Blitzer, Thinking Mathematically, 8e Chapter 1 Test Item File SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find a counterexample to show that the statement is false. 1) No women have sat on the bench of the U.S. Supreme Court. Objective: (1.1) Understand and Use Inductive Reasoning
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 2) If a number is multiplied by itself, the result is greater than 0. A) The number is 0.
B) The number is 0.1.
C) The number is 1.
D) The number is
Objective: (1.1) Understand and Use Inductive Reasoning
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) All U.S. presidents have been one-term presidents. Objective: (1.1) Understand and Use Inductive Reasoning
4) All actors are Academy Award winners. Objective: (1.1) Understand and Use Inductive Reasoning
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify a pattern in the list of numbers. Then use this pattern to find the next number. 5) 2, 9, 16, 23, 30, ___ A) 37 B) 32 C) 44
D) 36
Objective: (1.1) Understand and Use Inductive Reasoning
6) 1, 12, 1, 18, 1, 24, 1, _____ A) 36
B) 30
C) 1
D) 32
C) 0
D) 2
C) -3,375
D) 3,375
C) -1/32
D) -1/64
Objective: (1.1) Understand and Use Inductive Reasoning
7) 31, 26, 21, 16, 11 A) 6
B) 5
Objective: (1.1) Understand and Use Inductive Reasoning
8) 3, -15, 75, -375, 1,875 A) 9,375
B) -9,375
Objective: (1.1) Understand and Use Inductive Reasoning
9) 1, -
1 1 1 1 , ,- , 8 16 2 4
A) 1/32
B) 1/64
Objective: (1.1) Understand and Use Inductive Reasoning
1
1 . 2
10) 1, 5, 2, 10, 4, 20 A) 30
B) 8
C) 6
D) 40
Objective: (1.1) Understand and Use Inductive Reasoning
Identify a pattern in the sequence of figures. Then use the pattern to find the next figure in the sequence. 11)
A)
________________ C)
B)
Objective: (1.1) Understand and Use Inductive Reasoning
12)
A)
B)
C)
D)
Objective: (1.1) Understand and Use Inductive Reasoning
2
D)
The problem describes procedures that are to be applied to numbers. Repeat the procedure for four numbers of your choice. Write a conjecture that relates the result of the process to the original number selected. 13) Select a number. Multiply the number by 16. Add 16 to the product. Divide this sum by 8. Subtract 2 from the quotient. A) The result is one more than the original number. B) The result is one more than double the original number. C) The result is double the original number. D) The result is the original number. Objective: (1.1) Understand and Use Inductive Reasoning
Use inductive reasoning to predict the next line in the pattern. Then perform the arithmetic to determine whether your conjecture is correct. 14) 60 - 9 = 51 600 - 89 = 511 6,000 - 789 = 5,211
A) 60,000 - 6,789 = 593,211 C) 60,000 - 6,789 = 53,211
B) 6,000 - 6,789 = 53,211 D) 600,000 - 6,789 = 53,211
Objective: (1.1) Understand and Use Inductive Reasoning
15) 96 - 94 + 92 - 90 = 97 - 95 + 93 - 91 106 - 104 + 102 - 100 = 107 - 105 + 103 - 101 A) 116 + 114 - 112 - 110 = 117 + 115 - 113 + 111 C) 116 - 114 - 112 + 110 = 117 - 115 + 113 - 111
B) 116 + 114 - 112 + 110 = 117 + 115 - 113 + 111 D) 116 - 114 + 112 - 110 = 117 - 115 + 113 - 111
Objective: (1.1) Understand and Use Inductive Reasoning
16) 2 x 4 = 3 × 5 - 7 4 x 6 = 5 × 7 - 11 A) 6 × 8 = 7 × 9 + 13
B) 6 × 8 = 7 × 9 - 13
C) 6 × 8 = 7 × 9 - 15
D) 6 × 8 = 9 × 11 - 15
Objective: (1.1) Understand and Use Inductive Reasoning
17) 3 × 3 = 9 33 × 33 = 1,089 333 × 333 = 110,889 A) 3,333 × 3,333 = 112,889 C) 3,333 × 3,333 = 111,889
B) 3,333 × 3,333 = 11,108,889 D) 333 × 3,333 = 11,108,889
Objective: (1.1) Understand and Use Inductive Reasoning
18) 20 × 21 = 22 × 23 - (20 + 21 + 22 + 23) 21 × 22 = 23 × 24 - (21 + 22 + 23 + 24) A) 23 × 24 = 25 × 26 - (23 + 24 + 25 + 26) C) 23 × 24 = 25 × 26 - (22 + 21 + 20 + 19)
B) 22 × 23 = 24 × 25 - (20 + 21 + 22 + 23 + 24 + 25) D) 22 × 23 = 24 × 25 - (22 + 23 + 24 + 25)
Objective: (1.1) Understand and Use Inductive Reasoning
3
19) (1 × 9) - 9 = 0 (21 × 9) - 9 = 180 (321 × 9) - 9 = 2,880 A) (4321 × 9) - 9 = 3,879 C) (4321 × 9) - 9 = 28,880
B) (4321 × 9) - 9 = 38,880 D) (432 × 9) - 9 = 38,880
Objective: (1.1) Understand and Use Inductive Reasoning
20) (4 × 1) × (2 × 1) = 8 (4 × 10) × (2 × 2) = 160 (4 × 100) × (2 × 3) = 2,400 A) (4 × 1000) × (2 × 4) = 36,000 C) (4 × 1000) × (2 × 4) = 32,000
B) (4 × 1000) × (2 × 4) = 28,000 D) (4 × 1000) × (2 × 4) = 3,200
Objective: (1.1) Understand and Use Inductive Reasoning
21) 37,037 × 3 = 111,111 37,037 × 6 = 222,222 37,037 × 9 = 333,333 37,037 × 12 = 444,444 A) 111,111 × 15 = 1,666,665 C) 37,037 × 18 = 666,666
B) 37,037 × 13 = 481,481 D) 37,037 × 15 = 555,555
Objective: (1.1) Understand and Use Inductive Reasoning
1 1 1 = 13 2 3
22)
1 1 1 1 + = 13 9 2 9 1 1 1 1 1 = 1+ + 27 3 9 27 2 1 1 1 1 1 1 = 1+ + + 81 3 9 27 81 2
A)
1 1 1 1 1 1 1 = 1+ + + + 729 3 9 27 81 729 2
B)
1 1 1 1 1 1 1 = 1+ + + + 243 3 9 27 81 243 3
C)
1 1 1 1 1 1 1 + + + + = 1243 3 9 27 81 243 2
D)
1 1 1 1 1 1 1 + + + + = 1162 3 9 27 81 162 2
Objective: (1.1) Understand and Use Inductive Reasoning
4
23)
8(5) = 10(5 - 1) 8(5) + 8(25) = 10(25 - 1) 8(5) + 8(25) + 8(125) = 10(125 - 1) 8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)
A) 8(5) + 8(25) + 8(125) + 8(625) + 8(3125) = 8(3125 - 1) B) 8(5) + 8(25) + 8(125) + 8(625) + 8(1250) = 10(1250 - 1) C) 8(5) + 8(25) + 8(125) + 8(625) + 8(5000) = 10(5000 - 1) D) 8(5) + 8(25) + 8(125) + 8(625) + 8(3125) = 10(3125 - 1) Objective: (1.1) Understand and Use Inductive Reasoning
The following table relates an adult's body weight, in pounds, to his or her dosage of a certain medication, in milligrams. 24) Weight 100 125 150 175 200 225 Dosage 20 25 30 a. Use inductive reasoning to fill in the missing portions of the table. b. What would be the dosage of a person who weighs 375 pounds?
A) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 95 115
B) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 39 40
b. 80 mg
b. 70 mg
C) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 35 35
D) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 40 45
b. 65 mg
b. 75 mg
Objective: (1.1) Understand and Use Inductive Reasoning
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem using inductive reasoning. 25) Write the next three "square" figurate numbers.
Objective: (1.1) Understand and Use Inductive Reasoning
26) Write the next three "triangular" figurate numbers.
Objective: (1.1) Understand and Use Inductive Reasoning
5
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which reasoning process is shown in the following example? 27) We examine the genetic blueprints of 100 people. No two individuals from this group of people have identical genetic blueprints. We conclude that for all people, no two people have identical genetic blueprints. A) reasoning by counterexample B) deductive reasoning C) theoretical reasoning D) inductive reasoning Objective: (1.1) Understand and Use Deductive Reasoning
28) If Mary goes to the mall, she gets ice cream. Mary did not get ice cream. We conclude Mary did not go to the mall. A) inductive reasoning B) reasoning by counterexample C) theoretical reasoning D) deductive reasoning Objective: (1.1) Understand and Use Deductive Reasoning
The problem describes procedures that are to be applied to numbers. Represent the original number as n and use deductive reasoning to prove a conjecture that relates the result of the process to the number n. 29) Select a number. Multiply the number by 24. Add 24 to the product. Divide this sum by 12. Subtract two from the quotient. 24n + 24 24n + 24 - 2 = 2n + 2 - 2 = 2n -2=n+1-2=n-1 A) B) 12 24
C)
24n + 24 -1=n+1-1=n 24
D)
24n + 12 - 2 = 2n + 1 - 2 = 2n - 1 12
Objective: (1.1) Understand and Use Deductive Reasoning
Solve the problem. 30) Study the pattern, or trend, shown by the data. Then select the expression that best describes the number of tickets sold, in thousands, n years after Year 1.
A) 2.5 - 0.2n
B) 2.5 - 1.02n
C) 2.5 + 0.2n
D) 2.5 + 1.02n
Objective: (1.1) Understand and Use Deductive Reasoning
Round the number to the given place value. 31) In the past year, a company spent $693,749,312 on advertising. Round the advertising figure to the nearest hundred thousand. A) $693,800,000 B) $700,000,000 C) $693,700,000 D) $600,000,000 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
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32) A publishing company sold 16,267,591 books last year. Round the number of books sold to the nearest ten million. A) 16,270,000 B) 20,000,000 C) 16,000,000 D) 10,000,000 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
33) In a town in Nebraska, the average consumption of soft drinks per day per elementary school student is 14.189 ounces. Round this value to the nearest tenth. A) 14.2 ounces B) 15 ounces C) 14.3 ounces D) 14.1 ounces Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
34) According to his ultra-precise scale, Jeremy gained 3.558 pounds in a three-month period. Round this amount to the nearest hundredth. A) 3.57 pounds B) 0.56 pounds C) 4 pounds D) 3.56 pounds Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
35) In a laboratory course in veterinary biology, fleas gathered from Alexander, a volunteered pet dog, averaged 0.168209 inch in length. Round this amount to the nearest thousandth. A) 0.169 inch B) 0.168 inch C) 1 inch D) 0.167 inch Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
Solve the problem with estimation, but do not use a calculator. Use rounding to make the resulting calculations simple. 36) Estimate the cost to buy a refrigerator for $999, a stove for $459, and a dishwasher for $349. A) $1,800 B) $1,600 C) $1,900 D) $1,700 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
37) Estimate the cost of 101 shirts at $19.95 each. A) $1995 B) $2000
C) $2,014.95
D) $200
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
38) If a person earns $29.90 per hour, estimate that person's annual salary. A) $70,000 B) $60,000 C) $50,000
D) $40,000
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
39) Find an estimate of A) 36
0.245 × 72 . 0.538
B) 144
C) 9
D) 18
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
40) Estimate the number of seconds in a day. A) 3,600 seconds B) 72,000 seconds
C) 1,400 seconds
D) 600,000 seconds
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
41) If a person earns $19,500 per year, estimate that person's hourly salary. A) $10 B) $50 C) $100
D) $40
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
42) You rented an apartment for $815 per month for 4 years. What is the total amount you paid in rent? A) $9600 B) $4,800 C) $38,400 D) $3,200 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
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43) You spend $40.24 for a meal. If you want to leave a 15% tip, estimate the amount of the tip. A) $4 B) $6 C) $10 D) $8 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 44) Four people share the use of a cable modem service that costs $49.95 a month. Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
45) If Jessica can type 48 words per minute, estimate the number of words she can type in one hour. Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The map shows main roads between various towns in a certain county. Use the map to answer the question. 46)
90 a. Estimate the distance from State City to Capitol Park. b. If a vehicle travels at an average of 30 miles per hour, estimate the traveling time from State City to Capitol Park. A) a. 360 miles B) a. 180 miles C) a. 270 miles D) a. 90 miles b. 12 hours b. 6 hours b. 9 hours b. 3 hours Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
8
The circle graph shows the number of times a group of survey respondents watched the news in the past week. Use the chart to answer the question.
47) If the number of respondents in the study was approximately 44,779, estimate how many stated that they watched the news 5-6 times in the last week. A) 8000 respondents B) 12,000 respondents C) 6000 respondents D) 10,000 respondents Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
The bar graph below represents various colors of cars sold. Use the graph to answer the question(s).
48) Estimate the number of tan cars sold. A) 30,000 B) 35,000
C) 40,000
D) 25,000
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
49) Estimate the number of white cars sold. A) 50,000 B) 47,000
C) 40,000
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
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D) 52,000
50) Which color sold over 50,000 cars? A) White B) Tan
C) Silver
D) Red
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
51) Which color sold under 20,000 cars? A) White B) Black
C) Tan
D) Yellow
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
52) Estimate how many more black cars were sold than silver cars. A) 21,000 B) 11,000 C) 14,000
D) 31,000
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
53) Estimate how many more white cars were sold than tan cars. A) 22,000 B) 17,000 C) 7,000
D) 27,000
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
The bar graph shows the percentages of health clubs in a large city that offer the service listed on the left. Use the graph to answer the question.
54) Estimate the percentage of health clubs in this city that offer Pilates. A) 19% B) 26% C) 29%
D) 23%
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
55) Which services are offered at at least 20% of this city's health clubs and at most 45% of the clubs? A) massage, Pilates and nutritional counseling B) Pilates and nutritional counseling C) Pilates, nutritional counseling, and body fat testing D) massage, Pilates, nutritional counseling, and body fat testing Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
10
The bar graph shows the amount of scholarship money available to student athletes at State University in four consecutive years. Use the graph to answer the question.
56) Estimate the amount of scholarship money available to female student athletes at State University in year 1. A) $16,000 B) $11,000 C) $1,900 D) $7,000 Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
The line graph below shows the price of a stock over the course of the day. Use the graph to answer the question(s). 10 9 8 7 Stock Price 6 (in dollars) 5 4 3 2 1 9AM 10AM 11AM 12PM 1PM
2PM
3PM
4PM
57) At what time was the stock price highest? A) 12 PM B) 2 PM
5PM 6PM
C) 9 AM
D) 1 PM
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
58) At what time was the stock price the lowest? A) 6 PM B) 10 AM
C) 1 PM
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
11
D) 9 AM
The line graph shows the pollution rate for a certain lake over six decades. Use the graph to answer the question.
59) Find an estimate for the pollution rate of the lake at the beginning of decade 6. A) 2.5% B) 3% C) 1.5%
D) 1%
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
The bar-graph shows the average living expenses of an undergraduate student. Provide an appropriate response.
60) Estimate the yearly increase in living expenses. A) $750 B) $500
C) $450
D) $650
Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables
61) Write a mathematical model that estimates the average living expenses, E, of an undergraduate student for x years after 2000. A) E = 5000 + 750x B) E = 5000 + 450x C) E = 5000 + 500x D) E = 5000 + 650x Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables
62) Use a mathematical model to predict the average living expenses of an undergraduate student in 2015 A) $12,500 B) $11,750 C) $14,750 D) $16,250 Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables
12
State the necessary piece of information that is missing which prevents you from solving the problem. 63) A car traveled at an average rate of 55 miles per hour and then reduced its speed to 49 miles per hour for the rest of the trip. If the trip took 4 hours, determine how long the car traveled at each rate. A) the destination B) the time of day C) the time at each rate D) the distance of the trip Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
Solve the problem. Then identify the piece of information that is unnecessary to solve the problem. 64) A rental car company that rents cars for local-only use charges $30 plus $0.30 for each mile the rental car is driven. If a customer gives the rental attendant $100 for a charge of $54, how many miles did the customer drive? A) 40 miles unnecessary information: the $54 charge B) 79 miles unnecessary information: the $0.30 per-mile charge C) 180 miles unnecessary information: the $30 flat charge D) 80 miles unnecessary information: giving $100 to attendant Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
Use the four-step method in problem solving to solve the problem. 65) City A has an elevation of 3,189 feet above sea level while city B has an elevation of 77 feet below sea level. How much higher is City A than City B? A) -3,012 feet B) -3,112 feet C) 3,266 feet D) 3,366 feet Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
66) Ashley owns 16 acres of land which she rents to a timber grower for $3,886 per acre per year. Her property taxes are $776 per acre per year. How much profit does she make on the land each year? A) $49,760 B) $62,952 C) $74,592 D) $61,400 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
67) At the beginning of the year, the odometer on an SUV read 37,587 miles. At the end of the year, it read 51,847 miles. If the car averaged 23 miles per gallon, how many gallons of gasoline did it use during the year? A) 620 gallons B) 14,260 gallons C) 62 gallons D) 327,980 gallons Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
68) A couch sells for $820. Instead of paying the total amount at the time of purchase, the same couch can be bought by paying $400 down and $60 a month for 12 months. How much is saved by paying the total amount at the time of purchase? A) $960 B) $300 C) $100 D) $30 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
69) CD's were purchased at $55 per dozen and sold at $40 for four CD's. Find the profit on 7 dozen CD's. A) $15 B) $65 C) $105 D) $455 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
13
70) A college cafeteria pays student cashiers $7.50 per hour. Cashiers earn an additional $1.70 per hour for each hour worked over 35 hours per week. A cashier worked 37 hours one week and 42 hours the second week. How much did this cashier earn in this two-week period? A) $726.80 B) $607.80 C) $592.50 D) $540.30 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
71) A car rents for $230 per week plus $0.25 per mile. Find the rental cost for a three-week trip of 700 miles. A) $175.00 B) $865.00 C) $1,215.00 D) $405.00 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
72) An accountant receives a salary of $261,500 per year. During the year, he plans to spend $91,000 on his mortgage, $58,000 on food, $32,000 on clothing, $43,000 on household expenses, and $29,000 on other expenses. With the money that is left, he expects to buy as many shares of stock at $250 per share as possible. How many shares will he be able to buy? A) 33 shares B) 34 shares C) 31 shares D) 36 shares Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
73) Andrea decided to rollerblade to her mother's house. Six blocks from her home, one of the wheels on her skate broke, and she had to walk the remaining eight blocks to her mother's. She could not repair her skate and had to walk all the way back home. How many more blocks did Andrea walk than she skated? A) 14 blocks B) 22 blocks C) 16 blocks D) 28 blocks Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
74) A store received 200 containers of milk to be sold by February 1. Each container cost the store $0.81 and sold for $1.57. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by February 1. If 180 containers were sold by February 1, how much profit did the store make? A) $120.60 B) $130.60 C) $145.80 D) $136.80 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
Solve the problem using the strategy of making a list or using a diagram. 75) How many matches will be required to determine the champion in a single-elimination tennis tournament that starts with 58 players? A) 58 matches B) 48 matches C) 57 matches D) 29 matches Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
76) A coin is tossed four times. How many ways can it come up heads 3 times and tails once? A) 4 B) 2 C) 3 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
14
D) 1
Solve the problem using the strategy of your choice. 77) Can you place the digits 1 through 9 into a 3 x 3 square so that each row, column, and diagonal add up to the same total? Four digits have been inserted. ( ) 1 ( ) 3 ( )( ) 4 ( ) 2 A) B) C) D) 8 1 9 8 1 6 6 1 8 8 1 7 3 5 7 3 5 7 3 5 7 3 5 6 4 6 2 4 9 2 4 9 2 4 9 2 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 78) Some numbers in the printing of a division problem have become illegible. They are designated below by *. Fill in the blanks. 1 * * * * 5 * * * 3 6 * 7 2 * * * * ** * * * 0 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 79) Three people have telephone prefixes whose three digits have the same sum. One of the prefixes is 448. None of the prefixes contains a digit that is in one of the other prefixes. None of the prefixes has a first digit of 6 or 1. One of the prefixes begins with 5. Another ends with 2. What is the prefix that ends with 2? A) 372 B) 772 C) 962 D) 592 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
80) Find the number of squares in the figure.
A) 30
B) 55
C) 26
Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
15
D) 25
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. This exercise involves problems encountered in everyday life. Write seven or more short solutions that might be effective in solving the problem. 81) Your younger brother has just graduated college. You allow him to live in your house, rent-free, under the condition that he does all the household chores. However, after two months of living with you, your brother has not done any chores. What actions can you take to remedy this situation? Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
Solve the problem. 82) A certain Internet provider charges $16.95 for 150 hours of online usage per month and $0.95 for each additional hour. If Marc was online for 200 hours last month, what was his bill for that month? Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
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Answer Key Testname: UNTITLED1
1) Answers may vary. Sandra Day O'Connor is one possible answer. 2) A 3) Answers may vary. Sample answer: George Washington was elected to two terms. 4) Answers may vary. Sample answer: Actor Jim Carrey is not an Academy Award winner. 5) A 6) B 7) A 8) B 9) C 10) B 11) D 12) A 13) C 14) C 15) D 16) C 17) B 18) D 19) B 20) C 21) D 22) C 23) D 24) D 25) 16, 25, 36 26) 10, 15, 21 27) D 28) D 29) A 30) A 31) C 32) B 33) A 34) D 35) B 36) A 37) B 38) B 39) A
40) B 41) A 42) C 43) B 44) $50 ÷ 4 = $12.50 45) 50 × 60 = 3000 46) C 47) A 48) A 49) B 50) D 51) D 52) A 53) B 54) D 55) B 56) D 57) D 58) D 59) C 60) D 61) D 62) C 63) D 64) D 65) C 66) A 67) A 68) B 69) D 70) B 71) B 72) B 73) C 74) B 75) C 76) A 77) B 148 78) 36 5328 36
81) Answers may vary. Possible answers may include: 1. I could kick my brother out of my house. 2. I could start charging my brother rent. 3. I could make a list or schedule of chores that I want him to perform, in hopes of motivating him. 4. I could offer my brother an additional incentive for each chore he performs. 5. I could relentlessly follow my brother around the house to ensure that he performs his chores. 6. I can throw out the agreement completely and allow him to live in my house for free. 7. I could hire a maid and make my brother pay for it. 8. I could change all the locks on the doors. 82) $64.45
172 144 288 288 0
79) B 80) B 17
Blitzer, Thinking Mathematically, 8e Chapter 2 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the collection is not well defined and therefore not a set. 1) The collection of frogs and toads currently in tanks at a nature center A) well defined; set B) not well defined; not a set Objective: (2.1) Determine Whether the Collections are Well Defined or Not
2) The collection of beautiful oil paintings currently on display at an art gallery A) well defined; set B) not well defined; not a set Objective: (2.1) Determine Whether the Collections are Well Defined or Not
Write a word description of the set. 3) {January, February, March, April, May, June, July, August, September, October, November, December} A) seasons of the year B) days of the year C) days of the week D) months of the year Objective: (2.1) Use Three Methods to Represent Sets
4) {2, 4, 6, 8, ..., 100} A) odd numbers from 2 to 100 C) even numbers from 2 to 100
B) numbers from 2 to 100 D) all even numbers
Objective: (2.1) Use Three Methods to Represent Sets
5) {March, May} A) the set of months in the year C) the set of months that begin with M
B) the set of months in the Spring D) the set of months that are warm
Objective: (2.1) Use Three Methods to Represent Sets
6) {10, 11, 12, 13, ...} A) the set of natural numbers less than 14 C) the set of natural numbers
B) the set of two-digit natural numbers D) the set of natural numbers greater than 9
Objective: (2.1) Use Three Methods to Represent Sets
Express the set using the roster method. 7) the set of natural numbers less than or equal to 7 A) {0, 1, 2, 3, . . . , 6} B) {1, 2, 3, . . . , 7}
C) {1, 2, 3, . . . , 6}
D) {0, 1, 2, 3, . . . , 7}
C) {2, 4, 6, . . . , 14}
D) {1, 3, 5, . . . , 15}
C) {10,11,12,...}
D) {10,11,12}
Objective: (2.1) Use Roster Method
8) the set of odd natural numbers less than 15 A) {1, 3, 5, . . . , 13} B) {0, 1, 3, 5, . . . , 13} Objective: (2.1) Use Roster Method
9) {x | x % N and x is greater than 9} A) {9,10,11,...} B) {10,12,14,...} Objective: (2.1) Use Roster Method
1
10) {x | x % N and x lies between 0 and 4} A) {1, 2, 3, 4} B) {0, 1, 2, 3}
C) {0, 1, 2, 3, 4}
Objective: (2.1) Use Roster Method
List the elements in the set. 11) The set of the days of the week A) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} B) {Saturday, Sunday} C) {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} D) {Tuesday, Thursday} Objective: (2.1) Use Roster Method
Determine if the set is the empty set. 12) {0, +} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
13) {x|x is a living U.S. president born after 1700} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
14) {x|x is the number of living U.S presidents born before 1700} A) Yes, it is the empty set. B) No, it is not the empty set. Objective: (2.1) Define and Recognize the Empty Set
15) {x|x is a day of the week whose name begins with the letter Y} A) Yes, it is the empty set. B) No, it is not the empty set. Objective: (2.1) Define and Recognize the Empty Set
16) {x|x < 2 and x > 6} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
17) {x|x % Ν and 10 < x < 14} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
18) {x|x is a number less than 6 or greater than 10} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
Determine whether the statement is true or false. 19) 9 % {1, 3, 5, 7, 9} A) True
B) False
Objective: (2.1) Use the Symbols % and '
2
D) {1, 2, 3}
20) 7 % {1, 2, 3, ..., 15} A) True
B) False
Objective: (2.1) Use the Symbols % and '
21) 19 % {2, 4, 6, ..., 20} A) True
B) False
Objective: (2.1) Use the Symbols % and '
22) 14 ' {1, 2, 3, ..., 10} A) True
B) False
Objective: (2.1) Use the Symbols % and '
23) 11 ' {1, 2, 3, ..., 40} A) True
B) False
Objective: (2.1) Use the Symbols % and '
24) 3 ' {x|x % N and x is odd} A) True
B) False
Objective: (2.1) Use the Symbols % and '
25) 22 ' {x|x % N and 15 < x K 25} A) True
B) False
Objective: (2.1) Use the Symbols % and '
26) -5 ' N A) True
B) False
Objective: (2.1) Use the Symbols % and '
Find the cardinal number for the set. 27) {33, 35, 37, 39, 41} A) 4
B) 33
C) 6
D) 5
C) 60
D) 30
C) 3
D) 1
Objective: (2.1) Find the Cardinal Number for Each Set
28) {10, 12, 14, . . . , 68} A) 20
B) 15
Objective: (2.1) Find the Cardinal Number for Each Set
29) {x | x is a day of the week that begins with the letter N} A) 0 B) 2 Objective: (2.1) Find the Cardinal Number for Each Set
30) Determine the cardinal number of the set {x | x is a letter of the alphabet} A) 25 B) 26 C) 30
D) 23
Objective: (2.1) Find the Cardinal Number for Each Set
31) D = {seven} A) 1
B) 7
C) 0
Objective: (2.1) Find the Cardinal Number for Each Set
3
D) 5
32) B = {x|x % N and 1 K x < 9} A) 7
B) 9
C) 8
D) 10
C) 9
D) 16
Objective: (2.1) Find the Cardinal Number for Each Set
33) C = {x|x K 4 and x L 12} A) 0
B) 8
Objective: (2.1) Find the Cardinal Number for Each Set
Are the sets equivalent? 34) A is the set of residents age 45 or older living in the United States B is the set of residents age 45 or older registered to vote in the United States A) Yes B) No Objective: (2.1) Recognize Equivalent Sets
35) A = {11, 12, 13, 14, 15} B = {10, 11, 12, 13, 14} A) Yes
B) No
Objective: (2.1) Recognize Equivalent Sets
36) A = {13, 15, 17, 19, 21} B = {14, 16, 18, 20, 22} A) Yes
B) No
Objective: (2.1) Recognize Equivalent Sets
37) A = {11, 12, 12, 13, 13, 13, 14, 14, 14, 14} B = {14, 13, 12, 11} A) Yes
B) No
Objective: (2.1) Recognize Equivalent Sets
38) A = {Larry, Moe, Curly. Shemp} B = {Posh, Sporty, Baby, Scary} A) Yes
B) No
Objective: (2.1) Recognize Equivalent Sets
Are the sets equal? 39) {p, q, r, s} = {q, s, r, p} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
40) {20, 22, 24, 26, 28} = {22, 24, 26, 28} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
41) {7, 7, 11, 11, 16} = {7, 11, 16} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
4
42) A is the set of residents age 53 or older living in the United States B is the set of residents age 53 or older registered to vote in the United States A) Yes B) No Objective: (2.1) Recognize Equal Sets
43) A = {20, 21, 22, 23, 24} B = {19, 20, 21, 22, 23} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
44) A = {21, 23, 25, 27, 29} B = {22, 24, 26, 28, 30} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
45) A = {14, 15, 15, 16, 16, 16, 17, 17, 17, 17} B = {17, 16, 15, 14} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
Determine whether the set is finite or infinite. 46) {x | x % N and x L 100} A) Finite
B) Infinite
Objective: (2.1) Distinguish Between Finite and Infinite sets
47) {x | x % N and x K 1,000} A) Finite
B) Infinite
Objective: (2.1) Distinguish Between Finite and Infinite sets
48) The set of natural numbers less than 50 A) Finite
B) Infinite
Objective: (2.1) Distinguish Between Finite and Infinite sets
49) The set of natural numbers less than 1 A) Finite
B) Infinite
Objective: (2.1) Distinguish Between Finite and Infinite sets
Express the set using set-builder notation. Use inequality notation to express the condition x must meet in order to be a member of the set. 50) A = {14, 15, 16, 17, 18,...} A) {x | x % N and x K 14} B) {x | x % N and x L 14} C) {x | x % N and x > 14} D) {x | x % N and x L 18} Objective: (2.1) Apply Set Notation to Sets of Natural Numbers
51) A = {600, 601, 602, . . ., 6,000} A) {x | x % N and 600 K x K 6,000} C) {x | x % N and x L 600 }
B) {x | 600 < x < 6,000} D) {x | x % N and x K 6,000}
Objective: (2.1) Apply Set Notation to Sets of Natural Numbers
5
The bar graph shows the percentage of adults that use the Internet for specific tasks. Use the graph to represent the given set using the roster method. 52)
34 29
25 18 13
the set of tasks in which usage exceeds 23% A) {e-mail, information searches} C) {e-mail, information searches, news}
B) {e-mail, information searches, news, job} D) {job, school}
Objective: (2.1) Solve Applications
53)
33 28
24 17 12 {x | x is a task in which usage lies between 14% and 32%} A) {news, job} C) {email, information searches, news, job, school} Objective: (2.1) Solve Applications
6
B) {information searches, news, job} D) {news}
The line graph shows the percentage of obese adults in a certain city by age. Based on the information in the graph, represent the set using the roster method. 54)
30 25 20 15 10 5
{x | x is an age at which 20% of adults in city X are obese} A) {30} B) {40}
C) {60}
Objective: (2.1) Solve Applications
Write 5 or * in the blank so that the resulting statement is true. 55) {4, 6, 8} {3, 4, 5, 6, 8} A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
56) {3, 40, 45} A) 5
{9, 40, 45, 55} B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
57) {red, blue, green} _____ {blue, green, yellow, black} A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
58) {x | x is a tree} _____ {x | x is a spruce tree} A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
59) {c, a, n, d, i, d, a, t, e} _____ {a, c, d, e, i, t, a, n, d} A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
60)
8 3 11 7 , _____ , 11 7 8 3
A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
7
D) {50}
Use 5, *, 2, or both 2 and 5 to make a true statement. 61) {a, b} {z, a, y, b, x, c} A) * B) 2 and 5
C) 2
D) 5
C) 5
D) 2 and *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
62) {6, 7, 8} A) *
{6, 7, 8} B) 2
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
63) {x | x is a male who is registered with Selective Service} _____ {x | x is a male who is in the Army} A) 2 B) 5 and 2 C) * D) 5 Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
Determine whether the statement is true or false. 64) Alice 5 {Bob, Carol, Ted, Alice} A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
65) {Ted} 5 {Bob, Carol, Ted, Alice} A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
66) +5 {France, Germany, Switzerland} A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
67) {2, 9} * {9, 2} A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
68) {1} * + A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
List all the subsets of the given set. 69) {Siamese, domestic shorthair} A) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, B) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, { } C) {Siamese, domestic shorthair}, {domestic shorthair}, { } D) {Siamese}, {domestic shorthair}, { } Objective: (2.2) Determine the Number of Subsets of a Set
70) {12} A) {12}
B) { }
C) {0}, {12}, { }
Objective: (2.2) Determine the Number of Subsets of a Set
8
D) {12}, { }
71) + A) +
B) no subsets
C) { }, {0}
D) {+}
Objective: (2.2) Determine the Number of Subsets of a Set
Calculate the number of subsets and the number of proper subsets for the set. 1 1 1 1 , , , 72) 6 7 8 9 A) 15; 14
B) 14; 15
C) 15; 16
D) 16; 15
C) 64; 63
D) 63; 64
C) 510; 511
D) 511; 512
C) 16; 15
D) 8; 7
C) 64; 65
D) 128; 127
Objective: (2.2) Determine the Number of Subsets of a Set
73) {1, 3, 5, 7, 9, 11} A) 63; 62
B) 62; 63
Objective: (2.2) Determine the Number of Subsets of a Set
74) the set of natural numbers less than 10 A) 512; 511 B) 511; 510 Objective: (2.2) Determine the Number of Subsets of a Set
75) the set of words describing the colors on a stoplight A) 15; 16 B) 7; 8 Objective: (2.2) Determine the Number of Subsets of a Set
76) {x | x is a day of the week} A) 127; 126
B) 128; 129
Objective: (2.2) Determine the Number of Subsets of a Set
Provide an appropriate response. 77) If set A is equivalent to the set of natural numbers, then n(A) < E0 . A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
78) If set A is equivalent to the set of odd natural numbers, then n(A) = E0 . A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
79) The set {1, 2, 3, ..., 100} has 2 100 proper subsets. A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
80) {x|x % N and 45 < x < 70} 5 {x|x % N and 45 K x K 70} A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
81) +* {+ } A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
9
Consider below the branching tree diagram based on the number per 3000 American adults.
Let T = the set of Americans who like classical music R = the set of Republicans who like classical music D = the set of Democrats who like classical music I = the set of Independents who like classical music Determine whether the statement is true or false. 82) R % T A) True
B) False
Objective: (2.2) Solve Applications
83) D 2 T A) True
B) False
Objective: (2.2) Solve Applications
84) Let M = the set of Democratic men who like classical music W = the set of Democratic women who like classical music W 2T A) True B) False Objective: (2.2) Solve Applications
85) Let M = the set of Democratic men who like classical music W = the set of Democratic women who like classical music If x %D, then x %M. A) True B) False Objective: (2.2) Solve Applications
86) Let M = the set of Republican men who like classical music W = the set of Republican women who like classical music If x %W, then x %R. A) True B) False Objective: (2.2) Solve Applications
87) If x %R, then x'I. A) True
B) False
Objective: (2.2) Solve Applications
10
88) Let M = the set of Independent men who like classical music W = the set of Independent women who like classical music The set of elements in M and W combined is equal to set I. A) True B) False Objective: (2.2) Solve Applications
Use the formula for the number of subsets of a set with n elements to solve the problem. 89) Pasta comes with tomato sauce and can be ordered with some, all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli, shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for ordering pasta with tomato sauce? A) 128 B) 255 C) 127 D) 256 Objective: (2.2) Solve Applications
90) A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the situation, no engines, one engine, two engines, three engines, or all four engines can be sent to a fire. How many options does the dispatcher have for sending the fire engines to the scene of the caller? A) 15 B) 8 C) 7 D) 16 Objective: (2.2) Solve Applications
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Describe a universal set U that includes all elements in the given sets. Answers may vary. 91) A = {Copeland, Gershwin, Bernstein} B = {Strauss, Mendlssohn} Objective: (2.3) Understand the Meaning of a Universal Set
92) A = {fruit juice, coffee} B = {tea, spring water} Objective: (2.3) Understand the Meaning of a Universal Set
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set. 93) A = {2, 4, b, d} A) {1, 5, a, c, e} B) {1, 5, a, e} C) {1, 2, 4, 5, a, b, c, d, e} D) {1, 3, 5, a, c, e} Objective: (2.3) Understand the Meaning of a Universal Set
Let U = {21, 22, 23, ..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, ..., 39}, and D = {22, 24, 26, 28, ..., 40}. Use the roster method to write the following set. 94) A' A) A' = {21, 22, 23, . . . , 40} B) A' = {26, 28, 30, . . . , 40} C) A' = {27, 29, 31, . . . , 39} D) A' = {26, 27, 28, . . . , 40} Objective: (2.3) Understand the Meaning of a Universal Set
11
Let U = {21, 22, 23, 24, ...}, A = {21, 22, 23, 24, ..., 40}, B = {21, 22, 23, 24, ..., 50}, C = {22, 24, 26, 28, ...}, and D = {21, 23, 25, 27, ...}. Use the roster method to write the following set. 95) C' A) C' = {21, 23, 25, 27, ..., 39} B) C' = {21, 22, 23, 24, ...} C) C' = {21, 23, 25, 27, ...} D) C' = {22, 24, 26, 28, ...} Objective: (2.3) Understand the Meaning of a Universal Set
Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 96) (A 1 B)' A) {r, t, v, x} B) {s, u, w}
C) {r, s, t, u, v, w, x, z}
D) {t, v, x}
C) {s, u, w}
D) {q, s, t, u, v, w, x, y}
C) {q, s, u, v, w, x, y, z}
D) {w, y}
Objective: (2.3) Perform Operations with Sets
97) A' 1 B A) {r, s, t, u, v, w, x, z}
B) {q, r, s, t, v, x, y, z}
Objective: (2.3) Perform Operations with Sets
98) C' 1 A' A) {q, r, s, t, u, v, x, z}
B) {s, t}
Objective: (2.3) Perform Operations with Sets
99) B 1 C A) {q, s, u, w, y} C) {q, s, v, w, x, y, z}
B) {v, w, x, y, z} D) {q, r, s, t, u, v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
100) C 1 + A) {v, w, x, y, z}
B) {q, s, y, z}
C) { }
D) {q, s, u, w, y}
Objective: (2.3) Perform Operations with Sets
101) B 1 U A) {q, s, y, z} C) {q, r, s, t, u, v, w, x, y, z}
B) {q, s, u, w, y} D) {v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
102) A . B' A) {u, w}
B) {r, s, t, u, v, w, x, z}
C) {t, v, x}
D) {q, s, t, u, v, w, x, y}
C) {r, s, t, u, v, w, x, z}
D) {t, v, x}
C) {t, v, x}
D) {q, s, t, u, v, w, x, y}
Objective: (2.3) Perform Operations with Sets
103) (A 1 B)' A) {s, u, w}
B) {r, t, v, x}
Objective: (2.3) Perform Operations with Sets
104) (A . B)' A) {r, t, u, v, w, x, z}
B) {s, u, w}
Objective: (2.3) Perform Operations with Sets
12
105) A' 1 B A) {q, r, s, t, v, x, y, z}
B) {r, s, t, u, v, w, x, z}
C) {q, s, t, u, v, w, x, y}
D) {s, u, w}
C) {w, y}
D) {q, r, s, t, u, v, x, z}
C) {w, y}
D) {r, t}
C) {q, s, u, w, y, z}
D) {q, s, y}
Objective: (2.3) Perform Operations with Sets
106) C' 1 A' A) {s, t}
B) {q, s, u, v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
107) C' . A' A) {q, r, s, t, u, v, x, z}
B) {q, s, u, v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
108) A . B A) {r, t, u, v, w, x, z}
B) {v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
109) B 1 C A) {v, w, x, y, z} C) {q, s, u, w, y}
B) {q, s, v, w, x, y, z} D) {q, r, s, t, u, v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
110) A' A) {r, t, v, x, z} C) {q, r, s, t, u, v, w, x, y, z}
B) {s, u, w, y} D) {q, s, y, z}
Objective: (2.3) Perform Operations with Sets
111) (A . C)' A) {q, r, s, t, u, v, w, x, y, z} C) {q, s, y, z}
B) {w, y} D) {q, r, s, t, u, v, x, z}
Objective: (2.3) Perform Operations with Sets
112) C 1 + A) {q, s, u, w, y}
B) {q, s, y, z}
C) {v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
113) B 1 U A) {q, r, s, t, u, v, w, x, y, z} C) {q, s, y, z}
B) {q, s, u, w, y} D) {v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
13
D) { }
Use the Venn diagram to determine the set or cardinality. 114) A
A) {12, 15, 16}
B) {11, 13, 14, 17}
C) {11, 12, 13}
D) {13, 17}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
115) B
A) {12, 13, 15, 16, 17}
B) {14, 16, 17}
C) {11, 14}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
116) U
A) {12, 15, 16} C) {11, 12, 13, 14, 15, 16, 17, 18, 19}
B) {13, 17} D) {11, 14}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
14
D) {13, 17}
117) A . B
A) {%, @, &, one, six}
B) {@, &}
C) {%, one, six}
D) {77, 95}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
118) n(A 1 B)
A) 5
B) {%, @, &, one, six}
C) 2
D) {@, &}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
119) n(1) - n(B)
A) {%, 77, 95}
B) 4
C) 3
D) {%, @, &, 77, 95}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
Use the formula for the cardinal number of the union of two sets to solve the problem. 120) Set A contains 4 elements, set B contains 9 elements, and 2 elements are common to sets A and B. How many elements are in A 1 B? A) 11 B) 13 C) 12 D) 10 Objective: (2.3) Use the Formula for n(A 1 B)
121) Set A contains 8 letters and 12 numbers. Set B contains 12 letters and 8 numbers. Two letters and 5 numbers are common to both sets A and B. Find the number of elements in set A or set B. A) 40 B) 33 C) 27 D) 47 Objective: (2.3) Use the Formula for n(A 1 B)
15
122) Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A 1 B) then how many elements are in (A . B)? A) 13 B) 8 C) 17 D) 5 Objective: (2.3) Use the Formula for n(A 1 B)
In the exercise below, let U = {x|x % N and x < 10} A = {x|x is an odd natural number and x < 10} B = {x|x is an even natural number and x < 10} C = {x|x % N and 3 < x < 5} Find the set. 123) A 1 B A) {1, 3, 5, 7, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9}
B) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} D) B or {2, 4, 6, 8}
Objective: (2.3) Find Each of the Given Sets
124) B . U A) U or {1, 2, 3, 4, 5, 6, 7, 8, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B) B or {2, 4, 6, 8} D) B or {2, 4, 6, 8, 10}
Objective: (2.3) Find Each of the Given Sets
125) B . C' A) B or {2, 4, 6, 8, 10}
B) C or {4}
C) B or {2, 4, 6, 8}
Objective: (2.3) Find Each of the Given Sets
126) (A . C)' A) {1, 3, 4, 5, 7, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B) {1, 2, 3, 5, 6, 7, 8, 9} D) U or {1, 2, 3, 4, 5, 6, 7, 8, 9}
Objective: (2.3) Find Each of the Given Sets
Use the Venn diagram to list the elements of the set in roster form. 127)
A 1B A) {11, 12, 13, 14, 15, 16, 17, 18, 19} C) {13, 17}
B) {11, 12, 14, 15, 16} D) {11, 12, 13, 14, 15, 16, 17}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
16
D) {2, 6, 8}
128)
A .B A) {13, 17} C) {11, 12, 13, 14, 15, 16, 17}
B) {11, 12, 13, 14, 15, 16, 17, 18, 19} D) {11, 12, 14, 15, 16}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
129)
A'
A) {12, 15, 16, 18, 19}
B) {11, 13, 14, 17}
C) {11, 14, 18, 19}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
130)
B'
A) {11, 14} C) {12, 15, 16, 18, 19}
B) {11, 14, 18, 19} D) {11, 13, 14, 17, 18, 19}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
17
D) {12, 15, 16}
131)
(A . B)' A) {11, 12, 14, 15, 16, 18, 19} C) {13, 17}
B) {11, 12, 14, 15, 16} D) {18, 19}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
132)
(A 1 B)' A) {11, 12, 14, 15, 16} C) {13, 17}
B) {11, 12, 13, 14, 15, 16, 17} D) {18, 19}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
133)
A' . B A) {11, 13, 14, 17, 18, 19} C) {11, 14}
B) {12, 15, 16} D) {12, 15, 16, 18, 19}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
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Use the Venn diagram to list the elements of the set in roster form.
134) The set of students who studied Sunday A) {Kenneth, Miguel, Kavita} C) {Sam, Sophia, Kenneth, Miguel, Kavita}
B) {Kenneth, Miguel, Kavita, Vijay} D) {Sam, Sophia}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
135) The set of students who studied Saturday or Sunday A) {Karen, Charly, Vijay} B) {Sam, Sophia} C) {Karen, Charley, Sam, Sophia, Kenneth, Miguel, Kavita, Vijay} D) {Karen, Charley, Sam, Sophia, Kenneth, Miguel, Kavita} Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
136) The set of students who studied Sunday and not Saturday A) {Kenneth, Miguel, Kavita, Vijay} C) {Sam, Sophia}
B) {Karen, Charly} D) {Kenneth, Miguel, Kavita}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
137) The set of students who studied neither Saturday nor Sunday A) {Vijay} B) {U, Vijay} C) {} D) {Vijay, Karen, Charly} Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
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The bar graph shows the percentage of adults that prefer to do certain activities during the weekdays or weekends.
Use the information in the graph to place the indicated activity in the correct region of the Venn diagram below.
138) Cleaning A) II
B) I
C) IV
D) III
B) III
C) I
D) II
B) I
C) III
D) IV
B) II
C) III
D) I
Objective: (2.3) Solve Applications
139) Exercising A) IV Objective: (2.3) Solve Applications
140) Shopping A) II Objective: (2.3) Solve Applications
141) Reading A) IV Objective: (2.3) Solve Applications
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Use the following definition to place the indicated natural number in the correct region of the Venn diagram. A palindromic number is a natural number whose value does not change if its digits are reversed. U = the set of natural numbers A = the set of palindromic numbers B = the set of odd numbers
142) 160
A)
B)
160
160
C)
D)
160
160
Objective: (2.3) Understanding Palindromic Number
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143) 1,840
A)
B)
1,840
1,840
C)
D)
1,840
1,840
Objective: (2.3) Understanding Palindromic Number
22
144) 175
A)
B)
175
175
C)
D)
175
175
Objective: (2.3) Understanding Palindromic Number
23
145) 258
A)
B)
258
258
C)
D)
258
258 Objective: (2.3) Understanding Palindromic Number
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Many children do not have access to computers at home. School has an equalizing effect. Family income is a strong factor in access. Use the information in the graph to write the set in the exercise in roster form or express the set as +.
146) {x | x is home access by more than 34% of the students} . {x | x is school access by less than 73% of the students} A) {$75,000 or more} B) {$50,000 to $74,999} C) {$25,000 to $49,999} D) {Less than $25,000} Objective: (2.3) Solve Apps: Venn Diagram
147) the set of home access by more than 80% of the students and school access by less than 70% of the students} A) {$50,000 to $74,999} B) {$50,000 to $74,999, $75,000 or more} C) {Less than $25,000} D) + Objective: (2.3) Solve Apps: Venn Diagram
Solve the problem. 148) Let U = the set of the days of the week, A = {Monday, Tuesday, Wednesday, Thursday, Friday} and B = {Friday, Saturday, Sunday}. Find (A . B)'. A) {Saturday, Sunday} B) {Friday} C) {Monday, Tuesday, Wednesday, Thursday, Saturday, Sunday} D) + Objective: (2.3) Solve Apps: Venn Diagram
25
Many children do not have access to computers at home. School has an equalizing effect. Family income is a strong factor in access. Use the information in the graph to write the set in the exercise in roster form or express the set as +.
149) {x | x is home access by more than 34% of the students} 1 {x | x is school access by less than 81% of the students} A) {$50,000 to $74,999, $75,000 or more} B) {Less than $25,000, $75,000 or more} C) {$25,000 to $49,999, $50,000 to $74,999} D) {Less than $25,000, $25,000 to $49,999} Objective: (2.3) Solve Apps: Venn Diagram
150) the set of home access by more than 80% of the students or school access by less than 87% of the students} A) {Less than $25,000, $25,000 to $49,999, $50,000 to $74,999} B) {$50,000 to $74,999, $75,000 or more} C) {Less than $25,000, $25,000 to $49,999} D) {$25,000 to $49,999, $50,000 to $74,999, $75,000 or more} Objective: (2.3) Solve Apps: Venn Diagram
Use sets to solve the problem. 151) Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly beans, and 17 like both red and green jelly beans. How many of the students surveyed like neither red nor green jelly beans? A) 17 B) 13 C) 12 D) 8 Objective: (2.3) Solve Apps: Venn Diagram
152) Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the students surveyed own no cats? A) 15 B) 10 C) 27 D) 22 Objective: (2.3) Solve Apps: Venn Diagram
153) Monticello residents were surveyed concerning their preferences for candidates Moore and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen, 100 support both Moore and Allen, and 250 support only Moore. How many residents support Allen? A) 400 B) 250 C) 100 D) 150 Objective: (2.3) Solve Apps: Venn Diagram
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Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 154) A 1 (B . C) A) {q, y, z} B) {q, s, u, w, y, z}
C) {q, w, y}
D) {q, r, w, y, z}
C) {q, s, u, w, y, z}
D) {q, s, w, y}
C) {q, s, u, w, y, z}
D) {q, s, u, w, y}
C) {q, s, w, y}
D) {q, s, u, w, y}
C) {r, t, z}
D) {q, r, s}
C) {r, s, t, y, z}
D) {q, s, u, v, x, y}
C) {s, t}
D) {v, z}
Objective: (2.4) Perform Set Operations with Three Sets
155) A . (B 1 C) A) {q, y, z}
B) {q, r, w, y, z}
Objective: (2.4) Perform Set Operations with Three Sets
156) (A 1 B) . (A 1 C) A) {r, t, v, x}
B) {q, s, w, y}
Objective: (2.4) Perform Set Operations with Three Sets
157) (A . B) 1 (A . C) A) {r, t, u, v, x, z}
B) {q, s, v, w, y}
Objective: (2.4) Perform Set Operations with Three Sets
158) A' . (B 1 C') A) {q, s, u, v, x, y}
B) {q, r, s, t, z}
Objective: (2.4) Perform Set Operations with Three Sets
159) (A' . B) 1 (A' . C') A) {q, r, t, y, z}
B) {r, t, z}
Objective: (2.4) Perform Set Operations with Three Sets
160) (A 1 B 1 C)' A) {q, s}
B) {r, t}
Objective: (2.4) Perform Set Operations with Three Sets
161) (A . B . C)' A) {q, s, u, w, z} C) {q, r, s, t, u, v, w, x, z}
B) {r, t, v, x} D) +
Objective: (2.4) Perform Set Operations with Three Sets
162) (A 1 B)' . C A) {q, v, x}
B) {v, x}
C) {r, w}
D) {s, u, v, z}
C) {u}
D) {w}
Objective: (2.4) Perform Set Operations with Three Sets
163) (B 1 C)' . A A) {v}
B) +
Objective: (2.4) Perform Set Operations with Three Sets
27
Use the Venn diagram shown to answer the question.
164) Which regions represent set E? A) VIII B) II, III, V, VI
C) III
D) I, IV, VII
Objective: (2.4) Use Venn Diagrams with Three Sets
165) Which regions represent set D 1 F? A) I, II, IV, V, VI, VII C) VIII
B) I, II, IV, V, VI, VII, VIII D) III
Objective: (2.4) Use Venn Diagrams with Three Sets
166) Which regions represent set D . E? A) IV, V B) II, V
C) I, III, IV, VI
D) VIII
C) II, III, V, VI
D) I, IV, VII, VIII
Objective: (2.4) Use Venn Diagrams with Three Sets
167) Which regions represent set E'? A) II, V, VI B) VIII Objective: (2.4) Use Venn Diagrams with Three Sets
Construct a Venn diagram illustrating the given sets. 168) A = [4, 5, 6, 7, 8, 9], B = [3, 4, 5, 6, 10], C = [2, 3, 4, 5, 9], U = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
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A)
B)
C)
D)
Objective: (2.4) Use Venn Diagrams with Three Sets
Use set notation to identify the shaded region. 169)
A) B - A
B) A .B
C) B . A
D) A - B
C) A 1 B
D) A .B
Objective: (2.4) Use Venn Diagrams with Three Sets
170)
A) A - B
B) A . B
Objective: (2.4) Use Venn Diagrams with Three Sets
29