GRE Quantitative Practice PDF

GRE QUANTITATIVE PRACTICE GROUP #1 PROBABILITY AND DATA ANALYSIS CHAPTERS Probability and Statistics Permutation and Combination Interpreting and Analyzing Graphs  Probability& Statistics Practice 01 1. The media...

GRE QUANTITATIVE PRACTICE GROUP #1 PROBABILITY AND DATA ANALYSIS CHAPTERS Probability and Statistics Permutation and Combination Interpreting and Analyzing Graphs  Probability& Statistics Practice 01 1. The median is larger than the average for which one of the following sets of integers? (A) {8, 9, 10, 11, 12} (B) {8, 9, 10, 11, 13} (C) {8, 10, 10, 10, 12} (D) {10, 10, 10, 10, 10} (E) {7, 9, 10, 11, 12} 2. A hat contains 15 marbles, and each marble is numbered with one and only one of the numbers 1, 2, 3. From a group of 15 people, each person selects exactly 1 marble from the hat. Numbered Marble Number of People Who Selected The Marble 1 4 2 5 3 6 What is the probability that a person selected at random picked a marble numbered 2 or greater? (A) 5/15 (B) 9/15 (C) 10/15 (D) 11/15 (E) 1 3. Sarah cannot completely remember her four-digit ATM pin number. She does remember the first two digits, and she knows that each of the last two digits is greater than 5. The ATM will allow her three tries before it blocks further access. If she randomly guesses the last two digits, what is the probability that she will get access to her account? (A) 1/2 (B) 1/4 (C) 3/16 (D) 3/18 (E) 1/32 4. If x < y < z, z = ky, x = 0, and the average of the numbers x, y, and z is 3 times the median, what is the value of k? (A) –2 (B) 3 (C) 5.5 (D) 6 (E) 8 5. Three positive numbers x, y, and z have the following relationships y = x + 2 and z = y + 2. When the median of x, y, and z is subtracted from the product of the smallest number and the median, the result is 0. What is the value of the largest number? (A) –2 (B) π (C) 5 (D) 8 (E) 21/2 6. A jar contains only three types of objects: red, blue, and silver paper clips. The probability of selecting a red paper clip is 1/4, and the probability of selecting a blue paper clip is 1/6. What is the probability of selecting a silver paper clip? (A) 5/12 (B) 1/2 (C) 7/12 (D) 3/4 (E) 11/12 7. A bowl contains one marble labeled 0, one marble labeled 1, one marble labeled 2, and one marble labeled 3. The bowl contains no other objects. If two marbles are drawn randomly without replacement, what is the probability that they will add up to 3? (A) 1/12 (B) 1/8 (C) 1/6 (D) 1/4 (E) 1/3 8. A housing subdivision contains only two types of homes: ranch-style homes and townhomes. There are twice as many townhomes as ranch-style homes. There are 3 times as many townhomes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a townhome with a pool? (A) 1/6 (B) 1/5 (C) 1/4 (D) 1/3 (E) 1/2 Practice 02  Easy 1. In a jar, 2/5 of the marbles are red and 1/4 are green. 1/4 of the red balls and 1/5 of the green balls are broken. If no other balls in the jar are broken, then what is the probability that a ball randomly picked from the jar is a broken one? (E) 2/5 (A) 3/20 (B) 7/30 (C) 5/16 (D) 1/3 2. The minimum temperatures from Monday through Sunday in the first week of July in southern Iceland are observed to be –2°C, 4°C, 4°C, 5°C, 7°C , 9°C, 10°C. What is the range of the temperatures? (A) –10°C (B) –8°C (C) 8°C (D) 10°C (E) 12°C  Medium 3. What is the probability that a number randomly picked from the range 1 through 1000 is divisible by both 7 and 10? (A) 7/1000 (B) 1/100 (C) 7/500 (D) 7/100 (E) 1/10 1 4. What is the probability that the product of two integers (not necessarily different integers) randomly selected from the numbers 1 through 20, inclusive, is odd? (A) 0 (B) 1/4 (C) 1/2 (D) 2/3 (E) 3/4 5. Two data sets S and R are defined as follows: Data set S: 28, 30, 25, 28, 27 Data set R: 22, 19, 15, 17, 21, 25 By how much is the median of data set S greater than the median of data set R? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 6. If x and y are two positive integers and x + y = 5, then what is the probability that x equals 1? (A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5 (E) 1/6 7. The following values represent the number of cars owned by the 20 families on Pearl Street. 1, 1, 2, 3, 2, 5, 4, 3, 2, 4, 5, 2, 6, 2, 1, 2, 4, 2, 1, 1 What is the probability that a family randomly selected from Pearl Street has at least 3 cars? (A) 1/6 (B) 2/5 (C) 9/20 (D) 13/20 (E) 4/5 8. The following frequency distribution shows the number of cars owned by the 20 families on Pearl Street. The number of families having x x number of cars 1 2 2 2 3 a What is the probability that a family randomly selected from the street has at least 4 cars? 4 4 (A) 1/10 (B) 1/5 (C) 3/10 (D) 9/20 (E) 11/20 5 5 6 2 9. Set S is the set of all numbers from 1 through 100, inclusive. What is the probability that a number randomly selected from the set is divisible by 3? (A) 1/9 (B) 33/100 (C) 34/100 (D) 1/3 (E) 66/100 10. What is the probability that the sum of two different numbers randomly picked (without replacement) from the set S = {1, 2, 3, 4} is 5? (C) 1/4 (D) 1/3 (E) 1/2 (A) 1/5 (B) 3/16 11. The ratio of the number of red balls, to yellow balls, to green balls in a urn is 2 : 3 : 4. What is the probability that a ball chosen at random from the urn is a red ball? (A) 2/9 (B) 3/9 (C) 4/9 (D) 5/9 (E) 7/9 12. The frequency distribution for x is as given below. What is the range of f ? (A) 0 (B) 1 (C) 3 (D) 4 (E) 5 1 5 4 4 f 0 1 2 3 x 13. In a box of 5 eggs, 2 are rotten. What is the probability that two eggs chosen at random from the box are rotten? (A) 1/16 (B) 1/10 (C) 1/5 (D) 2/5 (E) 3/5 14. The table shows the distribution of a team of 16 engineers by gender and level. Junior Engineers Senior Engineers Lead Engineers Male 3 4 2 Female 2 4 1 If one engineer is selected from the team, what is the probability that the engineer is a male senior engineer? (A) 7/32 (B) 1/4 (C) 7/16 (D) 1/2 (E) 3/4 2 15. A prize of $200 is given to anyone who solves a hacker puzzle independently. The probability that Tom will win the prize is 0.6, and the probability that John will win the prize is 0.7. What is the probability that both will win the prize? (A) 0.35 (B) 0.36 (C) 0.42 (D) 0.58 (E) 0.88 16. If the probability that Mike will miss at least one of the ten jobs assigned to him is 0.55, then what is the probability that he will do all ten jobs? (A) 0.1 (B) 0.45 (C) 0.55 (D) 0.85 (E) 1 17. The probability that Tom will win the Booker prize is 0.5, and the probability that John will win the Booker prize is 0.4. There is only one Booker prize to win. What is the probability that at least one of them wins the prize? (A) 0.2 (B) 0.4 (C) 0.7 (D) 0.8 (E) 0.9 18. The following values represent the exact number of cars owned by the 20 families on Pearl Street. 1, 1, 2, 3, 2, 5, 4, 3, 2, 4, 5, 2, 6, 2, 1, 2, 4, 2, 1, 1 The number of This can be expressed in frequency distribution format as follows: families having x x number of cars What are the values of a and b, respectively? 1 5 (A) 1 and 1 (B) 1 and 2 (C) 2 and 1 (D) 2 and 2 (E) 2 and 3 2 7 3 a 4 3 5 b 6 1  Hard 19. A meeting is attended by 750 professionals. 450 of the attendees are females. Half the female attendees are less than thirty years old, and one-fourth of the male attendees are less than thirty years old. If one of the attendees of the meeting is selected at random to receive a prize, what is the probability that the person selected is less than thirty years old? (A) 1/8 (B) 1/2 (C) 3/8 (D) 2/5 (E) 3/4 20. Each Employee at a certain bank is either a clerk or an agent or both. Of every three agents, one is also a clerk. Of every two clerks, one is also an agent. What is the probability that an employee randomly selected from the bank is both an agent and a clerk? (A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5 (E) 2/5 21. Every one who passes the test will be awarded a degree. The probability that Tom passes the test is 0.3, and the probability that John passes the test is 0.4. The two events are independent of each other. What is the probability that at least one of them gets the degree? (A) 0.28 (B) 0.32 (C) 0.5 (D) 0.58 (E) 0.82 22. A national math examination has 4 statistics problems. The distribution of the number of students who answered the questions correctly is shown in the chart. If 400 students took the exam and each question was worth 25 points, then what is the average score of the students taking the exam? Question Number solved the question (A) 1 point 1 200 (B) 25 points 2 304 (C) 26 points (D) 69 points 3 350 (E) 263.5 points 4 250 3 DRILL 1 Exam Style Questions Question 1 In terms of y, what is the average (arithmetic mean) of 4y and 22 ? 4y + 22 4y + 11 4y − 22 2y + 11 2y + 22 Question 2 Quantity A Quantity B The average (arithmetic mean) of 14, 22, and 48 The average (arithmetic mean) of 12, 22, and 50 Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 3 2, 3, 5, 7 Quantity A Quantity B The average (arithmetic mean) of the numbers above The median of the numbers above Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 4 Susan travels by car at an average speed of 50 miles per hour for 4 hours and then at an average speed of 20 miles per hour for 2 hours. What is her average speed, in miles per hour , for the entire 6-hour trip? 25 30 35 40 45 Question 5 Liz owns 2 green t-shirts, 4 blue t-shirts, and 5 red t-shirts. Quantity A Quantity B The probability that Liz randomly selects a blue t-shirt Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 6 Quantity A Quantity B The average (arithmetic mean) of 4 numbers, each less than 6 The median of 6 numbers, each less and greater than 5 than 5 and greater than 4 Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 7 For which of the following values of x is the mode of 2x, x + 5, 3x − 2, 5x − 7, and 4x equal to 4 ? 2 3 4 5 7 4  Question 8 A hat contains 18 ra e tickets, numbered 1 through 18. If two ra e tickets are chosen at random from the hat, what is the probability that both tickets are even numbers? Question 9 k>j>0 Quantity A Quantity B The time it takes to read k words at j words per minute The time it takes to read (k + 10) words at (j + 10) words per minute Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 10 How many committees of 5 members can be chosen from a group of 8 people? 28 56 118 336 6,720 Question 11 The average (arithmetic mean) number of passengers on a subway car is 60. If the number of passengers on a car has a normal distribution with a standard deviation of 20 , approximately what percent of subway cars carry more than 80 passengers? 16% 48% 68% 88% 98% Question 12 If the average of 10, 12, n, and n is greater than 25, what is the least possible value of integer n ? 39 40 41 42 DRILL 2 Question 1 x,x2,xy,xy-1,x4,x6 x>1 Quantity A Quantity B The mode of the numbers above when y = 4 The median of the numbers above when y = 5 Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. 38 5  Question 2 Trip A is 6x miles long and takes 5y hours. Trip B is 5x miles long and takes 4y hours. Quantity A Quantity B The rate of trip A in miles per hour The rate of trip B in miles per hour Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 3 If the probability that the rst event will occur is , and the probability that the second event will occur is , then what is the probability that both events will occur? Question 4 Five numbers in a set are arranged from least to greatest. If the median of the rst two numbers is 13 and the average (arithmetic mean) of the remaining numbers is 23, what is the average (arithmetic mean) of the entire set? Question 5 A bag contains 12 marbles: 5 of the marbles are red, 3 are green, and the rest are blue. Quantity A Quantity B The probability of consecutively choosing two red marbles The probability of consecutively choosing a and a green marble without replacement red and two blue marbles with replacement Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 6 If the average (arithmetic mean) of 31, 41, and p is between 29 and 47, inclusive, what is the least possible value of (p – 7)2 = Question 7 Water ows into a 25-liter bucket through a hose and out through a hole in the bottom of the bucket. The rate of ow through the hose is 1 liter per minute. If the bucket is lled to capacity in 40 minutes , at what rate, in liters per minute, was water owing out of the bucket through the hole? Question 8 A pair of dice is tossed twice. What is the probability that the rst toss gives a total of either 7 or 11 and the second toss gives a total of 7 ? 6  Question 9 A photocopier can copy r pages per hour. How many pages can it copy in s seconds? 3,600rs Question 10 Quantity A Quantity B The average (arithmetic mean) cost per hinge for 16 hinges The average (arithmetic mean) cost per hinge that cost a total of 2p cents for 4 hinges that cost a total of cents Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 11 In both rural and urban areas of country G, the average annual number of holidays taken by citizens is 8, and the annual number of holidays follows a normal distribution. In rural areas, 2% of the citizens take more than 12 holidays per year. In urban areas, 2% of the citizens take more than 16 holidays per year. How much greater is the standard deviation of the annual number of holidays taken by urban citizens than that of rural citizens? Question 12 Three dice are rolled simultaneously. What is the probability that exactly two of the dice will come up as the same number? DRILL 3 Question 1 There are 32 students in Jamie’s eighth-grade class. Each student took a 50-point test; the class average (arithmetic mean) was 82% correct. The teacher has assigned one 4-point, extra-credit question. How many students will need to answer the extra-credit question correctly in order to bring the class average to 86% correct? 15 16 17 All of the students It will not be possible for the class to reach an average of 86% correct. Question 2 Vinay and Phil are driving in separate cars to Los Angeles, both leaving from the same place and traveling along the same route. If Vinay leaves at 1 a.m. and travels at 40 miles per hour, and Phil leaves at 5 a.m. and travels at 50 miles per hour, at what time does Phil catch up to Vinay? 1 p.m. 5 p.m. 7 p.m. 9 p.m. 11 p.m. Question 3 A set of six numbers consists of x, x + 3, x + 5, x + 7, x + 11, and x + 13. What is the median of this set, in terms of x ? x+5 x+6 x + 6.5 3x + 8 6x + 39 Question 4 Damon rolls three six-sided dice. What is the probability that his total will be greater than 16 ? 7  Question 5 John will spend the summer in one of the houses either on Surf Street or Breaker Way. Surf Street has 1 landside house and 4 beachside houses, and Breaker Way has 1 beachside house and 2 landside houses. A sea turtle randomly lays eggs in front of a beachside house on Surf Street, and another sea turtle randomly lays eggs in front of a beachside house on Breaker Way. What are the probabilities that a sea turtle lays its eggs in front of John’s house, depending on which street he lives on? Question 6 If x equals all prime numbers that satisfy the inequality what is the average value of x ? Question 7 Set A: {−7, −4, −1, 0, 5, 8, 10, 10, 13, 21} In Set A above, if positive integer x is subtracted from the 3 largest numbers in the list and x is added to the 3 smallest even numbers in the list, which of the following will be true ? The average of the set will increase by x. There will be no mode in the new set. The average of the set will decrease by x. The standard deviation of the set will stay the same. The average of the set will stay the same. The median of the set will stay the same. Question 8 The median of the set will increase by x. Alejandra took ve Spanish quizzes and scored a total of 227 points. Nigel took the same quizzes and scored a total of 189. What is the difference between Alejandra’s average score and Nigel’s average score? Question 9 Which of the following could be the median for a set of integers {97, 98, 56, x, 86}, given that 20 < x < 80? 71 86 91.5 97 397.5 Question 10 There are 40 marbles in a jar. If of the marbles are blue, of the remaining marbles are red, and 10 marbles are green. If a marble is selected at random, then what is the probability that the marble will not be blue, red, or green? Question 11 During a sales contest at a local electronics store, 65 employees sold a total of $91,000 worth of merchandise. If the standard deviation of sales among those employees was $130 and the sales were normally distributed, what percentage of employees sold $1270 or more worth of merchandise? 28% 50% 65% 84% 98% Question 12 On the most recent test in stats class, Jamal scored x points and Raya scored 73 points. If the average of Cli and Raya’s scores is 79 points, and the average of Jamal and Cliff’s scores is 89, then x = 8 DRILL 4 Question 1 After preparing the results of their measurement of the weight of children that participated in their pediatric study, Steph’s graduate assistant spilled co ee on their papers. If Steph is able to read that 50 lbs is the third standard deviation to the left of the mean, and 110 lbs also falls on a standard deviation, then which of the following could be the mean weight of the children in the study, assuming regular distribution? Indicate all possible values. 80 85 86 95 100 Question 2 Je and Ali race each other at the Tentleytown Speedway Ali’s car travels at 300 feet per second. and Je ’s car travels at 250 feet per second. If one lap around the track is 3000 feet long, and each car travels , at a constant rate, how many laps will it take Ali to overtake Jeff? 1 5 6 10 60 Question 3 Helen and Sergey must cut down a row of trees Helen can cut down the entire.row in 3 hours and Sergey can cut down the, entire row in 7 hours. If they simultaneously start cutting trees, each starting at one end of the row and working towards each other, what fraction of the trees will Sergey have cut at the time they meet? Question 4 In a set of five consecutive integers, which of the following must change the average of the set without changing its median ? Multiplying each of the numbers in the set by 6. Adding.5 to the 2 largest and to the 2 smallest Adding 10 to each of the numbers in the set. numbers in the set. Subtracting 3.5 from each of the numbers in the set Dividing each of the numbers in the set by 2. Adding 8.2 to the 2 largest numbers and subtracting It’s not possible to change the average of the set 8.2 from the 3 smallest numbers in the set.. without changing its median. Question 5 Paul is able to grade p essays every half hour, Paul isand ableSarah is able essa to rade to grade s evers essays every and half hour hour.Sara is If Paul and Sarah work together grading essays for h hours, then in terms of p, s, and h, how many essays will they grade? Indicate all such amounts. h(p + s) 2h(p + s) e h(2p + s) h(p + 2s) 2hp + hs Question 6 If the average of 5 numbers is 36 and the average of four of those numbers is 34, then what is the value of the fifth number? 2 34 35 36 44 9  Question 7 Noah’s contracting company builds road at a rate of 1 mile per week, except during the rainy season, when that rate drops to mile per week. If Noah is hired to build 11 miles of road, and his company begins construction 5 weeks before the start of the rainy season, how many weeks will it take Noah’s company to complete the contract? (Rainy season lasts 14 weeks.) Question 8 Three factory employees work at constant rates to produce DVDs. Employee A produces y DVDs in of an hour. Employee B produces y DVDs in of an hour. Employee C produces y DVDs in of an hour. Which of the following combinations of employees can produce at least 5y DVDs in 2 hours? Indicate all such statements. Employees A and B together Employee A alone Employees B and C together Employee B alone Employees A, B, and C together Employee C alone Even if all three employees work together, they will not finish the job h Question 9 ve Two cyclists, A and B, are 145 miles apart on a straight road. At 1:30 p.m., cyclist A begins riding at a constant speed of 20 miles per hour toward cyclist B. At 2:00 p.m., cyclist B begins riding toward cyclist h A at a constant speed. At 5:00 p.m. they meet. How fast, in miles per hour, was cyclist B riding? Question 10 Portia rates all her rst dates as either “duds” or “dudes.” Her date on Wednesday night was a dud. On the next night, she went on a date with someone else who was also a dud. If the probability of her getting two duds in a row was , what is the probability that her next date will be a dude ? Question 11 Victor is walking at a rate of 1 mile every 17 minutes Sarah is walking at a rate of. 1 mile every 14 minutes If they are 10 miles apart and are approaching each other along a straight road, how many. hours will it take them to meet, rounded to the nearest hundredth? 10  Answer Keys Pratice: 01 1 E 2 D 3 C 4 E 5 C 6 C 7 E 8 E Practice: 02 1 A 2 E 3 C 4 B 5 B 6 C 7 B 8 E 9 B 10 D 11 A 12 D 13 B 14 B 15 C 16 B 17 C 18 D 19 D 20 C 21 D 22 D Drill 1 Drill 2 Drill 3 Drill 4 1. D 1. C 1. B 1. A, C, D 2. C 2. B 2. D 2. B 3. A 3. A 3. B 3. 3/10 or 0.3 4. D 4. 19 4. 1/54 4. E 5. B 5. B 5. B, D 5. E, G 6. A 6. 64 6. 10/3 6. E 7. A 7. A 7. C 7. 17 8. B 8. A 8. 7.6 8. A, D, F 9. A 9. D 9. B 9. 25 10. B 10. C 10. 14/40 10. D 11. A 11. 2 11. D 11. 1.28 12. C 12. A 12. 93 11  PERMUTATION AND COMBINATION PRACTICE-1 1. There are 3 doors to a lecture room. In how many ways can a lecturer enter and leave the room? 12 1 3 6 9 (A) (D) (B) (C) (E) 2. There are 3 doors to a lecture room. In how many ways can a lecturer enter the room from one door and leave from another door? 12 1 3 6 9 (A) (D) (B) (C) (E) 3. How many possible combinations can a 3-digit safe code have? C3 103 P3 39 93 9 9 (A) (D) (B) (C) (E) 4. Goodwin has 3 different colored pants and 2 different colored shirts. In how many ways can he choose a pair of pants and a shirt? 12 2 3 5 6 (A) (D) (B) (C) (E) 5. In how many ways can 2 doors be selected from 3 doors? 12 1 3 6 9 (A) (D) (B) (C) (E) 6. In how many ways can 2 doors be selected from 3 doors for entering and leaving a room? 12 1 3 6 9 (A) (D) (B) (C) (E) 7. In how many ways can a room be entered and exited from the 3 doors to the room? 12 1 3 6 9 (A) (D) (B) (C) (E) 8. There are 5 doors to a lecture room. Two are red and the others are green. In how many ways can a lecturer enter the room and leave the room from different colored doors? 12 1 3 6 9 (A) (D) (B) (C) (E) 9. Four pool balls—A, B, C, D—are randomly arranged in a straight line. What is the probability that the order will actually be A, B, C, D ? 4 C4 4 P4 1/2! 1/3! 1 1 1/4 (A) (D) (B) (C) (E) 10. A basketball team has 11 players on its roster. Only 5 players can be on the court at one time. How many different groups of 5 players can the team put on the floor? (A) 511 (D) 115 (B) 11C 5 (E) 11!
5! (C) 11P5 11. How many different 5-letter words can be formed from the word ORANGE using each letter only once? (A) 6P6 (D) 66 (B) 36 (E) 6P5 (C) 6C 6 12 12. How many unequal 5-digit numbers can be formed using each digit of the number 11235 only once? (A) 5! 5 P5 5C5 (C) 5 5 (D) (E) (B) 5 P3 2! 2!
3! 2!
3! C 13. How many different six-digit numbers can be formed using all of the following digits: 3, 3, 4, 4, 4, 5 (A) 10 (B) 20 (C) 30 (D) 36 (E) 60 14. This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print? (A) 9 P6 (B) 9 P3 (C) C9 (D) 9 C6 (E) 69 9 15. How many different strings of letters can be made by reordering the letters of the word SUCCESS? (A) 20 (B) 30 (C) 40 (D) 60 (E) 420 16. A company produces 8 different types of candies, and sells the candies in gift packs. How many different gift packs containing exactly 3 different candy types can the company put on the market? (A) 8 C2 (B) C3 P3 (E) (C) 8 8 3P2 (D) 8 8 P 2! 17. Fritz is taking an examination that consists of two parts, A and B, with the following instructions: Part A contains three questions, and a student must answer two. Part B contains four questions, and a student must answer two. Part A must be completed before starting Part B. In how many ways can the test be completed? (A) 12 (B) 15 (C) 36 (D) 72 (E) 90 18. A menu offers 2 entrees, 3 main courses, and 3 desserts. How many different combinations of dinner can be made? (A dinner must contain an entrée, a main course, and a dessert.) (A) 12 (B) 15 (C) 18 (D) 21 (E) 24 19. In how many ways can 3 red marbles, 2 blue marbles, and 5 yellow marbles be placed in a row? 10! 10! 10! (D) 10! 10! 12! (E) (A) 2! 5! 3! (B) (C)

( 3!
2!
5!) 2 10! 3! 2! 5! 3!
2!
5! 20. The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that 3 of Sam’s 4 funds grew by at least 10% over last year? 6C3 6 C 3
4 C1 6 P3
4 P1 6 P3
4 P1 (A) 6 C 3
4 C1 (C) (D) (E) (B) 10 C 4 10 P4 10 C 4 10 P4 10 C 4 21. The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that at least 3 of Sam’s 4 funds grew by at least 10% over the last year? 6C3 6C3 4 C1+ 6 C 4 C1 6 P3
4 P1 6 C 3
46 C 3
4 C1 + 6C 4 (A) (B) (D) (C) (E) 10 C 4 10 C 4 10 P4 10 C 4 10 C 4 22. In how many ways can the letters of the word ACUMEN be rearranged such that the vowels always appear together? 6! 4!
3! (D) 3! (E)4! 3!
3! (A) 3! 3! (B) (C) 2! 2! letters of the word ACCLAIM be rearranged such 2! 23. In how many ways can the that the vowels always appear together? 5! 5! 3! 7! 4!
3! 4!
3! (D) (E)
(A) (B) (C) 2!
2! 2! 2! 2!
2! 2!
2! 2! 24. In how many ways can the letters of the word GARGANTUNG be rearranged such that all the G’s appear together? 8! 8!
3! 8! 10! 8! (B) (C) (D) (E) (A) 2!
2! 2!
2! 2!
3! 3!
2!
2! 3!
2!
2! 13 25. In how many ways can the letters of the word GOSSAMERE be rearranged such that all S’s and M’s appear in the middle? 9! 7 P6 7 P6 3 P3 (D) 6 P6 3 P3 (E) 10 P6 3 P3 (B) (C)


(A) 2!
2! 2! 2! 2! 2! 2! 2! 2!
2! 26. How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word GREGARIOUS such that each word starts with G and ends with R? (A) 8P2 8 P2 8 P4 10 P2 (B) (C) 8P4 (D) (E) 2!
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2! 27. A coin is tossed five times. What is the probability that the fourth toss would turn a head? 1 1 1 (E)1 (A) (B) 1 (D) 5 P3 P (C) 3 5 9 2 2! 2 28. In how many of ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin? (A) 5C 4 (B) 5P4 (C) 54 (D) 45 (E) 55 29. On average, a sharpshooter hits the target once every 3 shots. What is the probability that he will hit the target in 4 shots? (A) 1 (B) 1/81 (C) 1/3 (D) 65/81 (E) 71/81 30. On average, a sharpshooter hits the target once every 3 shots. What is the probability that he will not hit the target until 4th shot? (A) 1 (B) 8/81 (C) 16/81 (D) 65/81 (E) 71/81 31. A new word is to be formed by randomly rearranging the letters of the word ALGEBRA. What is the probability that the new word has consonants occupying only the positions currently occupied by consonants in the word ALGEBRA? (A) 2/120 (B) 1/24 (C) 1/6 (D) 2/105 (E) 1/35 32. Chelsea has 5 roses and 2 jasmines. A bouquet of 3 flowers is to be formed. In how many ways can it be formed if at least one jasmine must be in the bouquet? (A) 5 (B) 20 (C) 25 (D) 35 (E) 40 33. In how many ways can 3 boys and 2 girls be selected from a group of 6 boys and 5 girls? (A) 10 (B) 20 (C) 50 (D) 100 (E) 200 34. In how many ways can a committee of 5 members be formed from 4 women and 6 men such that at least 1 woman is a member of the committee? (A) 112 (B) 156 (C) 208 (D) 246 (E) 252 35. In how many ways can 5 boys and 4 girls be arranged in a line so that there will be a boy at the beginning and at the end? 3! 5! 5! 3! (A)
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㜡 5! 6! 3! 5! 7! 36. In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together? (A) 12 (B) 18 (C) 30 (D) 36 (E) 72 37. In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all consonants are together? (A) 12 (B) 18 (C) 30 (D) 36 (E) 42 38. In how many ways can 4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other? (A) 1032 (B) 1152 (C) 1254 (D) 1432 (E) 1564 14  39. In how many ways can 4 boys and 4 girls be arranged in a row such that boys and girls alternate their positions (that is, boy girl)? (A) 1032 (B) 1152 (C) 1254 (D) 1432 (E) 1564 40. The University of Maryland, University of Vermont, and Emory University have each 4 soccer players. If a team of 9 is to be formed with an equal number of players from each university, how many number of ways can the selections be done? (A) 3 (B) 4 (C) 12 (D) 16 (E) 25 41. In how many ways can 5 persons be seated around a circular table? (A) 5 (B) 24 (C) 25 (D) 30 (E) 120 42. In how many ways can 5 people from a group of 6 people be seated around a circular table? (A) 56 (B) 80 (C) 100 (D) 120 (E) 144 43. What is the probability that a word formed by randomly rearranging the letters of the word ALGAE is the word ALGAE itself? (A) 1/120 (B) 1/60 (C) 2/7 (D) 2/5 (E) 1/30 Question 1 Section 1 A club consists of 8 women and 8 men. The club has a president and a vice president. No club member can hold more than one position. Quantity A Quantity B The number of possible assignments such that a woman is The number of possible assignments such that both the president and a man is vice president president and vice president positions are filled by women Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 2 Given an alphabet of 26 letters, with 21 consonants, and 5 vowels, approximately how many three-letter words can be formed with a vowel as the middle letter and a consonant as the last letter? 1000 1500 2500 3500 4000 Question 3 Of the 100 eighth-graders at Easton Junior High, 60 students take gym, 40 take a foreign language, and 30 take both gym and a foreign language. Quantity A Quantity B 30 The number of students taking neither gym nor a foreign language Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 4 Graham’s Catering Service currently employs three chefs and o ers three di erent meals. For an upcoming event, the catering service must provide three meals, with each chef cooking one of the meals. Quantity A Quantity B The number of assignments of chefs to meals if each chef must The number of assignments of chefs to meals if each chef may cook a different meal cook any of the three meals Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 5 A certain password must contain 3 distinct digits followed by 2 distinct capital letters. Given ten digits and 26 capital letters, how many different passwords are possible? Question 6 190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie? 10 24 30 32 45 15 Question 7 Geo is setting up an aquarium and must choose 4 of 6 di erent sh and 2 of 3 di erent plants. How many di erent combinations of fish and plants can Geoff choose? 8 12 18 45 90 Question 8 If the current day and time is 9:30 p.m. on Tuesday, what time will it be (to the nearest minute) 100,000 seconds from now? 1:17 a.m., Wednesday 1:10 a.m., Thursday 2:17 a.m., Thursday Question 9 3:47 p.m., Wednesday 1:17 a.m., Thursday What is the di erence between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee? 0 84 252 420 504 Question 10 Six students compete in a table tennis tournament. Each student plays each of the other students four times. What is the total number of games played in the tournament? Question 11 A four-person leadership committee is to be chosen from a student council that consists of seven juniors and ve seniors. Q is the total number of different leadership committees that include three seniors and one junior. Quantity A Quantity B Q 75 Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 12 Contestants at a baking contest must use between 5 and 8 of 10 possible ingredients. Quantity A Quantity B The number of ingredients that must be used to get the The number of ingredients that must be used to get the largest smallest possible number of different combinations possible number of different combinations Quantity A is greater. The two quantities are equal. Quantity B is greater. The relationship cannot be determined from the information given. Question 13 Depending on the night, a pizza restaurant o ers anywhere from seven to nine di erent choices of toppings. Sam wants a pizza with three toppings. Which of the following could be the number of di erent ways that Sam can order his pizza with three di erent toppings? Indicate all possible values. 35 42 56 84 210 252 504 Question 14 Depending on the day, an ice cream shop o ers seven to nine possible ice cream avors and three to four possible sauces. A Deluxe Sundae consists of two di erent types of ice cream and two di erent sauces. Which of the following could be the number of di erent Deluxe Sundaes that Eva can order? Indicate all possible values. 36 54 84 216 432 864 Question 1 Section 2 Six state governors meet at an annual convention. They line up in random order to pose for a photograph. If the governors of Alaska and Hawaii are among the six governors, how many di erent ways can the governors line up for the picture so that these two governors are adjacent? 5 10 120 240 720 16 Question 2 If Je has four movies, and must choose to watch either 1, 2, or 3 di erent movies, which of the following represents a possible number of different arrangements of movies that Jeff could watch? Indicate all possible values. 4 6 7 9 12 24 Question 3 Jess has nine different statues and chooses three to arrange in a display. How many arrangements can she make? Question 4 Of a group of 10 PTA members, a committee will be selected that has 1 president and 3 other members. How many di erent committees could be selected? Question 5 Esteban’s restaurant o ers a lunch special. A customer can order a platter consisting of four di erent small dishes from a selection of twelve choices. How many different platters can a customer create? 24 144 495 11,880 20,736 Question 6 Kate and Chad are planning their wedding dinner and must select 3 of 12 entrees and 2 of 3 desserts for their guests to be able to choose from. How many different combinations of offerings are possible? Question 7 For her Halloween display, Margaret plans to arrange a row of alternating witch and ghost gurines. The row must begin with a witch gurine and end with a ghost gurine. Margaret plans to purchase either three of each type of gurine or four of each type of gurine, and each gurine will look unique. Depending on how many gurines she purchases, which of the following could be the number of ways that she could arrange her display? Indicate all possible values. 6 24 36 72 576 720 40,320 Question 8 There are six cars in a motorcade. How many different arrangements of cars in the motorcade are possible? 6 21 72 120 720 Question 9 Mark can take three friends with him on a vacation and is listing the possible combinations of friends. If he has ve friends to choose from and is numbering each possible combination sequentially beginning with 1, which of the following numbers will appear on his list of combinations? Indicate all possible values. 2 10 15 24 60 120 Question 10 Twelve runners enter a race to compete for first second and, third place How. many different combinations of winners are possible? Question 11 Sherry supervises a crew of maintenance engineers for an o ce building. If there are 5 experienced maintenance engineers and 3 apprentice engineers and the engineers are sent out on jobs in teams, which of the following must be true? Indicate all possible values. There are 10 different 3-person teams of experienced engineers she could send. There are 3 different 2-person - teams of apprentice engineers she could send. There are 2 different 2 person teams of apprentice engineers she could send. There are 10 different 2-person teams of experienced engineers she could send. There are 10 different 4-person teams of experienced en ineers she could send. Question 13 For his birthday, Brian will receive either three or four di erently colored ties, either two or three di erently colored shirts, and either one or two di erently colored jackets. Depending on how many ties, shirts, and jackets he receives, which of the following values could be the number of ways he could make an outfit with one tie, one shirt, and one jacket? Indicate all possible values. 6 8 9 10 12 16 18 Question 14 Paul and Allen are choosing ties out of a selection of three distinct red ties, ve distinct green ties, and six distinct blue ties. If Paul and Allen each wear one tie, how many different ways could they wear ties of the same color? 17  1 D, 2 C, 3 E, 4 D, 5 B, 6 B, 7 C, 8 E, 9 C, 10 B, 11 E, 12 B, 13 E, 14 D, 15 E, 16 B, 17 D, 18 C, 19 D, 20 B, 21 E, 22 D, 23 E, 24 B, 25 D, 26 A, 27 C, 28 D, 29 D, 30 B, 31 E, 32 C, 33 E, 34 D, 35 C, 36 D, 37 B, 38 B, 39 B, 40 B, 41 B, 42 E, 43 B. 14. 13. 12. 11. Drill 211. 9. 8. 7. 6. 5. 4. 3. 2. 1. B B A C C A D D D D 60 Section 1 C, D A, B, D 468,000 12. B 8. E 5. C 1. D 56 6. 660 4. 840 3. 504 Section 2 7. C, E 9. A, B 10. 1320 2. A, E, F 11. A, B, D 14.EXPLANATIONS ANSWER KEYS 13. A, B, C, E, F, G 18  Interpreting and Analyzing Graphs Questions 1-3 refer to the following data. Section 1 Question 1 What was the total number of inventoried airplanes purchased by both airlines from 1997 to 1999? 110 117 175 227 315 Question 2 In 1994, Airline A bought 25 airplanes. All of these airplanes either remained in Airline A’s inventory or were sold to another airline. What percent of these airplanes were sold to another airline? 4% 10% 40% 60% 90% Question 3 Which of the following can be inferred from the graph? Indicate all possible values. Airline A had fewer customers than Airline B over the period shown. In 2002, Airline B’s inventory of planes purchased in 1993 was twice that purchased by Airline A in the same year. If all airplanes were purchased new, then the median age of an airplane in Airline B’s inventory in 2002 was greater than that of an airplane in Airline A’s inventory in 2002. Questions 4-6 refer to the following data. Questions 4-6 refer to the following data. Question 4 In 2005, the ratio of the average annual cost to attend a private university to the average annual cost to attend a public university was the same as it was in 1990. If the average annual cost to attend a public university in 2005 was $11,000, what was the average annual cost to attend private university in that year, to the nearest $1,000? $18,000 $24,000 $29,000 $32,000 $34,000 19  Question 5 By approximately what percent did the average annual cost to attend a private university increase from 1980 to 2000? 27% 73% 138% 267% 367% Question 6 The average annual cost to attend a private university increased at a constant rate from 1995 to 2000, and 2.5 million students attended private universities in 1998. If 2 million students attended private universities in 1990, then by approximately what percent did the total dollar amount spent on private universities increase from 1990 to 1998? 25% 30% 55% 70% 90% Questions 7-8 refer to the following data. The following charts represent April 2008 plant sales at the Friendly Nursery. Question 7 Which of the following is most nearly the percent of plants sold at Friendly Nursery in April 2008 that were herbs? 70% 40% 24% 18% 8% Question 8 In April 2008 there were four varieties of tomatoes available at Friendly Nursery: Red Giants, Mortgage Lifters, Beefsteaks and Sun Golds. If 1000 plants were sold, which of the following could be the number of Beefsteak tomato plants sold? Indicate all possible values. 1 42 246 312 580 Question 9 refers to the following data. Question 9 If Happy Puppy Pet Depot saw the same percentage increase in total number of animals sold from 2003 to 2004 as it did from 2002 to 2003, 9how Question manyto animals, refers to the nearest the following data. integer, did the store sell in 2004? Questions 7-8 refer to the following data. Question 10 refers to the following data. 20 Question 10 refers to the following data. Question 10 For how many of the years shown in the graph was the number of nonviolent crimes (burglary and auto theft) greater than the number of violent crimes (assault and domestic violence)? None One Two Three Four Question 11 refers to the following data. estion 11 refers t Qu o the following data. Question 11 For which of the following months does the average monthly high temperature for City X fall within one standard deviation of the average annual high temperature? Indicate all possible values. January March May July September November Question 12 refers to the following data. 21 Question 12 For what year depicted in the graphs was the percent decrease from the previous year of the number of honey producing colonies most similar to the average percent increase of the average price of a pound of honey for the six-year period? QQuestion uestion 1313refers refersto to thethe following following data.data. 22  Question 13 Golf equipment manufacturing in the United States experienced the same percent growth rate from 2001 to 2008 as it did from 1994 to 2001. If the share of golf supplies production made up of bags, balls and training aids each increased anywhere from 1% to 5% from 2001 to 2008, which of the following could be the sum of the value of bags, balls and training aids produced in the United States in 2008, in millions of dollars? Indicate all possible values. 1,550 1,627 1,855 2,197 2,339 Question 14 refers to the following data. Question 14 How many maple trees had a diameter greater than 49.4 cm? Section 2 Questions 1-3 refer to the following data. Question 1 Approximately what was the percentage growth of Pluton’s GDP from 2010 to 2011 ? 4% 15% 25% 40% 115% Question 2 Question 14 refers to the following data. In which year was the change from the prior year of the combined GDP of the two countries the least? Question 3 Shinmark spends of its GDP on military expenditures, while Pluton spends of its GDP on military expenditures. For which years does Shinmark’s military spending exceed Pluton’s? Indicate all possible values. 2006 2007 2008 2009 2010 2011 23  Question 4 refers to the following data. Question 4 (Click here to view a larger image.) The population of the U.S. grew by 29% between 1979 and 2004, during which time per capita energy consumption doubled. If average per capita energy used from coal was 25 MBTUs in 1979, which of the following are in the range of per capita energy, measured in MBTUs, provided by a single fossil fuel (coal, natural gas or oil) in 2004 ? Question 4 refers Indicate to the following all possible values. data. 12 25 37 41 61 79 Question 5 refers to the following data. Question 5 refe Question 5 To the nearest percent, what was the percentage increase for the country that experienced the greatest percent increase in number of departures between 1990 and 2001 ? Questions 6-9 refer to the following data. Questio 6 9 f graphh isf all training The following ing data. log for a triathlete. It documents the number of hours she trained each week at each of three disciplines over a four week period. 24 Question 6 Which of the following fall within the range of ratios of hours spent biking to hours spent swimming per week in this four week period? Indicate all possible values. 1:4 1:2 2:1 3:1 3:2 Question 7 The athlete aims to spend between 12 and 16 percent of her weekly training time swimming. For which of the weeks does her swimming fall within that range? 1 2 3 4 Question 8 The athlete’s average running pace is 7 miles per hour every week. How many miles did she run in week 2 ? 0.7 5.1 36.4 44.6 161.0 Question 9 In week 5, the athlete plans to decrease her training time in each sport by 10% to 20% of the hours she trained in week 4. Which of the following are possible numbers of hours she could bike in week 5? 3.9 5.6 7.2 9.8 16.6 22.8 Question 10 refers to the following data. (Click here to view a larger image.) Question 10 Technology books have become an increasingly important subcategory of science/nature books. If technology books represent 30% of new adult science/nature books, half of used adult science/nature books, and of children’s science nature books, how many technology books were sold in 2005? 25 Questions 11-12 refer to the following data. Question 11 The number of assaults reported in Fairfax dropped every year from 2004 to 2010. For which year(s) was the rate of decrease greater than it had been the previous year? Indicate all possible values. 2006 2007 2008 2009 2010 Question 12 Total crime incidents reported in Fairfax decreased by 25% from 2005 to 2010. For which of the crime categories presented in the graph was the percent change from 2005 to 2010 greater than the percent change of all crimes reported? Indicate all possible values. Assault Burglary None of the above Domestic violence Auto theft Question 13 refers to the following data. 2002 AIRPLANE INVENTORY FOR AIRLINES A AND B BY YEAR OF PURCHASE (as a percent of the 2002 inventory) Question 13 New regulations go into e ect in 2003 that require all planes in inventory to be newer than ten years old. Each year following 2002, both airlines need to sell the planes the regulations force them to eliminate from inventory, and then use the proceeds of those sales to increase their inventory by 10% (rounded down because they are unable to buy fractions of planes). What is the combined number of planes owned by the two companies following their sales and purchases in 2004 ? 26 Question 14 refers to the following data. Question 14 The Great American Scholar (GAS) Grants cover 100% of students’ tuition but no other expenses. In 1995, 4,000 GAS Grants were awarded, of which between and were mandated to go to public university students. In 1995, 50% of public university students’ costs went to tuition, while 85% of private university students’ costs went to tuition. Which of the following are possible total dollar values of all GAS Grants awarded in 1995 ? $35,500,000 $57,000,000 $72,000,000 $42,000,000 $64,000,000 $96,000,000 Answers Keys 1. D 2. D 1. B 3. C 2. 2010 4. C 3. A, B, C, E, F 5. D 4. C, D, E 6. E 5. 285 Section 1 7. D 6. C, D 8. A, B, C 7. A Section 2 9. 11,111 8. C 10. D 9. C 11. B, C, E, F 10. 109 12. 1986 11. B, D 13. C, D 12. A, C, D 14. 8 13. 626 14. D D 27