. How many litters of 3 pups were born this year? 1 2 3 4 5

Practice test 1 #11 35 (5*4)=20 5*3=15 35

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?

11.15 q3 question 5 set up formulas find a number to times by the smaller one to get equal values in the larger one.

At a certain store, the briefcases are all the same price, the hats are all the same price, and the tables are all the same price. Furthermore, the total price of 8 briefcases, 5 hats, and 7 tables is $587, and the total price of 24 briefcases, 17 hats, and 21 tables is $1,797. What is the price of a hat? $18 $27 $36 $54 $108

Pg. 158 white book (200K-150K)/200K C

By approximately what percent did the median price of homes sold in Country T decrease from 2011 to 2012? 10% 15% 25% 33% 50%

kaplan gre pop quiz possible combinations: v,m,m 5 * (4*3)/(2*1) v,v,m (5*4/ 2*1) * 4 v,v,v (5*4*3)/ (3*2*1) add results up E

Chef James must select 3 different items for each dinner he will create. The items are to be chosen from among 5 different vegetarian and 4 different meat selections. If at least one of the selections must be vegetarian, how many different dinners can the chef create? A. 30 B. 40 C. 60 D. 70 E. 80

practice test 5 number 19 * diameter is largest segment that will fit inside a circle a &d

Circle O has a radius of 7. Which of the following figures could be drawn so that the complete figure fits inside Circle O ? Indicate all that apply. a. A semicircle with an arc length of 6π b. A circle whose area is π(14^2) c. A circle whose circumference is 21π d.A segment with a length of 4π e. A circle whose diameter is 7π

E times 1/3 times each containers possibility of choosing a silver add all the possbilities up at the end

Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else. Container C contains 1 gold coin, 4 silver coins, and nothing else. A container is chosen at random, and then a coin is chosen at random from that container. What is the probability that the chosen coin is silver? a. 4/15 b. 2/5 c. 7/15 d. 3/5 e. 2/3

number 11 pg. 153 in whitebook looking for the greatest deviation of y to x values. multiplication and division create the biggest changes answer is either x/3 or y=3x+20 e would be the answer because it also has subtraction.

Each of the following linear equations defines y as a function of x for all integers x from 1 to 100. For which of the following equations is the standard deviation of the y-values corresponding to all the x-values the greatest? a. y=(x/3) b. y=((x/2)+40)) c. y=x d. y=2x+50 e. y=3x-20

pg. 154 whitebook #12 m-12.1=1.5sd 2(m-12.1)=2m-24.2= 3sd m+3sd=17.5; (replace formula with 3sd mean + 2mean- 24.12= 17.45 m=13.9

For a certain distribution, the measurement 12.1 is 1.5 standard deviations below the mean, and the measurement 17.5 is 3.0 standard deviations above the mean. What is the mean of distribution? a. 13.8 b. 13.9 c. 14 d. 14.1 e. 14.2

D (5050+5050)+100*100

For each integer n>1, let A(n) denote the sum of the integers from 1 to n. For example, A(100)= 1+2+3+..+100= 5050. What is the value ofA(200)? 10,100 15,050 15,150 20,100 21,500

(24/87)

For the biological sciences and health sciences faculty combined, (1/3) of the adjunct and (2/9) of the non-adjunct faculty are medical doctors. What fraction of all the faculty in those fields combined are medical doctors?

A. Difficulty: hard Sets & Statistics (9!/4!)

How many different 4-digit integers are there, such that each digit is a distinct positive integer and the digits are arranged in increasing order from left to right? 126 378 420 1,080 5,040

OTDE question 18 (section 2) 166*6=996 <998 83*6=498 so 82*6= 492 166-82=84

How many integers from 498 through 998, inclusive, are multiples of 6 ? 82 83 84 166 167

C Algebra Difficulty: medium *have to multiply both sides of the equation by two

If ((a+3)/2)+a+3=3 then a = -3 -32 -1 0 1

e. (m+n)/9= (5m+4n)/20 cross multiply 20(m+n)=9(5m+4n) 20m+20n= 45m+36n -25m=16n or 25m=-16n

If (m+n/4+5)=m/4+n/5, which of the following statements must be true? a. m=n b. 5m=4n c. 5m=4n d. 25m=16n e. . 25m=-16n

practice test 4 number 13 because x-y= 8 x and y are either both negative or both odd if x-y= an even integer then they must equal a positive integer.

If x and y are integers and x - y = 8, then x + y CANNOT be a. 0 b. less then 8 c. greater than 8 d. an odd integer e. a positive integer

counting methods quiz 24-6= 18

If x is the number of different ways to arrange 4 people standing in a line, and y is the number of different ways to arrange 3 people standing in a line, then what is the value of x - y ? a.4 b. 6 c. 12 d. 16 e. 18

question 25 on pg. 208 in white book

In 1993 the average (arithmetic mean) price per card for all greeting cards sold was $1.25. For which of the following occasions was the number of cards sold in 1993 less than the total number of cards sold that year for occasions other than the ten occasions shown? a. Christmas b.V day c.Easter d. Mothers day e. fathers day f. graduation g. thanksgiving h. halloween

question 16 pg. 156 in whitebook b

In 1997, at the rate shown in the graph, the work time required to pay for which of the following food items was greatest? a. 10 pounds of bread b. 5 gallons of milk c. 3 pounds of coffee d. 20 pounds of sugar e. 5 dozen eggs

question 10 pg. 152 in whitebook 68/850= .08 73-.08= 65 E

In a distribution of 850 different measurements x centimeters is at the 73rd percentile. if there are 68 measurements in the distribution that are greater than y centimeters but less than x centimeters, then y is approximately at what percentile in the distribution? a. 45th b. 50th c. 55th d. 60th e. 65th

20 on pg. 206 in white book IF 3 ppl leave it doesnt state they currently left 8+3=11 11+1+10 22

In a single line of people waiting to purchase tickets for a movie there are currently 10 people behind Shandra. If 3 of the people who are currently in line ahead of Shandra purchase tickets and leave the line, and no one else leaves the line, there will be 8 people ahead of Shandra in line. How many people are in line currently?

A * keep everything in percents

Last year all purchases of a certain product were made either online or in a store. If 55% of purchases were made online what was the ratio of the number of purchases made online to the number of purchases made in a store? 11 to 9 11 to 5 10 to 9 9 to 11 9 to 10

OTDE Question 16 everything but 68 30%*200=60 d could be anything but not more than 60 people could choose it

Of the guests surveyed, which of the following could be the number of guests who estimated they spend exactly d days at the resort each season if d > 7? Indicate all such numbers. 1 10 17 34 60 68

#5 on formula practice set (OG value- new)/ OG value answer is 30%

Over the course of a one year period Freja paid down the principal on her student loans from $37,200 to $26,400. By approximately what percent did she reduce the principal on those loans? a. 11 b. 30 c. 40 d. 50 e. 67

B. Sets and Statistics Difficulty: low A: 10*12 B:(10*12)*2

P = {4, 7, 10, 12} Q = {1, 2, 10, 12} QA The product of the numbers that are in P that are also in Q QB The product of the numbers that are in Q

A Geometry Difficulty low x=y

Quantity A 180 - x QB y Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.

question 8 on page 152 in whitebook

R is a list of 15 consecutive integers, and T is a list of 21 consecutive integers. The median of the integers in list R is equal to the least integer in list T. If the two lists are combined into one list of 36 integers, how many different integers are on the combined list? a. 25 b.27 c. 28 d. 32 e. 36

question 6 pg. 150 in whitebook the total number of possible products would be 4(5)=20 however 4*2=8, 1*8=8, so A would be less than B

S= {1,4,7, 10} T={2,3,5,8,13} x is a number in set S and y is a number in set T Quantity A the number of different possible values of the product xy Quantity B 20

Practice test 5 # 8 the gaps are bigger in set B so the standard deviation will be bigger

Set A consists of the ten smallest positive odd integers. Set B consists of the ten smallest prime integers. Quantity A The standard deviation of Set A Quantity B The standard deviation of Set B

practice test 6 #16 F is budgeted food about in dollars 1.3F= 13,260 F= 10,200 I is clients income in dollars .20I= 10,200 I= 51,000 Carlos

Stefan is meeting one of his clients, who spends $13,260 on food each year. If this is 30% higher than the budgeted amount Stefan recommends, which of the clients listed is he meeting? a. Annette b. Carlos c. Jared d. Margo e. Priya

frequency distribution quiz 2

The frequency distribution above describes the number of unpaid parking tickets among the 7 defendants scheduled to appear in a small town's traffic court this week. If the average (arithmetic mean) number of tickets is 4, what is the mode?

#17 practice test 1 pier^2= 16(2pier) r=32 32*2= 64 any diameter less than 64 would fit in the circle

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 ? Indicate all such diameters. 25 36 42 48 54 66 70

practice test 4 #20 12*11*10= 1320

The program manager for an amateur performance night auditioned 12 acts, but there is only room for 3 acts on the program. How many different ways can the program manager arrange 3 different acts from the original 12?

A, C, &D just becasue the x intercept is in quadrant one doesn't mean it cant intersect other quadrants

The quadrants of the xy-plane are shown in the figure above. in the xy- plane line m (not shown) has a positive slope and a positive x-intercept. Line m intersects which of the following quadrants? a. quadrant i b. quadrant ii c. quadrant iii d. quadrant iv

question 15 pg. 203 in white book 14% of every normal distribution is between 1 &2 2% + 16% of the standard deviation is less than one 15%<16% so the 15th percentile is slightly below -1 -1 equals one value below the mean of 0 470-340=130 therefore the standard deviation has to be less than 130 below the mean.

The random variable Y is normally distributed with a mean of 470, and the value Y=340 is at the 15th percentile of the distribution. Of the following, which is the best estimate of the standard deviation of the distribution? a. 125 b. 135 c. 145 d. 155 e. 165

Proportions Difficulty: medium 1. add the ratios 2. 37x>160 3. find lowest possible value for x 4. 37(x)= lowest possible value for T

The ratio of the number of sophomores to the number of juniors to the number of seniors in a room is 7 to 18 to 12. The combined total of sophomores, juniors, and seniors in the room is T, in which T > 160. Quantity A The smallest possible value of T Quantity B 190

Practice test 3 (section 2) #16 asks for approximate ratio exact ratio is 37:19 19*2= 38 2 to 1 is the closest answer

What is the approximate ratio of the number of students who scored 70-89 on the midterm exam to the number of students who scored 80-89 on the final exam? 2 to 1 2 to 5 3 to 1 3 to 2 7 to 8

32 Geometry Difficulty level: high diameter is equal to the diagonal of a square diameter is the same as circumference but no pie diameter: 8√ 2= diagonal of square diagonal= hypotenuse of triangle the root two indicates 45-45-90 triangle, where hypotenuse is x (square root of two) and the other sides are x thus: one side of the square is 8 8* 4= 32

What is the perimeter of a square inscribed in a circle with a circumference of 8π√ 2

OTDE question 14 (27/88)+(28/88)

What is the probability that a female guest at the resort chose skiing or ice skating as her favorite winter sport? 0.27 0.28 0.375 0.55 0.625

OTDE question 16 (section 2) find out total books in future and robot books 21.4% of 14 is about 3 14.3% of 14 is about 2 total about 5 total amount of books: 50 (5/50)=10% closest answer is a

What percent of the books are future or robot books? 9.8% 14.3% 17.6% 19.6% 35.7%

question 21 page 206 in white book n(10^6)=9(1/n) n^2=(9/(10^6)) n=(3/(10^3) 10^3= 1,000 3/1,000= .003 whatever the root of 10 is = the amount of zeros the number has

When the decimal point of a certain positive decimal number is moved six places, the resulting number is 9 times the reciprocal of the original number. What is the original number?

9 find fist three multiples of 45 +18 divide each answer by first then second

When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n? 11 9 7 6 4

(1/16)^2, (4)^-4, (1/2)^8 Arithmetic Difficulty: medium * factor out 8

Which of the following are equal to (1/4)^4 ? Indicate all correct answer choices. (1/2)^2 (1/8)^2 (1/16)^2 (8)^-2 (4)^-4 (1/2)^8

E. triangle inequality theorem: one side of av triangle to be greater than the distance of the two other sides and smaller than the sum of the two other sides y-4<6 y-4>16

Which of the following describes the possible range of values of y ? 9 < y < 11 5 < y < 11 9 < y < 15 5 < y < 15 10 < y < 20

D least increase in amount not percent

Which of the following forms of annual pay increased the least from the first to the last of the ten years represented on the graph? a. Sum of Contract Pay per Year for rookies b. Sum of Contract Pay per Year for veterans c. Sum of Incentives/Endorsement pay for veterans d. Sum of Incentives/Endorsement pay for rookies e. Total annual pay for veterans

A. Algebra Difficulty (high) in order for a fraction to equal 0 the numerator must be 0 the denominator can never be 0 or negative y^2 will never be negative

Which of the following must be true if (x-4)/(y^2+36)(z-5)=0 ? x = 4 and z ≠ 5 x ≠ 4 and z ≠ 5 x = 4, y ≠ 6, and z ≠ 5 x = 4, y ≠ 6, y ≠−6, and z = 5 x ≠ 4, y≠ 6, y ≠−6, and z ≠ 5

Practice test 5 question 18 |6x-12|=36 6x-12=26 or 6x-12=-36 x=-4 or x=8

Which of the following numbers is a solution of the equation |6x − 12| = 36 ? Indicate all that apply. -4 -2 4 8

11.15 q2 question 4 divide (1/5) by original each and needs to be greater stated change in order to be LESS than 20 a & e 500,000> 425,000 470> 325

Which of the following situations represents a loss or gain of less than 20 percent? Indicate all possible correct answers. a. A loss of $425,000 from an invested $2,500,000 b. An increase of 7°F from the previous day's temperature of 33°F c. A plane dropping 12,000 ft from its altitude of 28,400 ft d. A dog's gaining 12 lbs from its original weight of 41 lbs e. The addition of a room of 325 sq ft to a house with 2,350 sq ft

D= 2Q first discover the bigger number between the comparison

Write equation: there are twice as many dimes as quarters

(2,-16) vertex formula= (-b)/2a x=2 plug in to formula y=-16

find the coordinates of the vertex y=x^2-4x-12

D. Algebra (high difficulty) if 1/a<1 a must be > 1; EX: (1/2). 1/b> 1 b must be <1; EX: (2/1)

a < 1 < b b < a < 1 a < b < 1 b < 1 < a 1 < a < b

D (#11 pg.72 in white book) 1. find distance between D &A 2. let ab be x bc 3x, cd x 3. set up formulat (1/6= 3x+x+x ) 4. subtract x from d

A=1/3 D=1/2 Points A, B, C are on a number line above, and AB=CD=1/3(BC). (13/30) (9/20) (11/24) (7/5) (29/60)

Practice test 2 #19 B&C Sets & Statistics Difficulty: high n* descending 3 digit numbers

Amanda is choosing photos to display in 2 frames. Each frame holds 4 photos. She is choosing from a number of family photos to arrange in the first frame and a number of vacation photos to arrange in the second frame. Which numbers of family photos and vacation photos would result in more than 500,000 ways to arrange the photos in the frames? Indicate all that apply. 5 family photos and 9 vacation photos 6 family photos and 8 vacation photos 7 family photos and 7 vacation photos 10 family photos and 4 vacation photos

D. from quantitative quiz one #1 Difficulty level: hard combined work formula T= (AJ/A+J) *1 fourth of an hour is 20 minutes

Amy can grade 100 tests in 7 hours. If Amy and Jan can grade 100 tests in 4 hours working together, how many hours would it take Jan to grade 100 tests if she worked alone? 3 hours 10 minutes 5 hours 22 minutes 7 hours 30 minutes 9 hours 20 minutes 9 hours 33 minutes

E. Number proportions 2(1.5)= 3

If 2a is an odd integer, which of the following must also be an integer? a a/2 a^2 3a 4a

12 find xy= (756/28) 27=9*3 (only two integers greater than 1 that are divisible by 27) x+y= 9+3

The integers x and y are greater than 1. If (4x)(7y)=756, what is the value of x+y?

18 &19 n+n+1=37 2n+1=37 2n=36 n=18 n+1= 19

The sum of two consecutive numbers is 37. What are they?

D. - Algebra -reverse foil

x2 + 3x - 70 = 0 Quantity A: x Quantity B: 4 a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

D. Arithmetic Difficulty: medium * x can be two different numbers

x^2 = 25 xy = 30 Quantity A y Quantity B 6

360 Geometry difficulty level: medium

In the figure above, what is the value of x + y + z ?

C. Proportions Back-solving find 20% of answer choices and then subtract amount from original price.

A clothing store discounts the price of a jacket by 20%. After the discount, the price of the jacket is $18.00. What was the price of the jacket before the discount? a. $14.40 b. $20.00 c. $21.60 d. $22.50 e. $24.40

B &C R is obviously steeper in 2003-2006 and 2004 to 2006 if slope is not obvious the highest starting value typically has the lowest percent change.

Based on the given information, during which of the following time periods did the average rate of change for revenues exceed the average rate of change for expenses? Select all that apply. a. 2002-2005 b. 2003-2006 c. 2004-2006 d. 2005-2011 e. 2006-2010 f. 2008-2011

D Arithmetic x+y=13n+5 n=1; x+y=18; 8>5 n=2; x+y= 81; 1<5

n is a positive integer, x=7n+2, and y= 6n+3 Quantity A The ones digit of x+y Quantity B 5

Quantitative quiz one $10 1. foil binomials 2. add together terms 3. where there is a -3x-4 replace it with 0 4. find the answer choice that equals xy+y B.

If -3x - 4 = 0, then (x + 2)(y - 2) - x - y = xy - 3y + x - 4 y(x + 1) x(y + 1) -y(x- 1) -4

A first find median and approximate whether the mean would be bigger or smaller than the mean from looking at the chart.

In the course of an experiment, 95 measurements were recorded, and all of the measurements were integers. The 95 measurements were then grouped into 7 measurement intervals. The graph above shows the frequency distribution of the 95 measurements by measurement interval. Quantity A the average (arithmetic mean) of the 95 measurements Quantity B the median of the 95 measurements

r=112.5 r+s=180 r/180=5/8 cross multiply r=112.5

In the figure above, if r/r+s= 5/8, what is the value of r?

C

Set S consists of all positive integers less than 81 that are not equal to the the square of an integer. Quantity A the number of integers in S Quantity B 72

E. Arithmetic Difficulty: low subtract difference from numerator and denominator

Each card in a certain deck of cards is 164 of an inch thick. If there are 122 cards in the deck, how thick is the deck, in inches? 1 1/6 1 15/16 1 19/32 1 41/64 1 29/32

B simplify Quadratic equation foil

a > 0 and b > 0. Quantity A (4a^2+24ab+36b^2)/a+3b QB 4(a + 5b) Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.

dividing my fractions is always bigger

dividing by fractional/ decimal values vs. multiplying by fractional/ decimal values

15 & 5

One number is 10 more than the other. The sum of twice the smaller plus three times the larger is 55. What are the two numbers?

B find areas of square & circle square is given: 16 1 side of square is 4 diagonal of square is 4 √2 area is (pie2 √2)^2= 8pie divide each area by four 2pie- 4

In the figure above, if the square inscribed in the circle has an area of 16, what is the area of the shaded region? a. 2pie-1 b. 2pie- 4 c. 4pie-2 d. 4pie-4 e. 8pie-4

B diameter is the longest line segment that goes across to both endpoints since a is not the diameter and b is then.

In the figure above, triangle RST is inscribed in a circle. The measure of angle RST is greater than 90, and the area of the circle is 25pie Quantity a The length of line segment RT Quantity B 10

D. Isosceles triangle is a triangle with two equal sides

Isosceles triangle ABC has a perimeter of 12. The length of side AB is 5. Quantity A AB + BC Quantity B 10 Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.

(3/4) find midpoint (average of x & average of y) find slope based on midpoint and x intercept

Line k lies in the xy plane. The x-intercept of line k is -4, and the line k passes through the midpoint of the line segment whose endpoints are (2,9) and (2,0). what is the slope of line k? Give your answer as a fraction.

B

List X and list Y each contain 60 numbers. Frequency distributions for each list are given above. The average (arithmetic mean) of the numbers in list X is 2.7 and the average of the numbers in list Y is 7.1. List Z contains 120 numbers : the 60 numbers in list X and the 60 numbers in list Y. Quantity A the average of the 120 numbers in list Z Quantity B the median of the 120 numbers in list Z

B. -geometry -find a+c first a+c< 180 + 47 a+c< 227

QA: a:+c QB: 230 a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

D

Quantity A The circumference of the circle Quantity B The perimeter of △ABC Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.

A Sets & Stats Difficulty: low 8 * 4 descending integers 7 * 4 descending integers

A code is to be sent by selecting five different positive integers and then sending these five different positive integers one at a time until all five positive integers have been sent. Quantity A The number of different possible codes that can be sent if 5 different integers are selected from the first 8 positive integers QB The number of different possible codes that can be sent if 5 different integers are selected from the first 7 positive integers

D. Sets & Statistics Difficulty (medium) * have to know there's 26 letters in the alphabet step 1: find number of possibility for each character step 2: multiply all possible options together

A computer password must be 5 characters long. The first character must be a capital letter. The second character must be a digit from 0 through 9, inclusive. The third character must be one of eight specified symbols. Each of the fourth and fifth characters can be any combination of capital or lowercase letters, digits, or symbols, where the symbols are from the 8 specified symbols. How many different passwords can be made using these rules? 1,274,000 2,548,000 5,096,000 10,192,000 40,768,000

B find the perimeter not area 6,000/ 12

A construction company will produce identical metal supports in the shape of a right triangle with legs of length 3 feet and 4 feet. The three sides of each triangular support are to be constructed of metal stripping. If the company has a total of 6,000 feet of metal stripping and there is no waste of material in the construction of the supporters what is the greatest possible number of supporters than the company can produce? a. 428 b. 500 c. 545 d. 600 e. 1,000

b, c, e, g set up formulas x+x+ y= 140 xy=2,400 y=140-2x x(140-2x)= 2,400 2x^2-140x-2,400 2(x^2-70-1,200) x=30, or 40 plug in 30y=2400 and 40y=2400

A flat, rectangular flower bed with an area of 2,400 square feet is bordered by a fence on three sides and by a walkway on the fourth side. If the entire length of the fence is 140 feet, which of the following could be the length, in feet, of one of the sides of the flower bed? Include all such lengths. a. 20 b. 30 c. 40 d. 50 e. 60 f. 70 g. 80

Quantitative quiz one #14 97= F+22r 55=F+10r 42=12r r=3.5 55=F+10(3.5) f=20 Algebra difficulty (hard) use combination formula (adding and subtracting equations)

A phone card charges a flat fee for the first minute of a phone call, plus an additional charge per each extra minute of the call. For a caller using the phone card, an 11-minute call costs 55 cents, and a 23-minute call costs 97 cents. How much does the phone card charge for the first minute of a call? 3.5 cents 7 cents 10 cents 16.5 cents 20 cents

practice test 3 #13 B find outcome for each event then find product of both outcomes.

A spinner has eight equal-sized sections numbered 1 through 8. The spinner is spun twice. What is the probability of first spinning an odd number then spinning an even number? a. 0.2 b. 0.25 c. 0.5 d. 0.75 e. 1.0

D. Sets & Statistics imagine she scored 100 on the previous 2 , therefore her average would be 100 60% more than 100 is 160 find the average of all three scores and then divide that score by 160 to percentage of average test score 200+ 160/3 =120 (160/120)= simplifies to 4/3= 1.33*100

A student's score on the final test in a certain course was 60 percent greater than the average (arithmetic mean) score of the 2 other tests the student took in the course. The student's score on the final test was what percent of the student's average test score for the entire course? 33 1/3% 40% 75% 133 1/3% 160%

A. make up numbers n=3 t=10 p=2 36 total pencils 26 given out 26/2=13 A=13

A third grade teacher has n boxes, each containing 12 pencils. After the teacher gives p pencils to each student in the class, the teacher has t pencils left over. Which of the following represents the number of students in the class a. (12n-t/p) b. (12n+t)/p c. (12n/p)-t d. (12p-t)/n e. (12p+t)/n

B Difficulty (high) Distance = rate *time find least common multiple of 21 and 28 (7*3*2*2)= 84 (half the length of the trip) 84*2= full distance of trip 84miles/ rate1; 84hrs/ rate 2 Finally: total distance/ total time=

A vehicle traveled from Town A to Town B without stopping. For the first half of the journey, it traveled at an average speed of 28 miles per hour, and for the second half of the journey, it traveled at an average speed of 21 miles per hour. The average speed of the vehicle over the entire distance was x miles per hour. Quantity A x Quantity B 24 1/2

B step 1: take of the x: (x(1+x+x^2+x^3))/4 therefore; x(60)/4= 15x

If 1+x+x^2+x^3=60, then the average of x, x^2, x^3, and x^4 is equal to which of the following? a. 12x b. 15x c. 20x d. 30x e. 60x

c first rewrite using 5 to get bases the same 1/(5^2)^n= (5^3)^3 rewrite as (5^2)^-n= (5^3)^3 ignore bases -2n=9

If 1/ (25)^n=125^3 , what is the value of n ? a. −9 b. −4 c.- 9/ 2 d. 3/ 2 e. 7

a. dont need to find original average 7 billion- 5 billion average would be 2 billion less per year would have to do 2 billion/ 10 to get 200 million

If it were discovered that the value of imports for 2007 was incorrect and should have been $5 billion instead, then the average (arithmetic mean) value of imports per year for the 10 years shown would have been approximately how much less? a. $200 million b. $50 million c. $20 million d. $7 million e. $5million

E Number proportions * positive number * negative number= always equals positive number - ex: 4*3, 5*8 * even numbers can not be factors of odd numbers s= 4, r= 27

If r is an odd integer and s is an even integer, which of the following must be true? r is a prime number. r2 is an even integer. rs is an odd integer. s - r is an even integer. s is not a factor of r.

A Data Interpretation Medium Difficulty

If women account for 40% of the science graduates employed in their field, as well as for 40% of the science graduates employed outside their field, what is the approximate ratio among science graduates of women employed in their field to men employed outside their field? 1:4 7:25 1:2 14:25 2:3

c make a right triangle hypothenus is 10 10/2/=5 5 squared is 25

In the coordinate plane, the endpoints of a diameter of a certain circle are (10, 4) and (4, 12). What is the area of the circle? a. 9π b. 16π c. 25π d. 64π e. 100π

B 125 degrees indicates it in not a rectangle area of a parallelogram is length of base times corresponding height which can not be slanted draw right triangle to right 6 is the hypothenuse therefore the height has to be less than 6, therefore less than 6*4

In the figure above, ABCD is a parallelogram. Quantity A the area of ABCD Quantity B 24

practice test 3 #20 the 7 previous scores need to add up to 70%, thus each test is worth 10 points minimum: 85*10 Maximum: 92*10 add up all the previous test scores: 623 850-623= 227/3 920-623= 297/3

Porter is in Mr. Jenkins' French class and has received the following test scores this semester: 86, 100, 78, 85, 88, 95, 91 Mr. Jenkins' grading scale is: A: 93-100 B: 85-92 C: 77-84 D: 70-76 F: 69 and below (All fractional scores are rounded to the nearest integer.) Porter just completed the final exam today, which is worth 30% of the overall grade. If Porter wishes his grade at the end of the semester to be a B, and if the seven previously scored tests are weighted equally, which of the following could be Porter's final exam grade? Indicate all that apply. 72 73 76 82 97 99

Practice test 5 (question 5) draw a circle in a square (horizonal radius) draw a square within a circle (diagonal radius) B

Quantity A the area of the largest circle that can be inscribed within a square of area 16 Quantity B The area of the largest square that can be inscribed within a circle of circumference 8π

D. Difficulty (hard) they both get x years older r+x=2(v+x)

Rachel is now r years old and Victor is now v years old. In x years, Rachel's age will be twice Victor's age. Which of the following is an equation for v in terms of r and x ? v = 2r 12 v=r2 v=(r-x)/2

D. cannot be determined Sets& statistics lowest possible value & highest possible value for x (9 &12) both means equal to 10 & fraction 12 is more than , 9 is less than

S = {2, 4, 8, x, 13, 16, 20} x is the median of the numbers in set S. QA: The average (arithmetic mean) of the numbers in set S QB: x

1.True when you divide like bases you subtract the exponents 2. False *cannot split up fraction

T/F 1. (2^5/2^3)=1/2^3 2. ((x+y)/5)= x+2+y+3

A. Difficulty (high) standard average formula

The average (arithmetic mean) of the 12 positive numbers in list A is greater than the average of the 10 positive numbers in list B. Quantity A The ratio of the sum of the numbers in list A to the sum of the numbers in list B Quantity B 87

d. formula: P(a)+P(b)- P(a*b)

The events A and B are independent. The probability that event A occurs is 0.4 and the probability that event B occurs is 0.3. What is the probability that at least one of the events A and B occurs? a. 0.12 b. 0.42 c. 0.49 d. 0.58 e. 0.7

216 area of small rectangle= 216 shaded region is garden and walkway combined width of big rectangle= 12+2(3)= 18 length of big rectangle= 18+2(3)= 24 area of big= 432-216= 216

The figure above represents a rectangular garden with a walkway around it. The garden is 18 feet long and 12 feet wide. The walkway is uniformly 3 feet wide, and its edges meet at right angles. what is the area of the walkway

C. Geometry area of square: (side)^2 perimeter of rectangle: 4 * 10

The figure above shows rectangle ABCD, which is made up of 10 identical squares. If the area of each square is x, what is the perimeter of rectangle ABCD ? 12x 12x√ 14x√ 16x√ 25x√

D f(-1)= wherever y is when x is -1; which is 2 f(2)= wherever y is when x is 2; which is 1

The figure above shows the graph of the function f in the xy-plane. What is the value of f(f(-1))? A. -2 B.-1 C. 0 D. 1 E.2

17 * if there's nowhere to plug in the x they all equal the same thing

The function f has the property that f(x)=f(x+1) for all numbers x. If f(4)=17. what is the value of f(8)?

A b and c give information about the center of the data

The penguins currently living on an island are of two types, Chinstrap penguins and Gentoo penguins. The range of the heights of the Chinstrap penguins on the island is 13.2 centimeters, and the range of the heights Gentoo penguins on the island is 15.4 centimeters. Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the penguins on the island? Include all a. the tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island b. the median height of the Gentoo penguins on the island is 1.1. centimeters taller than the tallest Chinstrap penguin on the island c. The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.

B draw distribution graph 850 is farther away from mean than 650 therefore the 75th percentile will be closer to the 60th percentile 75th percentile is halfway between the 60th and 90th so 750 will be greater.

The values of 650 and 850 are at the 60th level and 90th percentiles of the distribution of X, respectively. QA The value of the 75th percentile of the distribution X QB 750

A plug in (-1/2) for z

if |z|<= 1, which of the following statements must be true? Indicate all such statements z^2<=1 z^2<=z z^3>=z

a & c angle b is equal to the angle to the leftof a

ℓ 1 is parallel to ℓ 2 and ℓ 4 is perpendicular to ℓ 2 , which of the following must be true? Indicate all such statements. A . ℓ1⊥ℓ4 B. a = b C. a + b = 90