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Exam

Chapter 1

Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 1) 9 + 5 = 14 or 6 × 7 = 42 1)

Draw a Venn diagram to represent the given information. 2) In a complex of 60 apartments, 40 apartments have cable television, 25 apartments have a dishwasher, and 13 apartments have both cable television and a dishwasher. Decide whether the statement makes sense. Explain your reasoning. 3) Insurance policy A costs $250 and has no deductible. Insurance policy B costs $275 and has a $500 yearly deductible. Candace thinks the extra $25 per month is worth it to get the $500 deductible, so she buys policy B.

Draw a Venn diagram with three overlapping circles for the three given sets. Label the contents of every region. If a region has no members, state that fact clearly. 4) salty things, sweet things, tangy things 4)

Decide whether the statement makes sense. Explain your reasoning. 5) I know more of the names of the common fallacies in arguments than my father, so I can recognize fallacies better than he can.

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 6) "As your Senator, I cannot in good conscience oppose those who are against 6) deregulation." A seemingly simple argument is given. Identify at least two hidden assumptions. 7) Cardiovascular exercise is important, because to be healthy you need a strong heart.

Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 8) beverages and soft drinks 8) A categorical proposition is given. If it is not already in standard form, rephrase it. State the subject and predicate sets, and draw a Venn diagram for the proposition. Label all regions of the diagram clearly. 9) Movies are entertaining. 9)

Use your knowledge of the listed sets to draw a A Venn diagram illustrating the relationships among them. 10) real numbers, integers, positive numbers, negative numbers, irrational numbers 10)

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 11) The House of Representatives voted to override the veto of the communications bill. 11) The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 12) The sun is bigger than the moon and the sun rotates around the earth. 12) The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 13) There are 25 letters in the English alphabet or the letter c is a vowel. 13)

Analyze the situation and explain how you would make a decision. 14) Your current cell phone company charges $30 per month for unlimited minutes. Another company charges $20 per month for the first 500 minutes plus 5¢ a minute for any additional minutes. Should you keep your current service or switch to the other company?

14)

A categorical proposition is given. If it is not already in standard form, rephrase it. State the subject and predicate sets, and draw a Venn diagram for the proposition. Label all regions of the diagram clearly. 15) Some singers are not children. 15) Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 16) even numbers and odd numbers 16)

Describe how the sentence is ambiguous. 17) There was a 15% decrease in donations to the homeless shelter between 1996 and 2000, a year in which $50,000 was collected.

17)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 18) Premise: 6 + 13 = 19 18) Premise: 16 + 9 = 25 Premise: 34 + 35 = 69 Conclusion: Whenever we add an even number and an odd number, the result is an odd number. Provide an appropriate response. 19) The members of a union are on strike. They are satisfied with their hourly wage rate and benefits, but they want their overtime wage rate to be increased by 15% in their next contract. The head of management makes the following statement to the head of the union: "If you end the strike today and sign the contract, we will meet your demand and increase the overtime wage rate by 15%." Should the union head accept the offer? Explain.

19)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 20) George Washington was the first president of the United States of America and France is 20) in Europe.

A seemingly simple argument is given. Identify at least two hidden assumptions. 21) I should not go outside, because it is raining.

21)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or not the argument is valid. 22) Denying the conclusion 22)

Identify the type of argument and determine its validity with a Venn diagram. 23) Premise: If you cut me, I bleed. Premise: I do not bleed. Conclusion: You did not cut me.

23)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or not the argument is valid. 24) Affirming the hypothesis 24)

Decide whether the statement makes sense. Explain your reasoning. 25) A and B are disjoint sets, so an object is either a member of set A or a member of set B, but not a member of both sets. Identify the type of argument and determine its validity with a Venn diagram. 26) Premise: If you break curfew, then you will be punished. Premise: Thelma was punished. Conclusion: Thelma broke curfew. Draw a Venn diagram to represent the given information. 27) There are 12 girls and 15 boys in a kindergarten class. 8 of the girls and 10 of the boys are right handed.

25)

26)

27)

Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 28) motor vehicles and cars 28)

Analyze the situation and explain how you would make a decision. 29) The costs per day of driving to work are $5 for gas, $10 for parking, and $1 for wear-and-tear on the car. Taking the train to work costs $6.50 each way, plus $1.50 per day to park at the train station. Should you drive or take the train? Draw a Venn diagram to represent the given information. 30) In a survey of 80 pet owners, 50 had a dog, 33 had a cat, and 12 had both a cat and a dog. Draw a Venn diagram to determine whether the argument is valid. 31) Premise: All snakes have fangs. Premise: Teri's pet does not have fangs. Conclusion: Teri's pet is not a snake.

29)

30)

31)

The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 32) The grass is wet or the grass is dry. 32) Draw a Venn diagram with three overlapping circles for the three given sets. Label the contents of every region. If a region has no members, state that fact clearly. 33) teachers, bowlers, and men 33)

Identify the type of argument and determine its validity with a Venn diagram. 34) Premise: If you try hard, then you will succeed. Premise: You did not try hard. Conclusion: You will not succeed.

34)

The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 35) Cats reads books or dogs bark. 35)

Use your knowledge of the listed sets to draw a A Venn diagram illustrating the relationships among them. 36) clothes, shirts, pants, shoes, fancy duds 36) Decide whether the statement makes sense. Explain your reasoning. 37) The argument is weak, so its conclusion must be false.

37)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 38) (Diversion) We've just remodeled the restaurant, so our food is delicious! 38) Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 39) Premise: Monday is one of the days of the week. 39) Premise: Thursday is one of the days of the week. Premise: Saturday is one of the days of the week. Conclusion: All the days of the week have names that end in "day." A seemingly simple argument is given. Identify at least two hidden assumptions. 40) We should not vote for the incumbent because he has already been in office for three consecutive terms. Decide whether the statement makes sense. Explain your reasoning. 41) I am very upset because the results of my biopsy were not positive for cancer.

40)

41)

A reason for a particular political position is given. There may be other issues that are left unstated. Identify at least one unstated issue that could be the "real issue" of concern. 42) The dictator of a foreign country has enacted a ban on all firearms, citing prevention of 42) accidental deaths among children as the rationale.

Decide whether the statement makes sense. Explain your reasoning. 43) Your argument is valid, but it isn't sound.

43)

Describe how the sentence is ambiguous. 44) Our goal is to increase voter participation from 25% of the eligible voters, or 4000, to 50%.

44)

Decide whether the statement makes sense. Explain your reasoning. 45) I drew a Venn diagram for two sets, and I only used one circle.

45)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or not the argument is valid. 46) Affirming the conclusion 46) A reason for a particular political position is given. There may be other issues that are left unstated. Identify at least one unstated issue that could be the "real issue" of concern. 47) Smoking should be banned in all public places. Second-hand smoke is harmful, causing 47) lung cancer and heart disease.

Decide whether the statement makes sense. Explain your reasoning. 48) The premises are true and the conclusion is true, so the argument must be valid. Provide an appropriate response. 49) IRS guidelines state that a married person under 65 years of age who can be claimed as a dependent on another person's tax return must file a return if (i) unearned income was over $750; or (ii) earned income was over $3925; or (iii) total of earned and unearned income was at least $5 and your spouse files a separate return and itemizes deductions; or (iv) total of earned and unearned income was more than the greater of a) $750; or b) earned income (up to $3675) plus $250.

48)

49)

Julia is 45 years old and can be claimed as a dependent by her father. She had earned income of $3800 and unearned income of $200. Julia's husband Bret files a separate return but does not itemize deductions. Must Julia file a return? Explain.

51) No positive numbers are negative numbers.

51)

Decide whether the statement makes sense. Explain your reasoning. 52) Wayne's bank charges a $1 service charge for every transaction. To save money, he withdraws $100 cash every other week instead of withdrawing $50 every week.

52)

53) Your argument has no fallacies, so your conclusion must be true. A seemingly simple argument is given. Identify at least two hidden assumptions. 54) Jeremy needs a new bike, because the new models have a safer braking system. Draw a Venn diagram to determine whether the argument is valid. 55) Premise: All clowns wear makeup. Premise: Bozo is a clown. Conclusion: Bozo wears makeup. Describe how the sentence is ambiguous. 56) Two stores with more than 1000 pieces of merchandise will have grand openings at the mall this weekend. Decide whether the statement makes sense. Explain your reasoning. 57) Your argument is sound, but it isn't valid.

53)

54)

55)

56)

57)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 58) (False Cause) Since I brought my umbrella, it didn't rain. 58) Decide whether the statement makes sense. Explain your reasoning. 59) If you have $5, then you will buy a hot dog; and, contrapositively, if you don't have $5, then you won't buy a hot dog. (Hint: focus on whether the word "contrapositively" is used correctly.)

60) If "unconscious" means "not located in the United States," then Florida is not unconscious.

59)

60)

A set of propositions is listed. Draw a Venn diagram that represents all the information in the propositions and use it (and no other assumptions) to answer the question. Explain your reasoning. 61) No dogs are cats. No gerbils are cats. All dogs have fleas. Some cats are thirsty. No thirsty 61) creatures have fleas. Question: Could a gerbil be a dog?

Decide whether the statement makes sense. Explain your reasoning. 62) The propositions "I am hungry" and "I am not hungry" are both true, since sometimes I am hungry and sometimes I am not hungry. Analyze the situation and explain how you would make a decision. 63) You are flying out on Monday morning and returning home Tuesday night. You need to decide how to get to and from your home airport. Driving each way costs $2 in gas, and long-term parking costs $10 per full or partial day. If you take taxis, it will cost $11 each way. Which option is better?

62)

63)

Provide an appropriate response. 64) Consider the following ballot initiative: "Shall there be an amendment to the state constitution to prohibit the state legislature from adopting any law which inhibits the freedom of religious expression?" Explain the meaning of a "no" vote. Decide whether the statement makes sense. Explain your reasoning. 65) I did not convince my friend that I was right, so I must not have argued logically.

64)

65)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 66) Premise: I get lower grades than my best friend in math, chemistry, and English. 66) Conclusion: My friend is smarter than I am. The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 67) There are seven days in a week and there are 24 hours in a day. 67) A categorical proposition is given. If it is not already in standard form, rephrase it. State the subject and predicate sets, and draw a Venn diagram for the proposition. Label all regions of the diagram clearly. 68) All horses are animals. 68)

Provide an appropriate response. 69) Consider the following clause in a rental lease: "Lessee may terminate this lease at the end of the initial term by providing Lessor with at least sixty (60) days prior written notice, to commence upon the first day of the month following the month in which said notice is delivered or immediately if delivered on the first day of any month." If the initial term of the lease ends on March 31 and the Lessee provides the Lessor written notice on April 1, as of what date can the lease be terminated? What if he provides notice on April 2?

69)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 70) 6 + 7 = 13 and 9 × 4 = 45 70)

Draw a Venn diagram to determine whether the argument is valid. 71) Premise: No surfers speak French. Premise: Pierre speaks French. Conclusion: Pierre is not a surfer.

71)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or not the argument is valid. 72) Denying the hypothesis 72) Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 73) fish and birds 73)

74) athletes and high school students

74)

Decide whether the statement makes sense. Explain your reasoning. 75) The time I spend studying is a subset of the time I spend playing basketball. Analyze the situation and explain how you would make a decision. 76) You want a new car but plan to use it for only 2 years. The cost of leasing is $2,000 down and $300 per month. The cost of buying is $20,000, and you can expect to sell it in two years for approximately $12,000. Which is the better option?

77) You need a rental car for four days. The daily rate is $20 per day plus 20¢ per mile. The

75)

76)

77)

weekly rate is $100, and mileage is included. Which is the better option?

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 78) (Straw Man) Mayor Brown opposes a tax increase to build new schools. His opponent in 78) the upcoming election states: Mayor Brown is not concerned with improving the quality of education for our children. Identify the type of argument and determine its validity with a Venn diagram. 79) Premise: If you are hot, then you will sweat. Premise: James is hot. Conclusion: James will sweat.

79)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 81) Premise: Calvin Coolidge was over 35 years old when he became President of the United 81) States. Premise: Bill Clinton was over 35 years old when he became President of the United States. Premise: Ronald Reagan was over 35 when he became President of the United States. Conclusion: Every United States politician is at least 35 years old. The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 82) The councilman does not oppose the anti-pollution measure. 82) The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 83) (Appeal to Emotion) A television commercial shows a happy, attractive family dining at 83) Ma & Pa's Restaurant. The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 84) Springfield is the capital of Illinois and Chicago is the capital of Illinois. 84)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 85) (Hasty Generalization) Isabelle had vegetarian food for lunch every day last week, so she 85) must be a vegetarian. Draw a Venn diagram with three overlapping circles for the three given sets. Label the contents of every region. If a region has no members, state that fact clearly. 86) truck drivers, employed, unemployed 86)

A seemingly simple argument is given. Identify at least two hidden assumptions. 87) All bills should be paid on time because a bad credit report will make it difficult to get a loan.

87)

A set of propositions is listed. Draw a Venn diagram that represents all the information in the propositions and use it (and no other assumptions) to answer the question. Explain your reasoning. 88) All cars have wheels. All trucks have wheels. Some toys have wheels. No grandmothers 88) have wheels. Question: Could a car be both a truck and a toy? Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 89) astronauts and fathers 89)

Provide an appropriate response. 90) IRS guidelines state that a married person under 65 years of age who can be claimed as a dependent on another person's tax return must file a return if (i) unearned income was over $750; or (ii) earned income was over $3925; or (iii) total of earned and unearned income was at least $5 and your spouse files a separate return and itemizes deductions; or (iv) total of earned and unearned income was more than the greater of a) $750; or b) earned income (up to $3675) plus $250.

90)

Kevin is 25 years old and can be claimed as a dependent by his mother. He had earned income of $3500 and unearned income of $700. Kevin's wife Linda files a separate return but does not itemize deductions. Must Kevin file a return? Explain.

91) You mention to an acquaintance that you wish to buy a Rolex watch, but the model you're

91)

interested in is too expensive for your budget. He says that his cousin sells watches, and he'll see if he can get you a deal. Sure enough, his cousin offers you the same watch for 50% of the price. Does this sound like a deal worth taking?

Decide whether the statement makes sense. Explain your reasoning. 92) The answer to the question is a whole number but it is not an integer.

92)

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 93) The state assembly repealed the ban on anti-smoking resolutions. 93)

A seemingly simple argument is given. Identify at least two hidden assumptions. 94) It is important to visit the dentist every 6 months to insure healthy teeth and gums. Analyze the situation and explain how you would make a decision. 95) You are leasing a summer home for twelve weeks and are required to cut the grass every week. You can buy a new power mower for $340 and sell it at the end of the summer for $100. You can rent a power mower for $20 per day. The neighbor's son will charge you $10 per hour for 2 hours and provide his own equipment. Which is the best option?

94)

95)

Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of the other, disjoint sets, or overlapping sets. 96) doctors and poets 96)

Decide whether the statement makes sense. Explain your reasoning. 97) Javier takes a shower to save time. When he gets into the shower at 6:50, he is out by 7:10. When he used to take baths, it would take him a quarter of an hour. Analyze the situation and explain how you would make a decision. 98) Betty has to go to New Orleans on business. If she flies there and back on the same day her round trip airfare will cost $700. If she stays overnight, her round trip airfare will cost $400, her hotel will cost $100, and three extra meals will cost $75. Which is the better option?

97)

98)

A reason for a particular political position is given. There may be other issues that are left unstated. Identify at least one unstated issue that could be the "real issue" of concern. 99) I think term limits should be enacted for the Senate. A senator should not be allowed to 99) serve more than two consecutive terms, because professional politicians become too focused on getting reelected. A categorical proposition is given. If it is not already in standard form, rephrase it. State the subject and predicate sets, and draw a Venn diagram for the proposition. Label all regions of the diagram clearly. 100) Some dogs are adorable. 100)

A seemingly simple argument is given. Identify at least two hidden assumptions. 101) The campfire should be extinguished before we go fishing because the park ranger can cite us for illegal activities.

101)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 102) Premise: Baseball, football, basketball, golf, hockey, and tennis are all played with a ball. 102) Conclusion: All sports are played with a ball. Decide whether the statement makes sense. Explain your reasoning. 103) Your conditional deductive argument is valid. Therefore, it must be an example of "Affirming the Hypothesis."

103)

Draw a Venn diagram to determine whether the argument is valid. 104) Premise: All lawyers wear suits. Premise: Jack wears a suit. Conclusion: Jack is a lawyer.

104)

Draw a Venn diagram to represent the given information. 105) In a freshman class of 50 students, 30 students are taking math, 24 students are taking history, and 15 students are taking both math and history.

105)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is a proposition. 106) One inch is 2.54 meters. A) Not a proposition

106) B) Proposition

Evaluate the validity of the chain of conditionals. 107) Premise: If you loved me, then you would buy me a new car. Premise: If you wanted me to be happy, then you would buy me a new car. Conclusion: If you loved me, then you would want me to be happy. A) Valid B) Invalid

107)

Rephrase the statement as a conditional proposition with the form "if p, then q." 108) Showing up at the party is sufficient to get a door prize. A) If you got a door prize, then you showed up at the party.

108)

B) If you show up at the party, then you will get a door prize. C) If you don't show up at the party, then you will not get a door prize. D) If you get a door prize, then you don't have to show up at the party. Solve the problem. 109) The following Venn diagram describes the types of cookies in a bakery. Use it to determine how many cookies have neither chocolate chips nor walnuts.

A) 17

B) 7

C) 10

D) 3

109)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 110) -13 110) A) Integers B) Whole numbers

C) Natural numbers

D) Rational numbers

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 111) not (p or q); (not p)and (not q) 111) A) No B) Yes Solve the problem. 112) The following Venn diagram describes the cars on a used car lot. Use it to determine how many Fords are on the lot.

A) 23

B) 17

C) 30

Determine whether the statement is true or false. 113) If 9 + 2 = 19, then Canada is in North America. A) True

112)

D) 20

113) B) False

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 114) 16 114) A) Integers B) Natural numbers

C) Real numbers

D) Whole numbers

Solve the problem. 115) The following Venn diagram describes the cars on a used car lot. Use it to determine how many cars on the lot are not red.

A) 55

B) 58

C) 35

D) 38

The argument given or described involves some kind of fallacy. Identify the fallacy. 116) After getting new dishes, I started to sneeze. I must be allergic to the new dishes. A) Hasty generalization B) False cause

C) Circular reasoning

115)

116)

D) Personal attack (ad hominem)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 117) q and (not r) and s

B) q r s q and (not r) and s T T T F T T F F T F T T T F F T F T T F F T F F F F T F F F F F

q r s q and (not r) and s T T T F T T F T T F T F T F F F F T T F F T F F F F T F F F F F

D) q r s q and (not r) and s T T T F T T F F T F T T T F F F F T T F F T F F F F T F F F F F

q r s q and (not r) and s T T T T T T F F T F T F T F F F F T T F F T F F F F T F F F F F

117)

Write the negation of the proposition. 118) Some athletes are musicians. A) No athlete is a musician.

118) B) All athletes are musicians. D) Not all athletes are musicians.

C) Some athletes are not musicians. Determine whether the statement is a proposition. 119) 0.3 = .03 A) Not a proposition

119) B) Proposition

Decide whether the argument is inductive or deductive. 120) For any positive number p, -p = p. Therefore,|-12| = 12 A) Deductive B) Inductive

120)

Solve the problem. 121) The following Venn diagram describes the desserts people ordered at a party. Use it to determine how many people ordered cake.

121)

A) 43

B) 21

C) 7

D) 28

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 122) p or q; not [(not p) and (not q)] 122) A) Yes B) No The argument given or described involves some kind of fallacy. Identify the fallacy. 123) You should brush your teeth every day because brushing your teeth is very important. A) Diversion (red herring) B) False cause

C) Circular reasoning

123)

D) Hasty generalization

Use braces to write the members of the set, or state that the set has no members. 124) The letters needed to spell the following words: tear, rate, rat, tea A) {a, e, r, t} B) {t, e, a, r, r, a, t, e, r, a, t, t, e, a}

C) {tear, rate, rat, tea}

D) {r, a, t}

124)

Write the converse, inverse, or contrapositive off the proposition, as indicated. 125) If the sum of the interior angles of a geometric figure is 180 degrees, then the figure is a triangle. (contrapositive) A) If a geometric figure is not a triangle, then the sum of the interior angles is 180 degrees.

125)

B) If the sum of the interior angles of a geometric figure is not 180 degrees, then the figure is

not a triangle. C) If a geometric figure is not a triangle, then the sum of the interior angles is not 180 degrees.

D) If a geometric figure is a triangle, then the sum of the interior angles is 180 degrees. Write the negation of the proposition. 126) Susie lives in a green house. A) Susie lives in a blue house.

126)

B) Susie does not live in a house that is not green. C) Billy lives in a green house. D) Susie does not live in a green house. Use braces to write the members of the set, or state that the set has no members. 127) The days of the week A) {Saturday, Sunday}

127)

B) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} C) {Monday, Tuesday, Wednesday, Thursday, Friday} D) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 128) 23 128) A) Rational numbers B) Natural numbers

C) Whole numbers

D) Real numbers

Rephrase the statement as a conditional proposition with the form "if p, then q." 129) I will lose weight if I diet. A) If I lose weight, then I will diet. B) If I diet, then I will lose weight.

C) If I don't diet, then I won't lose weight.

129)

D) If I diet, then I will gain weight.

State whether or is being used in the exclusive or inclusive sense in the given statement. 130) The insurance policy will not cover misuse or acts of God. A) Exclusive B) Inclusive

131) The prize is a new car or $10,000 cash. A) Inclusive

130)

131) B) Exclusive

Decide whether the argument is inductive or deductive. 132) Every coach must know his sport well. Steve Spurrier is a football coach, so Steve Spurrier knows football well. A) Deductive B) Inductive

132)

Use braces to write the members of the set, or state that the set has no members. 133) The integers from 2 to 6 (inclusive) A) {3, 4, 5} B) {2, 3, 4, 5, 6} C) {2, 3, 4, 5}

133) D) {3, 4, 5, 6}

Rephrase the statement as a conditional proposition with the form "if p, then q." 134) Cats chase mice. A) If a cat is chasing it, then it is a mouse. B) If it is a cat, then it chases mice.

C) If cats chase, then they chase mice.

134)

D) If cats, then mice.

135) Having a computer is necessary for taking this class. A) If you have a computer, then you must take this class. B) If you take this class, then you must have a computer. C) If you take this computer, then you must have a class. D) If don't take this class, then you must not have a computer.

135)

136) All chocolate is good. A) If it isn't good, then it's chocolate. C) If it's good, then it's chocolate.

136) B) If it's chocolate, then it's good. D) If it isn't chocolate, then it isn't good.

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 137) not (p and q); (not p) or q 137) A) No B) Yes Determine whether the statement is true or false. 138) If a triangle is a parallelogram, then all rectangles are squares. A) True B) False Evaluate the validity of the chain of conditionals. 139) Premise: If I take a shower, I use soap. Premise: If I use soap, my skin becomes dry. Conclusion: If I take a shower, my skin becomes dry. A) Valid B) Invalid

138)

139)

Decide whether the argument is inductive or deductive. 140) Fresh fruit is expensive in winter. This is January, so these fresh strawberries will be expensive. A) Inductive B) Deductive

140)

Determine whether the statement is a proposition. 141) Go fly a kite. A) Proposition

141) B) Not a proposition

142) Do you like this color? A) Proposition

142) B) Not a proposition

Decide whether the argument is inductive or deductive. 143) The last four stoplights were green. Therefore, the next one will be green. A) Deductive B) Inductive

144) All U.S. Presidents have come from the contiguous 48 states. No person from Alaska can be President. A) Inductive

143)

144)

B) Deductive

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 145) r and not s

145)

B) r s r and not s T T T T F F F T F F F F

r s r and not s T T T T F T F T F F F T

D) r s r and not s T T F T F T F T F F F F

r s p and not s T T F T F T F T F F F F

Write the negation of the proposition. 146) Everyone is asleep. A) Nobody is awake.

146) B) Not everyone is asleep. D) Everyone is awake.

C) Nobody is asleep.

Evaluate the validity of the chain of conditionals. 147) Premise: If I pay my bills on time, then my credit will be good. Premise: If my credit is good, then I will become a movie star. Conclusion: If I pay my bills on time, then I will become a movie star. A) Valid B) Invalid

147)

Decide whether the argument is inductive or deductive. 148) 31 + 19 = 50, 13 + 47 = 60, 5 + 37 = 42. Therefore, the sum of two prime numbers is even. A) Inductive B) Deductive

148)

Determine whether the statement is a proposition. 149) 5 + 7 = 13 A) Proposition

149) B) Not a proposition

The argument given or described involves some kind of fallacy. Identify the fallacy. 150) When confronted with questions from the press about alleged scandals, a congressman replies that the allegations against him should be ignored since his accuser is part of a vast right-wing conspiracy. A) Circular reasoning B) Limited choice

C) Appeal to popularity

150)

D) Personal attack (ad hominem)

Use braces to write the members of the set, or state that the set has no members. 151) The positive-integer powers of 3 A) {3, 6, 9, 12, 15, . . .} B) {1, 3, 9, 27, 81, 243, . . .}

C) {3, 9, 27, 81, 243, . . .}

151)

D) {1, 8, 27, 64, 125, . . .}

State whether or is being used in the exclusive or inclusive sense in the given statement. 152) I don't know if I should wear my new skirt or my new dress tonight. A) Exclusive B) Inclusive

152)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 153) -4 153) A) Real numbers B) Integers

C) Rational numbers

D) Whole numbers

Determine whether the statement is true or false. 154) If baseball is a sport, then the letter e is a consonant. A) True

154) B) False

Solve the problem. 155) The following Venn diagram describes the optional features ordered by new telephone customers in a certain region. Use it to determine how many customers did not order caller ID.

A) 67

B) 103

C) 76

Determine whether the statement is true or false. 156) If Florida is in the United States, then all rectangles are squares. A) True B) False

155)

D) 77

156)

Evaluate the validity of the chain of conditionals. 157) Premise: If the moon is made of cheese, then what goes up must come down. Premise: If what goes up must come down, then most Americans like apple pie. Conclusion: If the moon is made of cheese, then most Americans like apple pie. A) Invalid B) Valid The argument given or described involves some kind of fallacy. Identify the fallacy. 158) We must limit immigration to the United States in order to sustain the prosperous economy. A strong economy is vital to the health and wealth of the American people and the future of our children. A) False cause B) Diversion (red herring)

C) Appeal to force

157)

158)

D) Straw man

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 159) -21.1 159) A) Rational numbers B) Natural numbers

C) Real numbers

D) Integers

Solve the problem. 160) The following Venn diagram describes the optional features ordered by new telephone customers in a certain region. Use it to determine how many customers ordered call waiting.

A) 77

B) 36

C) 76

160)

D) 40

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 161) -64 161) A) Natural numbers B) Real numbers

C) Whole numbers

D) Integers

Write the converse, inverse, or contrapositive off the proposition, as indicated. 162) If I pass, then I'll celebrate. (contrapositive) A) If I don't celebrate, then I didn't pass. B) If I pass, then I won't celebrate.

C) If I celebrate, then I'll pass.

D) If I don't pass, then I won't celebrate.

162)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 163) 0 163) A) Natural numbers B) Integers

C) Rational numbers

D) Whole numbers

The argument given or described involves some kind of fallacy. Identify the fallacy. 164) One candidate favors eliminating affirmative action programs. The other candidate states: My opponent doesn't think there's anything wrong with discrimination." A) Straw man B) Personal attack (ad hominem)

C) Limited choice

164)

D) Hasty generalization

Use braces to write the members of the set, or state that the set has no members. 165) The integers between 3 and 7 (not inclusive) A) {4, 5, 6, 7} B) {3, 4, 5, 6, 7} C) {3, 4, 5, 6}

165) D) {4, 5, 6}

The argument given or described involves some kind of fallacy. Identify the fallacy. 166) If Proposition Q fails, your children won't have good schools. A) Appeal to ignorance B) Appeal to emotion

C) Hasty generalization

166)

D) Diversion (red herring)

167) A television commercial shows two people who fall in love while wearing a certain brand of blue

167)

jeans.

A) Limited choice C) Hasty generalization

B) Appeal to ignorance D) Appeal to emotion

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 168) not (p and q); (not p) and (not q) 168) A) Yes B) No State whether or is being used in the exclusive or inclusive sense in the given statement. 169) Shaun will win the race if he eats carbohydrates beforehand or if he has slept well. A) Exclusive B) Inclusive

169)

Write the negation of the proposition. 170) Emily has brown eyes. A) Jason has brown eyes.

170) B) Emily does not have green eyes. D) Emily has green eyes.

C) Emily does not have brown eyes.

Write the converse, inverse, or contrapositive off the proposition, as indicated. 171) If the sun shines, they will bask. (inverse) A) If the sun does not shine, then they will not bask.

B) If they bask, then the sun shines. C) If they do not bask, then the sun shines. D) If they do not bask, then the sun does not shine. 20

171)

Write the negation of the proposition. 172) Some people don't like walking. A) Some people don't like driving.

172) B) Nobody likes walking. D) Everyone likes walking.

C) Some people like walking. 173) No fifth graders play soccer. A) Not all fifth graders play soccer. C) At least one fifth grader plays soccer.

173) B) No fifth grader does not play soccer. D) All fifth graders play soccer.

Determine whether the statement is a proposition. 174) Not all flowers are roses. A) Not a proposition

174) B) Proposition

Determine whether the statement is true or false. 175) If horses have six legs, then Benjamin Franklin was the first president of the United States. A) True B) False

175)

Determine whether the statement is a proposition. 176) Mary has a cat. A) Not a proposition

176) B) Proposition

Draw a Venn diagram to represent the given information. 177) Patients in a (hypothetical) hospital on a single day were taking antibiotics (A), blood pressure medication (BP), and pain medication (P) in the following numbers: A only BP only P only None

10 A and BP only 7 A and P only 22 BP and P only 2 All three

14 25 18 20

Draw a three-circle Venn diagram that summarizes the results in the table.

177)

Write the converse, inverse, or contrapositive off the proposition, as indicated. 178) If you received a refund of over $1000, then you cannot make a claim. (inverse) A) If you can make a claim, then you received a refund of over $1000.

B) If you cannot make a claim, then you did not receive a refund of over $1000. C) If you did not receive a refund of over $1000, then you can make a claim. D) If you can make a claim, then you did not receive a refund of over $1000.

178)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 179) if q, then not r

179)

B) q r if q, then not r T T T T F F F T F F F F

q r if q, then not r T T F T F T F T F F F F

D) q r if q, then not r T T F T F T F T T F F T

q r if q, then not r T T T T F F F T T F F T

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 180) 2.1 180) A) Real numbers B) Integers

C) Natural numbers

D) Rational numbers

Rephrase the statement as a conditional proposition with the form "if p, then q." 181) Being in California is sufficient for being in Los Angeles. A) If you are in California, then you are not in Los Angeles.

181)

B) If you are in Los Angeles, then you are in California. C) If you are in Los Angeles, then you might be in California. D) If you are in California, then you are in Los Angeles. 182) Attending practice is necessary for staying on the team. A) If you don't stay on the team, then you must not attend practice. B) If you stay on the team, then you must attend practice. C) If you attend practice, then you must stay on the team. D) If you don't attend practice, then you must stay on the team. Use braces to write the members of the set, or state that the set has no members. 183) The whole numbers greater than 1 and less than 5 A) {1, 2, 3, 4} B) {2, 3, 4} C) {1, 2, 3, 4, 5}

182)

183) D) {2, 3, 4, 5}

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 184) 3,645 184) A) Natural numbers B) Whole numbers

C) Integers

D) Rational numbers

Write the converse, inverse, or contrapositive off the proposition, as indicated. 185) If the alarm beeps every thirty seconds, then you have to replace the battery. (converse) A) If you have to replace the battery, then the alarm does not beep every thirty seconds.

185)

B) If you have to replace the battery, then the alarm beeps every thirty seconds. C) If the alarm does not beep every thirty seconds, then you do not have to replace the battery. D) If you do not have to replace the battery, then the alarm does not beep every thirty seconds. Solve the problem. 186) The following Venn diagram describes the types of cookies in a bakery. Use it to determine how many chocolate chip cookies do not also have walnuts.

A) 25

B) 10

C) 15

Write the negation of the proposition. 187) Not all people like football. A) Some people like football.

D) 32

187) B) All people like football. D) Some people do not like football.

C) All people do not like football.

Solve the problem. 188) The following Venn diagram describes the desserts people ordered at a party. Use it to determine how many people ordered ice cream but not cake.

A) 36

186)

B) 21

C) 7

D) 15

188)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 189) 3 189) 5

A) Rational numbers C) Integers

B) Real numbers D) Natural numbers

The argument given or described involves some kind of fallacy. Identify the fallacy. 190) Each of my brother's three dogs has fleas. Therefore, all dogs have fleas. A) False cause B) Straw man

C) Hasty generalization

190)

D) Circular reasoning

Determine whether the statement is true or false. 191) If Florida is in the United States, then all squares are rectangles. A) True B) False

191)

Write the negation of the proposition. 192) She earns more than me. A) She earns the same as me.

192) B) She earns less than me. D) She does not earn less than me.

C) She does not earn more than me.

Decide whether the argument is inductive or deductive. 193) Practice makes perfect. Therefore, if I practice, I'll be perfect. A) Inductive B) Deductive

193)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 194) (p or q) or r; p or (q or r) 194) A) Yes B) No Make a truth table for the given statement. The letters p, q, r, s represent propositions. 195) p or q

B) p q p or q T T T T F F F T T F F F

C) p q p or q T T T T F F F T F F F F

p q p or q T T T T F T F T T F F F

195) D) p q p or q T T F T F F F T F F F T

Answer Key Testname: CHAPTER 1

1) True. Both individual propositions are true. The disjunction is true if either or both propositions are true. 2) Answers may vary. Possible answer:

3) Does not make sense. Candace is paying an additional $25 per month ($300 per year) to get a $500 deductible.

However the deductible (what you pay out of pocket before the insurance kicks in) is a cost, not a benefit! All other things being equal, policy A is clearly the better deal. (Explanations will vary.)

I = things that are salty, but neither sweet nor tangy II = things that are both salty and sweet, but not tangy III = things that are sweet, but neither salty nor tangy IV = things that are salty and tangy, but not sweet V = things that are salty, sweet, and tangy VI = things that are sweet and tangy, but not salty VII = things that are tangy, but neither sweet nor salty VIII = things that are neither salty, sweet, nor tangy 5) Does not make sense. Learning the fancy names for the fallacies is far less important than learning to recognize the faulty reasoning. (Explanations will vary.) 6) Answers may vary. One possibility: There are four negations in that statement: cannot, oppose, those who are against, and deregulation. A quadruple negation (not not not not p) has the same truth value as the original proposition p. In short, the Senator is for regulation of the area in question. 7) Answers may vary. One possibility: Cardiovascular exercise leads to a strong heart. Being healthy is important.

Answer Key Testname: CHAPTER 1

The set "soft drinks" is a subset of the set "beverages." All soft drinks are beverages, but some beverages (e.g., water) are not soft drinks. 9) In standard form: All movies are things that are entertaining. The subject set is "movies" and the predicate set is "things that are entertaining."

10) Answers may vary. One possibility:

Note that there is exactly one element in region I, since the number 0 is the only integer that is neither negative nor positive. Note also that there are no elements in region II, since each irrational number is either negative or positive.

Answer Key Testname: CHAPTER 1

11) Answers may vary. One possibility: This is a double negation. The veto of the bill (presumably by the President) is the

first negation. The overriding of the veto is the second negation. The two cancel each other out, and the result is that the communications bill is passed. In general, a double negation (not not p) has the same same truth value as the original proposition p. 12) False. Is is true that the sun is bigger than the moon, but it is not true that the sun rotates around the earth. (The earth rotates around the sun.) Since one of the individual propositions if false, the conjunction is false. 13) False. Since there are 26 letters in the English alphabet, the first proposition is false. Since the letter c is not a vowel but a consonant, the second proposition is false. Since both propositions are false, the disjunction is false. 14) Answers may vary. One possibility: The relative cost of the two options depends primarily on how many minutes per month you use. The new company's plan would cost $30 for up to 700 minutes a month, since $20 + $0.05(700 - 500) = $30. Therefore, if you expect to use less than 700 minutes a month, you would tend to profit from switching companies. However, there are other factors to consider: Does one company have more dependable cellular service? Better sound quality? Better customer service? You should also look for hidden costs. For example, if you switch companies, you may need to buy a new cell phone. 15) The subject set is "singers" and the predicate set is "children."

The X indicates that the non-overlapping region of the "singers" circle has at least one member. No claim is made about whether other regions also have members.

16)

The set "even numbers" is disjoint from the set "odd numbers" because the two sets have no members in common. An even number cannot be odd, and an odd number cannot be even. 17) It is unclear whether the year in which $50,000 was collected was 1996 or 2000. 18) Answers may vary. Possible answer: The premises are true. The argument is relatively strong, and the conclusion is true. 19) Answers may vary. One possibility: The union head should ask for more information. Even though management has apparently agreed to the demand for a 15% increase in the overtime wage rate, it is not clear that the overall deal is a good one. It is entirely possible that management has lowered the hourly wage rate, reduced the benefits, or made other changes to the contract to the detriment of the members of the union. Before making any promises, before giving up leverage by ending the strike, and certainly before signing anything; these issues must be clarified.

Answer Key Testname: CHAPTER 1

20) True. Both individual propositions are true, so the conjunction is true. 21) Answers may vary. One possibility:

I do not want to get wet. It is not raining inside; that is, the roof is keeping the rain outside. 22) Answers will vary. The structure of the argument should be as follows: Premise: If p, then q. Premise: q is not true. Conclusion: p is not true. The argument is valid.

23)

The type of argument is called Denying the Conclusion. We have p = you cut me and q = I bleed. The second premise asserts that q is false for me, which we show by putting an X outside the q circle. Since the p circle is inside the q circle, the X is outside the p circle, too. The Venn diagram shows that the premises lead necessarily to the conclusion, so the argument is valid. 24) Answers will vary. The structure of the argument should be as follows: Premise: If p, then q. Premise: p is true. Conclusion: q is true. The argument is valid. 25) Does not make sense. It is true that if A and B are disjoint sets, then an object cannot be a member of both sets. However, that does not mean it has to be a member of either set. It can also be a member of neither. The X in the following diagram represents an object that is a member of neither set A nor set B. If set A were the set of animals, and set B were the set of vegetables, then the X might represent a mineral. (Explanations will vary.)

Answer Key Testname: CHAPTER 1

26)

The type of argument is called Affirming the Conclusion. We have p = you break curfew and q = you will be punished. The second premise asserts that Thelma was punished, which we show by putting an X in the q circle. However, the premise says nothing about whether Thelma broke curfew, so we put the X on the border of the p circle to indicate that we don't know whether the X belongs inside or outside this circle. The Venn diagram shows that the premises do not lead necessarily to the conclusion, so the argument is invalid. Thelma may have been punished for some other reason. 27) Answers may vary. Possible answer:

28)

The set "cars" is a subset of the set "motor vehicles." Every car is a motor vehicle, but there are some motor vehicles, such as trucks, that are not cars. 29) Answers may vary. One possibility: Since driving costs $16 ($5 + $10 + $1 = $16) per day and taking the train costs $14.50 ($6.50 × 2 + $1.50 = $14.50) per day, it appears that taking the train is a better option. However, you should also consider other factors. If you have a spouse who might need the car during the day, then that's another reason to take the train (that would also save you the $1.50 parking fee). If you take the train, you might be able to read the newspaper or do work on the way to work. However, if the train tends to be crowded and you prefer being alone, then it might be worth the extra $1.50 per day to drive.

Answer Key Testname: CHAPTER 1

30) Answers may vary. Possible answer:

31)

The X represents Teri's pet. The conclusion follows necessarily from the premises, and the argument is valid. 32) True. If the first proposition is false (the grass is not wet), then the second proposition is true (the grass is dry). If the second proposition is false (the grass is not dry), then the first proposition is true (the grass is wet). Thus, one of the propositions is true, so the disjunction is true.

33)

I = female teachers who are not bowlers II = female teachers who are bowlers III = female bowlers who are not teachers IV = male teachers who are not bowlers V = male teachers who are bowlers VI = male bowlers who are not teachers VII = men who are neither teachers nor bowlers VIII = women who are neither teachers nor bowlers

Answer Key Testname: CHAPTER 1

34)

The type of argument is called Denying the Hypothesis. We have p = you try hard and q = you will succeed. The second premise asserts that p is false for you, which we show by putting an X outside the p circle. However, we do not know whether the X should also be outside the q circle, because the premise says nothing about whether you succeeded. Thus, we put the X on the border of the q circle. The Venn diagram shows that the premises do not lead necessarily to the conclusion, so the argument is invalid. It is possible that, despite your not trying hard, you might still succeed. 35) True. Although cats do not read books, dogs do bark. The disjunction is false only if both individual propositions are false. 36) Answers may vary. One possibility:

37) Does not make sense. The strength of an inductive argument is not necessarily related to the truth of its conclusion.

The argument "The earth rotates around the sun because I said so" is extremely weak, but its conclusion happens to be true. For a long time people found the argument "The sun rotates around the earth" to be quite compelling, but its conclusion turned out to be false. (Explanations will vary.) 38) Answers may vary. Possible answer: The conclusion of this argument (our food is delicious) is not related to the premise (We've just remodeled the restaurant). This argument represents the fallacy of diversion because it attempts to divert attention from the real issue (the taste of the food) by focusing on another issue (the remodeling of the restaurant). The issue to which attention is diverted is sometimes called a red herring. 39) Answers may vary. Possible answer: The premises are true. The strength of the argument is relatively weak, since things aren't always named logically and consistently. (For example, the months September, November, and December all end in "ember", but none of the other nine months do!) The conclusion is true.

Answer Key Testname: CHAPTER 1

40) Answers may vary. One possibility:

Four consecutive terms is too many. The incumbent is running in the election. 41) Does not make sense. In this context, the word "positive" means "indicating the presence of." The fact that the results were not positive for cancer suggests that you don't have cancer. Perhaps there is an unusual explanation for why that would make you upset (e.g., masochism), but in general it does not make sense. (Explanations will vary.) 42) Answers may vary. One possibility: The dictator may believe that an unarmed populace is easier to control. 43) Makes sense. An argument is valid if its conclusion follows necessarily from its premises, regardless of the truth of its premises or conclusions. An argument is sound if it is valid and its premises are all true. Many valid arguments have false premises and are thus not sound. For example: Premise: When I close my eyes, I become invisible. Premise: When I am invisible, I can speak Portugese. Conclusion: When I close my eyes, I can speak Portugese. The argument is valid, but its premises are clearly false so it isn't sound. (Explanations will vary.) 44) It is unclear whether 4000 is the number of eligible voters or 25% of the number of eligible voters (which would make 16,000 the number of eligible voters). 45) Makes sense. Generally it takes two circles to draw a Venn diagram for two sets, for example when the sets are overlapping or disjoint. Even when one set is the subset of the other, it generally takes two circles to draw a Venn diagram. However, if the two sets are equal, then they have precisely the same members and the same circle describes both sets. Incidentally, if two sets are equal then they are both subsets of each other. (Explanations will vary.) 46) Answers will vary. The structure of the argument should be as follows: Premise: If p, then q. Premise: q is true. Conclusion: p is true. The argument is invalid. 47) Answers may vary. One possibility: The person stating this opinion may not like the smell of cigarettes and cigars. He may not like the smell getting into his clothes and causing him to spend more money on dry cleaning. In addition, he may find second-hand smoke unpleasant because it irritates his eyes. 48) Does not make sense. For an argument to be valid, its conclusion must follow necessarily from its premises. Just because the premises and the conclusion are true does not mean the conclusion follows necessarily from the premises. For example, consider the following argument: Premise: Dogs bark. Premise: Cats meow. Conclusion: Pigs oink. The premises and the conclusion are all true, but the conclusion has nothing to do with the premises. (Explanations will vary.) 49) Yes, Julia must file a return. She is a married person under 65 years of age who can be claimed as a dependent on another person's tax return. As such, she must file a return if any of (i)-(iv) apply. (i) does not apply since $200 < $750; (ii) does not apply because $3800 < $3925; (iii) does not apply because although her spouse (Bret) files a separate return, he does not itemize; (iv) does apply. Part (b) is a little confusing. It says to start with earned income, but only earned income up to $3675. Since $3800 > $3675, we start with $3675. Then we add $250 to get $3925. The greater of (a) $750 or (b) $3925 is clearly $3925. The total of Julia's earned and unearned income is $4000 ($3800 + $200). Since $4000 > $3925, (iv) applies and Julia must file a return. (Explanations will vary.)

Answer Key Testname: CHAPTER 1

50) The subject set is "flight attendants" and the predicate set is "men."

The X indicates that the overlapping region has at least one member. No claim is made about whether other regions also have members. 51) The subject set is "positive numbers" and the predicate set is "negative numbers."

52) Makes sense. By taking out the same amount of money but reducing the number of withdrawals, he saves money on

service charges ($0.50 per week). What would make even more sense would be to find a bank that doesn't charge a fee for every transaction. (Explanations will vary.) 53) Does not make sense. By using false assumptions for premises, it is possible to create a solid argument even for a conclusion that is clearly false. (Explanations will vary.) 54) Answers may vary. One possibility: Safer bikes are better bikes. Buying a new braking system for Jeremy's old bike is not a reasonable option.

55)

The X represents Bozo. The conclusion follows necessarily from the premises, and the argument is valid.

56) It is unclear whether the two stores combined have more than 1000 pieces of merchandise or whether each store itself has more than 1000 pieces of merchandise.

Answer Key Testname: CHAPTER 1

57) Does not make sense. An argument is valid if its conclusion follows necessarily from its premises, regardless of the

truth of its premises or conclusions. An argument is sound if it is valid and its premises are all true. By definition, if an argument is sound it is also valid. To put it another way, the set of sound arguments is a subset of the set of valid arguments. (Explanations will vary.) 58) Answers may vary. Possible answer: The premises tells us that one thing (bringing the umbrella) happened before another (it didn't rain), but they don't prove any connection between them. That is, we cannot conclude that bringing the umbrella was the cause of the fact that it didn't rain. The fact that one event came before another is not proof that the first event caused the second event. 59) Does not make sense. The contrapositive of "If p, then q" is "If not q, then not p." The contrapositive of "If you have $5, then you will buy a hot dog" is "If you will not buy a hot dog, then you don't have $5." What is actually given is the inverse. (Explanations will vary.) 60) Makes sense. You might think the statement does not make sense since the definition of "unconscious" is not actually "not located in the United States"and the assertion about Florida does not, on its own, make sense. However, the only question is whether if the definition were correct, the assertion about Florida would be correct. If "unconscious" means "not located in the United States," then "Florida is not unconscious" could be rephrased as "Florida is not not located in the United States" and then, replacing the double negation, "Florida is located in the United States." That assertion is clearly true. (Explanations will vary.) 61) Answers may vary. One possibility:

Yes, a gerbil could be a dog. We know from the first proposition that the set "dogs" is disjoint from the set "cats," and we know from the second proposition that the set "gerbils" is disjoint from the set "cats." However, we do not know the relationship between the sets "dogs" and "gerbils." It is possible that the two sets are not disjoint; if so, they will overlap in region a. A gerbil who is a dog would necessarily have fleas, since all dogs have fleas. Such a gerbil would not be thirsty, since no thirsty creatures have fleas. 62) Does not make sense. The second proposition is the negation of the first proposition. If a proposition is true, then its negation must be false, and vice versa. Thus, the two propositions cannot both be true. But, you argue, I was hungry at 7:00 this morning, but then I ate breakfast and I was not hungry at 8:00. The explanation is that "I was hungry at 7:00 this morning" and "I was hungry at 8:00 this morning" are two different propositions. The first one is true and its negation is false, while the second one is false and its negation is true. (Explanations will vary.)

Answer Key Testname: CHAPTER 1

63) Answers may vary. One possibility: Taking taxis will cost you $22 (2 trips × $11/trip), while driving will cost you $24

(2 days × $10/day + 2 trips × $2/trip). Driving appears to be a better option. However, before you make your decision, you should consider hidden costs and benefits. What if your trip is extended or your return flight is delayed? Each additional day of long-term parking will cost you $10. In addition, there is the wear-and-tear on the car and the fact that your car would be left in a public lot, where the risk of theft or vandalism might be greater. Those factors would make taking taxis the better option. On the other hand, if you are on a tight schedule, you might not want to rely on a taxi to pick you up on time. 64) Answers may vary. One possibility: A "no" vote means that you believe that the state legislature should have the authority to restrict religious expression. 65) Does not make sense. Arguing logically may not change the other person's position, but it can help the other person understand you, and vice versa. (Explanations will vary.) 66) Answers may vary. Possible answer: Since the example is fictitious, there is no way to determine the truth of the premise. The argument is weak. Perhaps my friend studies harder than I do, perhaps my friend cheats in his classes, or perhaps I get higher grades in biology, history, and art. Moreover, academic smarts are only one measure of intelligence. Since the example is fictitious, there is no way to assess the truth of the conclusion. 67) True. Both individual propositions are true, so the conjunction is true. 68) The subject set is "horses" and the predicate set is "animals."

69) Answers may vary. One possibility: If written notice is provided on April 1, then the lease can be terminated on May

30. If written notice is provided on April 2, then the lease cannot be terminated until June 29. In delaying notice until after the first of the month, the tenant makes himself responsible for another month of rent. That's one expensive day! 70) False. The proposition 6 + 7 = 13 is true, but the proposition 9 × 4 = 45 is false. Since one of the individual propositions is false, the conjunction is false.

71)

The X represents Pierre. The conclusion follows necessarily from the premises, and the argument is valid.

Answer Key Testname: CHAPTER 1

72) Answers will vary. The structure of the argument should be as follows: Premise: If p, then q. Premise: p is not true. Conclusion: q is not true. The argument is invalid.

73)

The set "fish" is disjoint from the set "birds" because the two sets have no members in common. A fish cannot be a bird, and a bird cannot be a fish.

74)

The sets are overlapping. It is possible for a person to be both an athlete and a high school students, but not all athletes are high school students and not all high school students are athletes. 75) Does not make sense. For this to be true, all the time you spent studying would have to be time you also spent playing basketball. This could be true if you spend literally no time studying or if you did all your reading while dribbling a basketball, but both possibilities strain credulity. (Explanations will vary.) 76) Answers may vary. One possibility: If you lease the car for two years, it will cost $9200 ($2000 + 24 months × $300/month). If you buy it, it will cost $8000 ($20,000 - $12,000). At first glance, it appears that buying is a better option. However, you need to consider other factors before you make your decision. How do you know that you will be able to sell the used car for $12,000 in two years? If your estimate is off by only 10% ($1200), then leasing will already be as cost-effective. In addition, you need to consider how the time value of money makes buying a less attractive option. The higher the interest rate, the more it will implicitly cost to buy the car (whether you borrow and pay interest expense or pay cash and forego interest income). Moreover, you should read all the fine print of the lease agreement. Are you locked into the lease for two years? Can you keep it longer if you wish? Are there any additional costs due when you return the car?

Answer Key Testname: CHAPTER 1

77) Answers may vary. One possibility: The answer depends on how many miles you drive the car. If you know you will drive less than 100 miles, then the daily rate is a better option, since $20/day × 4 days + $0.20/mi × 100 mi = $100. If you know you will drive more than 100 miles, then the weekly rate is a better option. If you aren't sure, then the weekly rate is probably preferable since the risk is limited. Even if you drove the minimum (zero miles), you would only spend $20 more by choosing the weekly rate. But for every 100 miles after the first 100, you would save $20 with the weekly rate. If you drive 500 miles, that's $80 in savings. You should also consider a hidden factor. If you might end up only needing the car 1-3 days, then the daily rate will tend to be a better option. However, if you might end up needing the car for 5-7 days, then the weekly rate is a better option since those days will not cost you extra. 78) Answers may vary. Possible answer: Mayor Brown has not said that he is not concerned with improving the quality of children's education, merely that he opposes this particular tax increase to build new schools. (Perhaps he would prefer a tax increase to improve the current schools instead of building new ones, or perhaps he thinks the quality of education can be improved without raising taxes) Mayor Brown's opponent has distorted his views. Any argument based on a distortion of someone else's ideas or beliefs is called a straw man.

79)

The type of argument is called Affirming the Hypothesis. We have p = you are hot and q = you will sweat. The second premise asserts that James is hot, which we show by putting an X in the p circle. Because the X is also in the q circle, q must also be true for James. The Venn diagram shows that the premises lead necessarily to the conclusion, so the argument is valid. 80) In standard form: No beggars are choosers. The subject set is "beggars" and the predicate set is "choosers."

81) Answers may vary. Possible answer: The premises are true. The strength of the argument is relatively weak. First, the examples may have been cherry picked from all the presidents (43 and counting). Second, the examples are of presidents, not of United States politicians in general. The conclusion is false. Although one must be at least 35 years old to be President of the United States, one can be younger and still occupy many other positions. 82) Answers may vary. One possibility: Since "does not oppose" is a double negation, the councilman supports the measure. The term "anti-pollution" is an additional negation, so in supporting the measure, the councilman is acting against pollution. A triple negation (not not not p) has the opposite truth value as the original proposition p.

Answer Key Testname: CHAPTER 1

83) Answers may vary. Possible answer: If we can consider this an argument at all, it has the form

Premise: You want your family to be happy and attractive. Conclusion: You should eat at Ma & Pa's Restaurant. The argument appeals to emotion, not logic. The advertisers hope that the image of happy and attractive people will evoke positive emotions and make you want to eat at the restaurant. In other cases, the appeal is to negative emotions. 84) False. Springfield is the capital of Illinois, but Chicago is not the capital of Illinois. (Even if you don't know the capital of Illinois, you can determine that at least one of the propositions is false.) Since one of the individual propositions is false, the conjunction is false. 85) Answers may vary. Possible answer: The premise of this argument cites one case in which Isabelle ate vegetarian food. But one case is not enough to establish a pattern, let alone to conclude that Isabelle always eats vegetarian food.

86)

I = truck drivers who are neither employed nor unemployed II = employed truck drivers III = non-truck drivers who are employed IV = unemployed truck drivers V = truck drivers who are both employed and unemployed VI = non-truck drivers who are both employed and unemployed VII = non-truck drivers who are unemployed VIII = non-truck drivers who are neither employed nor unemployed This region has no members. 87) Answers may vary. One possibility: Paying bills late will result in bad credit. It is important to be able to get a loan.

Answer Key Testname: CHAPTER 1

88) Answers may vary. One possibility:

Yes, a car could be both a truck and a toy. We know from the first two propositions that the set "cars" and the set "trucks" are subsets of the set "things that have wheels," but we do not know whether the two subsets are disjoint or overlapping or whether one is a subset of the other. We know from the third proposition that the set "toys" overlaps the set "things that have wheels," but we do not know whether it also overlaps either or both of the sets "cars" and "trucks." Depending on whether or not "cars," "trucks," and "toys" overlap; the regions a, b, c, and d may or may not have any elements. Since region b might have elements, a car could be both a truck and a toy.

89)

The sets are overlapping. It is possible for a person to be both an astronaut and a father, but not all astronauts are fathers and certainly not all fathers are astronauts. 90) Yes, Kevin must file a return. He is a married person under 65 years of age who can be claimed as a dependent on another person's tax return. As such, he must file a return if any of (i)-(iv) apply. (i) does not apply since $700 < $750; (ii) does not apply because $3500 < $3925; (iii) does not apply because although his spouse (Linda) files a separate return, she does not itemize; (iv) does apply. The total of earned and unearned income ($3500 + $700 = $4200) is greater than both (a) $750 and (b) earned income (up to $3675) plus $250 ($3500 + $250 = $3750). Thus, Kevin must file a return. (Explanations will vary.) 91) Answers may vary. One possibility: No. There is too much missing information and too many red flags. Why is the cousin of an acquaintance willing to give you such a good deal? Perhaps he's just a generous guy, but there are other possibilities to consider. He claims it's "the same watch," but how do you know it's not counterfeit? Even if it's authentic, how do you know it's not used or broken? Even if it's in mint condition, how do you know it's not stolen? In trying to save money, you might cost yourself money or even end up in jail.

Answer Key Testname: CHAPTER 1

92) Does not make sense. The set of integers includes the whole numbers and their negatives, and thus the set of whole

numbers is a subset of the set of integers. As such, all members of the set of whole numbers are also members of the set of integers. Therefore, if the answer to the question is a whole number it must also be an integer. (Explanations will vary.) 93) Answers may vary. One possibility: The expression "repealed the ban" is a double negation. In repealing the ban on the resolutions in question, the state assembly in effect allowed them. Since the resolutions are "anti-smoking," a third negation is involved. A triple negation (not not not p) has the opposite truth value as the original proposition p. In short, the assembly is now allowing resolutions that prohibit smoking. If one were a lobbyist for the tobacco companies, this might be a setback. 94) Answers may vary. One possibility: Healthy teeth are important. Healthy gums are important. 95) Answers may vary. One possibility: Option 1 (buying a power mower) will cost you $240 ($340 - $100). Option 2 (renting a power mower) will cost you $240 (12 × $20). Option 3 (hiring the neighbor's son) will cost you $240 ($10 × 2 × 12). The cost of each of the three options appears to be equal. Let's see if there are hidden factors that might help you make a decision. Options 1 and 2 require you to mow the lawn yourself each week. Your time could be spent doing other things (including earning money!), so this is a hidden expense. Then again, you might appreciate the opportunity to exercise, get a tan, and meet the neighbors; so depending on your preferences this could actually be a hidden benefit. Option 1 requires you to resell the mower at the end of the summer. Unless there is a buyer in place (e.g., has the owner of the home or the hardware store already offered to buy it back?), you will have to spend time and energy negotiating the sale of the used mower. Option 2 most likely requires you to pick up and drop off the mower each week. When all the costs are considered, Option 3 might end up being the least expensive, but there are some hidden factors there, too. What happens if the neighbor's son does an unsatisfactory job? What if it takes him more than 2 hours to complete the job? Are you obliged to pay him for the additional time?

96)

The sets are overlapping. It is possible for a person to be both a doctor and a poet, but a doctor is not necessarily a poet and a poet is not necessarily a doctor. 97) Does not make sense. A quarter of an hour is 15 minutes, while the time between 6:50 and 7:10 is 20 minutes. It takes him five more minutes to shower, so to do it to save time doesn't make sense. (Explanations will vary.) 98) Answers may vary. One possibility: It will cost her $575 to stay overnight ($400 + $100 + $75), and it will cost her $700 to fly back the same day. It appears that staying overnight is the better option, since it will save her $125. However, she could consider other factors before making a decision. Will staying overnight force her to miss all or part of a day of work? If so, that could cost her more than $125. Is it important to her to be home with her family? If so, the potential $125 savings may be illusory. Then again, she might enjoy having a night to herself and ordering room service.

Answer Key Testname: CHAPTER 1

99) Answers may vary. One possibility: The person stating this opinion may not like one of his current senators (or may

even want the job for himself!). In addition, he may want the balance of power to shift from the legislative branch to the executive branch and may feel that term limits will give senators less overall influence. 100) In standard form: Some dogs are creatures that are adorable. The subject set is "dogs" and the predicate set is "creatures that are adorable."

The X indicates that the overlapping region has at least one member. No claim is made about whether other regions also have members. 101) Answers may vary. One possibility: An unattended campfire is illegal. Getting a citation from the park ranger would be a bad thing. 102) Answers may vary. Possible answer: The premise is false. Most of the sports listed are played with a ball, but hockey is played with a puck. The argument is weak, and the conclusion is false. Many sports, in addition to hockey, do not involve a ball, including wrestling, swimming, and skiing. 103) Does not make sense. There are four basic structures for conditional arguments. Two of them, "Affirming the Conclusion" and "Denying the Hypothesis," are invalid. The other two, "Affirming the Hypothesis" and "Denying the Conclusion," are valid. Since it might be an example of ""Denying the Conclusion," it is not true that it must be an example of "Affirming the Hypothesis." (Explanations will vary.)

104)

The X represents Jack. We do not have enough information to know whether the X should be inside or outside the "lawyers" circle. Therefore, the conclusion does not follow necessarily from the premises, and the argument is invalid.

Answer Key Testname: CHAPTER 1

105) Answers may vary. Possible answer:

106) B 107) B 108) B 109) B 110) A 111) B 112) A 113) A 114) B 115) A 116) B 117) C 118) A 119) B 120) A 121) D 122) A 123) C 124) A 125) C 126) D 127) D 128) D 129) B 130) B 131) B 132) A 133) B 134) B 135) B 136) B 137) A 138) A 43

Answer Key Testname: CHAPTER 1

139) A 140) B 141) B 142) B 143) B 144) A 145) C 146) B 147) A 148) A 149) A 150) D 151) C 152) A 153) A 154) B 155) A 156) B 157) B 158) B 159) A 160) C 161) D 162) A 163) D 164) A 165) D 166) B 167) D 168) B 169) B 170) C 171) A 172) D 173) C 174) B 175) A 176) B 177) A 178) C 179) C 180) D 44

Answer Key Testname: CHAPTER 1

181) D 182) B 183) B 184) A 185) B 186) C 187) B 188) D 189) A 190) C 191) A 192) C 193) B 194) A 195) C

Exam

Chapter 2

Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether the statement makes sense. Explain your reasoning. 1) To convert from Kelvin to Celsius, you subtract 273.15. For example, -100 K = -373.15 °C.

2) I can walk on my hands for 5 meters before falling down, but my goal is to walk a full

1) 2)

decimeter without losing my balance.

Solve the problem. 3) Two bicyclists, 42 miles apart, begin riding toward each other on a long straight avenue. One cyclist travels 15 miles per hour and the other 20 miles per hour. At the same time, Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 38 miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?

4) A trader bought a stock for $20 and then sold it for $30. He bought it back for $44 and

5) Paul and Saul ran a 50-meter race. When Paul crossed the finish line, Saul had run only

then sold it again for $54. How much did he gain or lose on these transactions?

48 meters. Then they ran a second race, with Paul starting 2 meters behind the starting line. Assuming that both runners ran at the same pace as in the first race, who won the second race?

Decide whether the statement makes sense. Explain your reasoning. 6) Our utility company charges 10 cents per joule for the energy we use. Solve the problem. 7) Suppose that 8 turns of a wire are wrapped around a pipe with a length of 60 inches and a circumference of 4 inches. What is the length of the wire?

8) Abe, Boris, Cal, and David all proposed to Ellie on Friday. Abe proposed at 5:00, Boris

9) Suppose that you have 10 white socks and 6 black socks in a clothes dryer. How many

proposed at 6:00, Cal proposed at 7:00, and David proposed at 8:00. Ellie accepted the last of the four proposals. Some clues: (1) The times may be A.M. or P.M. (2) Boris proposed before Abe (3) At least one suitor proposed between the proposals of Cal and David. (4) Cal did not propose between Boris and Al. Whose proposal did Ellie accept?

socks must you withdraw from the dryer (without looking) to be certain of having a pair of white socks?

10) A curved bridge rises over a river, so that the two endpoints of the bridge are 180 yards

10)

apart horizontally. You walk across the bridge with a device to measure its length and discover that the walking distance is 188 yards. Approximately how high does the bridge rise above the horizontal?

Decide whether the statement makes sense. Explain your reasoning. 11) I found a rock at the bottom of our swimming pool. It had a mass of 500 grams and a volume of 1000 cubic centimeters, so its density was 0.5 g/cm3 . Solve the problem. 12) Suppose that you begin with a red bucket containing 12 red marbles and a yellow bucket containing 12 yellow marbles. You move three marbles from the red bucket to the yellow bucket, and then you move any four marbles from the yellow bucket to the red bucket. Which is greater, the number of yellow marbles in the red bucket or the number of red marbles in the yellow bucket? Decide whether the statement makes sense. Explain your reasoning. 13) I drove really far, almost 200 kilometers per hour. Solve the problem. 14) Cheddar cheese comes in 2-pound bags, and mozzarella cheese comes in 5-pound bags. Using entire bags, you make a 47-pound mixture of cheese. How many bags of each type of cheese did you use? Find all the possible solutions to the problem.

11)

12)

13)

14)

Decide whether the statement makes sense. Explain your reasoning. 15) The container was big enough to hold a barrel of water, but it wasn't big enough to hold a barrel of petroleum.

15)

16) I figured out the number of seconds in a week by multiplying 7 by 24 by 60 by 60.

16)

17) To convert square yards to square inches, I multiplied by 122 or 144.

17)

Solve the problem. 18) How do you measure 6 minutes with a 7-minute hourglass and a 5-minute hourglass? Assume that the hourglasses can only measure 7-minute and 5-minute intervals, respectively, and cannot be used to measure other time intervals. Decide whether the statement makes sense. Explain your reasoning. 19) Whether it's a problem in mathematics or something else, I always find it's best to complete the work by looking back to check, interpret, and explain my solution. Solve the problem. 20) A father and son are in a terrible car accident. The father is killed. The son, badly injured, is brought to the hospital for emergency surgery. The surgeon takes one look at the patient and exclaims, "That's my son!" How is this possible?

18)

19)

20)

Decide whether the statement makes sense. Explain your reasoning. 21) My friend wants to lose 15 pounds, but I think that's too much. I think 10 kilograms would make more sense. Solve the problem. 22) A curved bridge rises over a canyon. The two endpoints of the bridge are one mile apart horizontally. The bridge rises to a height of 368 feet above the horizontal. Approximately what is the walking distance along the bridge, in feet?

21)

22)

23) It takes you 78 seconds to walk from the first (ground) floor of a building to the fourth

23)

24) You are considering buying 15 silver coins that look alike, but you have been told that one

24)

floor. How long will it take to walk from the first floor to the 10th floor (at the same pace, assuming that all floors have the same height)?

of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale?

Decide whether the statement makes sense. Explain your reasoning. 25) I got pulled over by a police officer for speeding. I was going 150 kiloliters per second.

25)

26) If you complete the four-step problem-solving process carefully and thoroughly, then

26)

you will have no uncertainty about your final answer.

Solve the problem. 27) There is a large jar of marbles, containing red, blue, yellow, black, and white marbles. How many marbles must you draw (without looking) from the jar to be sure of getting at least three of one color? Decide whether the statement makes sense. Explain your reasoning. 28) It is not recommended that you use approximations to solve a problem, because then your solution is only an approximation. Solve the problem. 29) Three boxes are labeled "CDs," "DVDs," and "CDs & DVDs." Each label is wrong. Bey selecting just one item from just one box, how can you determine the correct labeling of the boxes? Decide whether the statement makes sense. Explain your reasoning. 30) I donated 64 fluid ounces of blood today.

31) The boat leaked and started filling with water. There must be 50 gallons of water in it already.

27)

28)

29)

30) 31)

Solve the problem. 32) A traffic counter consists of a thin black tube stretched across a street or highway and connected to a "brain box" at the side of the road. The device registers one "count" each time a set of wheels (that is, wheels on a single axle) rolls over the tube. A normal automobile (two axles) registers two counts, and a light truck (three axles) registers three counts. Suppose that, during a one-hour period, a particular counter registers 41 counts on a residential street on which only two-axle vehicles (cars) and three-axle vehicles (light trucks) are allowed. How many cars and light trucks passed over the traffic counter? Find all the possible solutions to the problem.

33) Suppose that China's population policy is modified so that every family could have

32)

33)

children until either a boy is born or two children are born, whichever comes first. Assuming that every family chooses to have as many children as possible under this policy, and that boys and girls are equally likely, how many children would be born in a typical group of 1000 families?

Decide whether the statement makes sense. Explain your reasoning. 34) I figured out the distance we had traveled by dividing our speed by the amount of time we had traveled.

35) We will need 1800 cubic feet of carpeting to cover the floors in our three-story house. Solve the problem. 36) There are 20 bags filled with coins that all look alike. The coins in 19 of the bags are authentic and weigh 10 ounces each. The coins in one of the bags are counterfeit and weigh 11 ounces each. With only one weighing on a scale, how can you determine which bag contains the counterfeit coins?

34)

35)

36)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the following question involving a conversion within the USCS system. 37) The customer bought a peck of flour. How many cubic inches of flour did he buy? A) 33.6 in.3 B) 67.2 in.3 C) 268.8 in.3 D) 537.6 in.3

37)

State how much larger or smaller the first unit is than the second. 38) gigagram, microgram A) Larger by a factor of 1018 B) Larger by a factor of 1015

38)

C) Larger by a factor of 109

D) Larger by a factor of 1012

Use units to help you answer the question. If necessary, round your answer to two decimal places. 39) A stockbroker sold 90 shares of stock for $18.32 each. What was the total amount of the sale? A) $1,648.9 B) $1,648.91 C) $1,648.80 D) $1,648.7

39)

Solve the problem. 40) Recently, one U.S. dollar was worth about 0.6158 British pounds. How much would a car have cost in U.S. dollars that cost 11,340 British pounds? A) $22,062.26 B) $5,828.76 C) $6,983.17 D) $18,415.07

41) A warehouse is 44 yards long and 31 yards wide with a height of 14 yards. What is the volume of the warehouse? A) 1,364 yd2

B) 1,364 ft2

C) 19,096 yd3

40)

41)

D) 19,096 ft3

Evaluate.

42) 1 + 1 5

42)

A) 40 13

B) 13

C) 13

D) 13 40

Convert the measurement to the units specified. Round your answer to the nearest tenth. 43) 14 cubic inches to milliliters A) 0.9 milliliters B) 414 milliliters

C) 0.5 milliliters

43)

D) 229.4 milliliters

Use the following table of exchange rates to solve the problem. Round your answer when appropriate. Currency Dollars per Foreign Foreign per Dollar British pound 1.624 0.6158 Canadian dollar 1.005 0.9950 European euro 1.320 0.7576 Japanese yen 0.0120 83.33 Mexican peso 0.07855 12.73

44) Which is worth most, 1 British pound, 1 Canadian dollar, 1 European euro, or 1 dollar? A) 1 European euro B) 1 dollar C) 1 Canadian dollar D) 1 British pound Solve the problem. 45) 106 - 104

A) 110,000

44)

45) B) 1,010,000

C) 100

Answer the following question involving a conversion within the USCS system. 46) If a horse ran 9 furlongs, how many yards did it run? A) 1,980 yd B) 15,840 yd C) 7,920 yd

D) 990,000

46) D) 47,520 yd

Evaluate.

47) 2 × 17 17

47)

A) 2 9

B) 9

C) 1

D) 2

48) 15 × 1 11

48)

A) 2

B) 1

C) 3

D) 3

Solve the problem. 49) Your electrical bill states that you used 630 kilowatt-hours of energy in September. Determine your average power use, in watts. A) 1,050 watts B) 875 watts C) 962.5 watts D) 846.8 watts Identify the units you would expect for the given quantity. 50) The amount of electricity utilized, calculated by multiplying power in kilowatts by time in hours. A) kilowatt-hours B) kilowatts per hour

C) kilowatts per second

49)

50)

D) hours per kilowatt

Answer the following question involving a conversion within the USCS system. 51) How many quarts are in 58 barrels of water? A) 2,436 qt B) 1,798 qt C) 9,744 qt

51) D) 7,192 qt

Decide which of the two given prices is the better deal. 52) The same kind of water is sold in two types of bottle. Which type has the lower unit price? Five 10-oz bottles for $2.50 Seven 14-oz bottles for $5.29 A) equal value B) Five 10-oz bottles

C) Seven 14-oz bottles

52)

D) not enough information

Answer the following question involving a conversion within the USCS system. 53) The container holds 6 gallons of water. How many fluid ounces is that? A) 768 fl oz B) 384 fl oz C) 192 fl oz

53) D) 1,536 fl oz

Convert the measurement to the units specified. Round your answer to the nearest tenth. 54) 35 pounds to grams A) 77.2 grams B) 15,876 grams C) 15.9 grams D) 77,175 grams Use units to help you answer the question. If necessary, round your answer to two decimal places. 55) You are buying carpet to cover a room that measures 12 feet by 17 feet. The carpet costs $27.50 per square yard. How much will the carpet cost? A) $741.82 B) $623.33 C) $204.00 D) $1870.00 Solve the problem. 56) Suppose you burn 400 Calories while exercising for 50 minutes. What is your average power while exercising, in watts? A) 557.9 watts B) 446.3 watts C) 836.8 watts D) 669.4 watts

54)

55)

56)

57) Find a conversion factor between cubic inches and cubic yards. Write it in three forms. A) 1 in.3 = (36 yd)3 = 46,656 yd3 B) 1 yd3 = (36 in.)3 = 46,656 in.3 C) 1 yd2 = (36 in.)2 = 1296 in.2 D) 1 yd3 = (3 ft)3 = 27 ft3 Decide which of the two given prices is the better deal. 58) You can buy laundry product in a 24-ounce bottle for $2.88 or in a 20-ounce bottle for $2.20. A) 20-ounce bottle for $2.20 B) equal value

C) 24-ounce bottle for $2.88

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 60) -35°C, into Fahrenheit A) 12.6°F B) -31°F C) -95°F D) -3°F Solve the problem. 108

C) 104

B) 10-4

60)

D) 1012

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 62) 109 77

A) 1.416

59)

61)

104

A) 1032

58)

D) not enough information

Solve the problem. 59) Suppose a necklace is made from 18-karat gold and weighs 54 grams. Find the weight, in grams, of the pure gold in the necklace. A) 18 grams B) 6 grams C) 40.5 grams D) 54 grams

61)

57)

B) 1.226

C) 1.526

D) 0.706

Use units to help you answer the question. If necessary, round your answer to two decimal places. 63) Assume that you breathe once every 10 seconds. How many breaths do you take in 3 weeks? A) 181,440 B) 25,920 C) 260,480 D) 3024 Solve the problem. 64) Recently, one U.S. dollar was worth about 12.73 Mexican pesos. How much would 585 U.S. dollars be worth in Mexican pesos? A) $45.95 B) $7,447.05 C) $6,616.35 D) $53.82 Carry out the indicated unit conversion. Round your answer, if appropriate. 65) Convert a lot size of 2 acre to square feet (1 acre = 43,560 ft2 ). 9

A) 968 square feet C) 979 square feet

B) 9,790 square feet D) 9,680 square feet

62)

63)

64)

65)

Decide which of the two given prices is the better deal. 66) You can buy hair product in a 8-ounce bottle for $2.16 or in a 6-ounce bottle for $1.50. A) 8-ounce bottle for $2.16 B) not enough information

C) equal value

66)

D) 6-ounce bottle for $1.50

Identify the units you would expect for the given quantity. 67) The price of pudding, found by dividing its cost in dollars by its weight in ounces. A) dollars per ounce B) dollar-ounces

C) ounce-dollars

67)

D) ounces per dollar

Use units to help you answer the question. If necessary, round your answer to two decimal places. 68) Assuming that your heart beats 70 times per minute, how many times does your heart beat in 6 days? A) 36,288,000 B) 604,800 C) 201,600 D) 25,200

68)

Identify the units you would expect for the given quantity. 69) The gas mileage of a car, when you travel 5,020 kilometers using 10 gallons of gas. A) gal/km B) $/gal C) 50 D) km/gal

69)

State how much larger or smaller the first unit is than the second. 70) centiliter, microliter A) Smaller by a factor of 10,000 B) Larger by a factor of 10,000

70)

C) Larger by a factor of 1000

D) Smaller by a factor of 1000

Solve the problem. 71) 102 + 109

71)

A) 100,000,100 C) 100,000,000,000

B) 1,000,001,000 D) 1,000,000,100

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 72) -70°C, into Kelvin A) 147.15 K B) -343.15 K C) 103.15 K D) 203.15 K Use units to help you answer the question. If necessary, round your answer to two decimal places. 73) An acre is equal to 43,560 square feet, and there are 5280 feet in a mile. If a farm has the shape of a rectangle measuring 0.9 miles by 1.5 miles, what is the area of the farm in acres? A) 1050 acres B) 0.16 acres C) 11.14 acres D) 864 acres Convert the measurement to the units specified. Round your answer to the nearest tenth. 74) 21 feet to meters A) 8.5 meters B) 19.2 meters C) 6.4 meters D) 68.9 meters

72)

73)

74)

Solve the problem. 75) An average 12-ounce can of beer contains about 15 grams of alcohol. Consider a person with approximately 6 liters (6000 milliliters) of blood, who quickly drinks two cans of beer. If all the alcohol were immediately absorbed into the bloodstream, what blood alcohol content would we find? A) 0.025 g/100 ml B) 0.25 g/100 ml C) 0.05 g/100 ml D) 0.5 g/100 ml

76) A 14-gram object has a volume of 35 cubic centimeters. Find its density. A) 21 cm3 B) 490 g-cm3 C) 2.5 cm3 /g

76) D) 0.4 g/cm3

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 77) 384 64

A) 7

B) 5

C) 6

75)

77)

D) 6.4

78) 651

78)

878

A) 0.551

B) 0.851

C) 0.748

D) 0.741

Evaluate.

79) 5 + 3 3

79)

A) 6

B) 19

C) 12

D) 19 6

80) You return from a trip with 3,200 Japanese yen. How much are your yen worth in dollars? A) $2,424.32 B) $266,656 C) $38.40 D) $251.36 Solve the problem. 81) Your electrical bill states that you used 680 kilowatt-hours of energy in January. Determine your total electrical energy use, in joules. A) 2,448,000,000 joules B) 217,600,000 joules

C) 244,800,000 joules

80)

81)

D) 2,176,000,000 joules

82) How many cubic inches are in 11 cubic feet? A) 19,008 in.3 B) 1,584 in.3

82) C) 14,256 in.3

D) 513,216 in.3

83) A swimming pool 3 meters deep, 11 meters long, and 6 meters wide is filled with water. What is the area of the water's surface? A) 198 m 3 B) 66 m 2

C) 18 m 2

D) 33 m 2

Use units to help you answer the question. If necessary, round your answer to two decimal places. 84) A community garden contains 25 rectangular plots each measuring 6 yd by 10 yd. What is the total area available for gardening? A) 1,525 yd2 B) 800 yd2 C) 60 yd2 D) 1,500 yd2 Answer the following question involving a conversion within the USCS system. 85) How many gallons are in 76 barrels of petroleum? A) 2,356 gal B) 3,192 gal C) 1.8 gal

83)

84)

85) D) 3,952 gal

86) A boat is moving at 41 miles per hour. What is its speed in knots (nautical miles per hour)? A) 33.6 knots B) 35.6 knots C) 49.2 knots D) 47.2 knots Solve the problem. 87) A supermarket in Japan sells soy milk for 393 yen per liter. If there are 83.12 yen per dollar, then what is the price in dollars per quart? A) $3.76 per quart B) $4.47 per quart C) $4.73 per quart D) $5.00 per quart

86)

87)

Evaluate.

88) 1 - 1 5

88)

A) - 1

B) 1

C) 1

D) - 1 5

89) 7 - 1 5

89)

A) 9 7

Write as a common fraction. 90) 0.23 A) 16 5

B) 44

C) 53

D) 54 35

90) B) 8

C) 23

100

D) 23 10

Solve the problem. 91) Find a conversion factor between square feet and square yards. Write it in three forms. A) 1 yd2 = (3 ft)2 = 9 ft2 B) 1 yd3 = (3 ft)3 = 27 ft3

C) 1 ft2 = (3 yd)2 = 9 yd2

D) 1 ft3 = (3 yd)3 = 27 yd3

91)

92) How many Mexican pesos can you buy for $120? A) 1.44 pesos B) 1,527.6 pesos

92) C) 9.426 pesos

D) 9,999.6 pesos

Convert the measurement to the units specified. Round your answer to the nearest tenth. 93) 2,200 square yards to square meters A) 2,633 square meters B) 1,839.5 square meters

C) 2,406.8 square meters

93)

D) 2,011.7 square meters

Solve the problem. 94) An object has a total volume of 6 liters (which is 6,000 cubic centimeters) and a mass of 4 kilograms. What is its density? Will it sink or float in water? A) 1.5 g/cm3; sink B) 0.67 g/cm3 ; float

C) 0.67 g/cm3 ; sink

94)

D) 1.5 g/cm3; float

Use units to help you answer the question. If necessary, round your answer to two decimal places. 95) Suppose water flows from a shower at a rate of 0.32 cubic feet per minute. Do you use more water by taking a 12-minute shower or by filling a bathtub with 0.4 cubic yards of water, and by how much? A) Shower uses an additional 3.44 ft3 of water

95)

B) Shower uses an additional 6.96 ft3 of water C) Bath uses an additional 3.44 ft3 of water D) Bath uses an additional 6.96 ft3 of water Convert the measurement to the units specified. Round your answer to the nearest tenth. 96) 9 kilometers to yards A) 76,473.9 yards B) 25,491.3 yards C) 9,843 yards D) 29,528.9 yards Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 97) 13 45

A) 3.462

B) 0.199

C) 0.289

D) 0.449

96)

97)

98) A fresh juice stand in Montreal sells a large glass of orange juice for 4.90 Canadian dollars. If you buy 4 glasses, how much have you spent in (U.S.) dollars? A) $14.85 B) $25.87 C) $19.50

D) $19.70

State how much larger or smaller the first unit is than the second. 99) cubic micrometer, cubic meter A) Smaller by a factor of 1012 B) Smaller by a factor of 1018

C) Smaller by a factor of 109

Write as a common fraction. 101) 7.35 A) 147 2

B) 10

C) 1.5

100)

D) 3.5

101) B) 753

C) 147

100

D) 147 200

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 102) 8 11

A) 0.615

99)

D) Smaller by a factor of 106

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 100) 5 2

A) 2.5

98)

B) 0.8

C) 0.072

D) 0.727

Solve the problem. 103) How many cubic furlongs are in a cubic mile? (1 mile = 8 furlongs) A) 4096 cubic furlongs B) 8 cubic furlongs

C) 512 cubic furlongs

102)

103)

D) 64 cubic furlongs

State how much larger or smaller the first unit is than the second. 104) square decimeter, square kilometer A) Smaller by a factor of 106 B) Smaller by a factor of 103

C) Smaller by a factor of 104

D) Smaller by a factor of 108

104)

Solve the problem. 105) A certain land area is 450,000 square miles, and it holds a population of 65.3 million people. Calculate the population density. A) 69 people/mi2 B) 689 people/mi2

C) 1,451 people/mi2 Write as a common fraction. 106) 0.0009 A) 9 10000

D) 145 people/mi2

106) B) 9 1000

C) 9 100

Carry out the indicated unit conversion. Round your answer, if appropriate. 107) Convert a distance of 42 feet into yards. A) 126 yards B) 14 yards C) 17 yards Write as a common fraction. 108) 0.991 A) 991 1000

105)

D) 9 100000

107) D) 28 yards

108) B) 991

C) 991

10000

100

D) 991 10

Solve the problem. 109) A swimming pool 3 meters deep, 12 meters long, and 8 meters wide is filled with water. What volume of water does the pool contain? A) 24 m 2 B) 96 m 2 C) 288 m 3 D) 309 m 3 Identify the units you would expect for the given quantity. 110) The price of gravel, found by dividing its total cost in dollars by its total weight in tons. A) dollars per ton B) ton-dollars C) cubic tons D) tons per dollar Solve the problem. 111) There are 1000 meters in 1 kilometer. Find a conversion factor between cubic meters and cubic kilometers. Write it in three forms. A) 1 m 3 = (1000 km)3 = 1,000,000 km3 B) 1 km3 = (1000 m)3 = 1,000,000,000 m 3

C) 1 km2 = (1000 m)2 = 1,000 m 2

109)

110)

111)

D) 1 km3 = (1000 m)3 = 100,000 m 3

Evaluate.

112) 3 ÷ 5 5

112)

A) 9

B) 3

C) 25

D) 1

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 113) 330 K, into Celsius A) 156.85°C B) 256.85°C C) 56.85°C D) -89.82°C

113)