TEST BANK for Using and Understanding Mathematics A Quantitative Reasoning Approach 7e Jeffrey Benne by digitaldownload87

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. 21) Affirming the hypothesis 21)

Identify the type of argument and determine its validity with a Venn diagram. 22) Premise: If you try hard, then you will succeed. Premise: You did not try hard. Conclusion: You will not succeed. Decide whether the statement makes sense. Explain your reasoning. 23) The argument is weak, so its conclusion must be false. 24) 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.

22)

23) 24)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 25) Premise: 8 + 11 = 19 25) Premise: 12 + 7 = 19 Premise: 38 + 33 = 71 Conclusion: Whenever we add an even number and an odd number, the result is an odd number. Decide whether the statement makes sense. Explain your reasoning. 26) I did not convince my friend that I was right, so I must not have argued logically.

26)

A seemingly simple argument is given. Identify at least two hidden assumptions. 27) Cardiovascular exercise is important, because to be healthy you need a strong heart.

27)

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 28) The House of Representatives voted to override the veto of the communications bill. 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? Decide whether the statement makes sense. Explain your reasoning. 30) 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 to represent the given information. 31) There are 12 girls and 15 boys in a kindergarten class. 8 of the girls and 10 of the boys are right handed.

29)

30)

31)

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. 32) Denying the conclusion 32)

The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 33) Cats reads books or dogs bark. 33)

34) There are 25 letters in the English alphabet or the letter c is a vowel.

34)

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. 35) truck drivers, employed, unemployed 35)

Identify the type of argument and determine its validity with a Venn diagram. 36) Premise: If you are hot, then you will sweat. Premise: James is hot. Conclusion: James will sweat.

36)

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. 37) doctors and poets 37)

Describe how the sentence is ambiguous. 38) Two stores with more than 1000 pieces of merchandise will have grand openings at the mall this weekend.

38)

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. 39) teachers, bowlers, and men 39)

A seemingly simple argument is given. Identify at least two hidden assumptions. 40) The campfire should be extinguished before we go fishing because the park ranger can cite us for illegal activities. Analyze the situation and explain how you would make a decision. 41) 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?

40)

41)

Provide an appropriate response. 43) IRS guidelines state that a married person under 65 years of age who can be claimed as a 43) 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. 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.

Draw a Venn diagram to determine whether the argument is valid. 44) Premise: All lawyers wear suits. Premise: Jack wears a suit. Conclusion: Jack is a lawyer.

44)

Decide whether the statement makes sense. Explain your reasoning. 45) The time I spend studying is a subset of the time I spend playing basketball.

45)

A seemingly simple argument is given. Identify at least two hidden assumptions. 46) I should not go outside, because it is raining.

46)

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. 47) beverages and soft drinks 47)

Provide an appropriate response. 48) 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.

48)

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. 49) athletes and high school students 49) The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 50) There are seven days in a week and there are 24 hours in a day. 50)

Identify the type of argument and determine its validity with a Venn diagram. 51) Premise: If you break curfew, then you will be punished. Premise: Thelma was punished. Conclusion: Thelma broke curfew.

51)

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. 52) motor vehicles and cars 52)

Analyze the situation and explain how you would make a decision. 53) You need a rental car for four days. The daily rate is $20 per day plus 20¢ per mile. The weekly rate is $100, and mileage is included. Which is the better option?

53)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 54) Springfield is the capital of Illinois and Chicago is the capital of Illinois. 54) 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. 55) Some singers are not children. 55)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 56) (Hasty Generalization) Isabelle had vegetarian food for lunch every day last week, so she 56) must be a vegetarian. 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. 57) astronauts and fathers 57)

A seemingly simple argument is given. Identify at least two hidden assumptions. 58) Jeremy needs a new bike, because the new models have a safer braking system. Decide whether the statement makes sense. Explain your reasoning. 59) 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.

58)

59)

The statement connects two individual propositions with the word and. State whether the entire statement is true or false, and explain why. 60) 7 + 8 = 15 and 5 × 3 = 20 60)

61) The sun is bigger than the moon and the sun rotates around the earth. A seemingly simple argument is given. Identify at least two hidden assumptions. 62) We should not vote for the incumbent because he has already been in office for three consecutive terms.

61)

62)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 63) Premise: Baseball, football, basketball, golf, hockey, and tennis are all played with a ball. 63) Conclusion: All sports are played with a ball. A seemingly simple argument is given. Identify at least two hidden assumptions. 64) All bills should be paid on time because a bad credit report will make it difficult to get a loan. 6

64)

Decide whether the statement makes sense. Explain your reasoning. 65) Your argument is valid, but it isn't sound.

65)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 66) (False Cause) Since I brought my umbrella, it didn't rain. 66) 67) (Straw Man) Mayor Brown opposes a tax increase to build new schools. His opponent in the upcoming election states: Mayor Brown is not concerned with improving the quality of education for our children.

67)

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. 68) Denying the hypothesis 68) 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. 69) Movies are entertaining. 69)

Decide whether the statement makes sense. Explain your reasoning. 70) I am very upset because the results of my biopsy were not positive for cancer.

70)

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

71)

72) 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.)

72)

73) Your argument has no fallacies, so your conclusion must be true.

73)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 74) Premise: Calvin Coolidge was over 35 years old when he became President of the United States. 74) 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. 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. 75) No dogs are cats. No gerbils are cats. All dogs have fleas. Some cats are thirsty. No thirsty 75) creatures have fleas. Question: Could a gerbil be a dog?

Draw a Venn diagram to represent the given information. 76) 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.

76)

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. 77) All cars have wheels. All trucks have wheels. Some toys have wheels. No grandmothers have 77) wheels. Question: Could a car be both a truck and a toy?

Analyze the situation and explain how you would make a decision. 78) Betty has to go to New Orleans on business. If she flies there and back on the same day her round 78) 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? Draw a Venn diagram to determine whether the argument is valid. 79) Premise: All clowns wear makeup. Premise: Bozo is a clown. Conclusion: Bozo wears makeup.

79)

The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 80) The state assembly repealed the ban on anti-smoking resolutions. 80) 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. 81) Some flight attendants are men. 81)

Provide an appropriate response. 82) Consider the following clause in a rental lease: 82) "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? 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. 83) salty things, sweet things, tangy things 83)

Analyze the situation and explain how you would make a decision. 84) 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? Describe how the sentence is ambiguous. 85) There was a 15% decrease in donations to the homeless shelter between 1996 and 2000, a year in which $50,000 was collected. Decide whether the statement makes sense. Explain your reasoning. 86) The answer to the question is a whole number but it is not an integer.

84)

85)

86)

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. 87) The dictator of a foreign country has enacted a ban on all firearms, citing prevention of 87) accidental deaths among children as the rationale. 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. 88) All horses are animals. 88) 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) even numbers and odd numbers 89)

Provide an appropriate response. 90) You mention to an acquaintance that you wish to buy a Rolex watch, but the model you're 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. 91) I know more of the names of the common fallacies in arguments than my father, so I can recognize fallacies better than he can. Analyze the situation and explain how you would make a decision. 92) 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?

90)

91)

92)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 93) Premise: I get lower grades than my best friend in math, chemistry, and English. 93) Conclusion: My friend is smarter than I am. Decide whether the statement makes sense. Explain your reasoning. 94) I drew a Venn diagram for two sets, and I only used one circle. Provide an appropriate response. 95) 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.

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) fish and birds 96)

Determine the truth of the premises, discuss the strength of the argument, and assess the truth of the conclusion. 97) Premise: Monday is one of the days of the week. 97) 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." The statement contains a double or multiple negation. Analyze the statement, explaining what it means. 98) The councilman does not oppose the anti-pollution measure. 98) Draw a Venn diagram to represent the given information. 99) In a survey of 80 pet owners, 50 had a dog, 33 had a cat, and 12 had both a cat and a dog. Analyze the situation and explain how you would make a decision. 100) 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?

99)

100)

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. 101) Beggars can't be choosers. 101) The statement connects two individual propositions with the word or. State whether the entire statement is true or false, and explain why. 102) 6 + 2 = 8 or 9 × 4 = 36 102)

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. 103) (Diversion) We've just remodeled the restaurant, so our food is delicious! 103) Decide whether the statement makes sense. Explain your reasoning. 104) The propositions "I am hungry" and "I am not hungry" are both true, since sometimes I am hungry and sometimes I am not hungry. A seemingly simple argument is given. Identify at least two hidden assumptions. 105) It is important to visit the dentist every 6 months to insure healthy teeth and gums.

104)

105)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the converse, inverse, or contrapositive off the proposition, as indicated. 106) If I pass, then I'll celebrate. (contrapositive) A) If I don't pass, then I won't celebrate. B) If I celebrate, then I'll pass. C) If I don't celebrate, then I didn't pass. D) If I pass, then I won't celebrate. Determine whether the statement is true or false. 107) If horses have six legs, then Benjamin Franklin was the first president of the United States. A) True B) False

106)

107)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 108) if q, then not r A) B) q r if q, then not r q r if q, then not r T T T T T F T F F T F T F T T F T T F F T F F T C) D) q r if q, then not r q r if q, then not r T T T T T F T F F T F T F T F F T F F F F F F F

108)

Decide whether the argument is inductive or deductive. 109) All U.S. Presidents have come from the contiguous 48 states. No person from Alaska can be President. A) Deductive B) Inductive Write the negation of the proposition. 110) Emily has brown eyes. A) Emily does not have brown eyes. C) Emily does not have green eyes.

109)

110)

B) Emily has green eyes. D) Jason has brown eyes.

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 111) -88 111) A) Whole numbers B) Integers C) Natural numbers D) Real numbers

Solve the problem. 112) The following Venn diagram describes the desserts people ordered at a party. Use it to determine how 112) many people ordered cake.

A) 28

B) 7

C) 43

D) 21

The argument given or described involves some kind of fallacy. Identify the fallacy. 113) A television commercial shows two people who fall in love while wearing a certain brand of blue jeans. A) Limited choice B) Appeal to ignorance C) Hasty generalization D) Appeal to emotion Write the negation of the proposition. 114) She earns more than me. A) She earns less than me. C) She does not earn less than me.

B) She earns the same as me. D) She does not earn more than me.

Determine whether the statement is true or false. 115) If baseball is a sport, then the letter e is a consonant. A) True

B) False

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 116) p or q A) B) C) p q p or q p q p or q p q p or q T T T T T T T T T T F F T F T T F F F T T F T T F T F F F F F F F F F F

113)

114)

115)

116) p q p or q T T F T F F F T F F F T

Determine whether the statement is true or false. 117) If 9 + 2 = 19, then Canada is in North America. A) True

B) False

Write the negation of the proposition. 118) Some people don't like walking. A) Everyone likes walking. C) Nobody likes walking.

B) Some people don't like driving. D) Some people like walking.

117)

118)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 119) 2 119) A) Whole numbers B) Rational numbers C) Real numbers D) Natural numbers

Use braces to write the members of the set, or state that the set has no members. 120) The letters needed to spell the following words: tear, rate, rat, tea A) {tear, rate, rat, tea} B) {a, e, r, t} C) {t, e, a, r, r, a, t, e, r, a, t, t, e, a} D) {r, a, t}

120)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 121) r and not s A) B) r s p and not s r s r and not s T T F T T T T F T T F T F T F F T F F F F F F T C) D) r s r and not s r s r and not s T T T T T F T F F T F T F T F F T F F F F F F F

121)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 122) -10 122) A) Whole numbers B) Rational numbers C) Natural numbers D) Integers

Determine whether the statement is a proposition. 123) 0.8 = .08 A) Not a proposition

B) Proposition

The argument given or described involves some kind of fallacy. Identify the fallacy. 124) After getting new dishes, I started to sneeze. I must be allergic to the new dishes. A) Personal attack (ad hominem) B) Hasty generalization C) Circular reasoning D) False cause Decide whether the argument is inductive or deductive. 125) Every coach must know his sport well. Steve Spurrier is a football coach, so Steve Spurrier knows football well. A) Deductive B) Inductive Write the negation of the proposition. 126) Everyone is asleep. A) Nobody is asleep. C) Not everyone is asleep.

B) Everyone is awake. D) Nobody is awake.

123)

124)

125)

126)

Solve the problem. 127) The following Venn diagram describes the optional features ordered by new telephone customers in a 127) certain region. Use it to determine how many customers ordered call waiting.

A) 36

B) 40

C) 77

D) 76

Rephrase the statement as a conditional proposition with the form "if p, then q." 128) All chocolate is good. A) If it isn't good, then it's chocolate. B) If it's good, then it's chocolate. C) If it's chocolate, then it's good. D) If it isn't chocolate, then it isn't good.

128)

Solve the problem. 129) The following Venn diagram describes the cars on a used car lot. Use it to determine how many Fords are 129) on the lot.

A) 17

B) 20

C) 30

D) 23

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 130) 6.3 130) A) Integers B) Rational numbers C) Natural numbers D) Real numbers

Rephrase the statement as a conditional proposition with the form "if p, then q." 131) Being in California is sufficient for being in Los Angeles. A) If you are in California, then you are not in Los Angeles. B) If you are in California, then you are in Los Angeles. C) If you are in Los Angeles, then you might be in California. D) If you are in Los Angeles, then you are in California.

131)

State whether or is being used in the exclusive or inclusive sense in the given statement. 132) The insurance policy will not cover misuse or acts of God. A) Exclusive B) Inclusive

132)

Determine whether the statement is true or false. 133) If Florida is in the United States, then all rectangles are squares. A) True B) False

133)

Write the negation of the proposition. 134) Susie lives in a green house. A) Susie does not live in a house that is not green. B) Susie lives in a blue house. C) Susie does not live in a green house. D) Billy lives in a green house.

134)

The argument given or described involves some kind of fallacy. Identify the fallacy. 135) If Proposition Q fails, your children won't have good schools. A) Appeal to emotion B) Hasty generalization C) Appeal to ignorance D) Diversion (red herring) Rephrase the statement as a conditional proposition with the form "if p, then q." 136) Cats chase mice. A) If it is a cat, then it chases mice. B) If cats chase, then they chase mice. C) If cats, then mice. D) If a cat is chasing it, then it is a mouse. Determine whether the statement is a proposition. 137) Mary has a cat. A) Proposition

B) Not a proposition

Write the converse, inverse, or contrapositive off the proposition, as indicated. 138) If the sum of the interior angles of a geometric figure is 180 degrees, then the figure is a triangle. (contrapositive) A) If the sum of the interior angles of a geometric figure is not 180 degrees, then the figure is not a triangle. B) If a geometric figure is a triangle, then the sum of the interior angles is 180 degrees. C) If a geometric figure is not a triangle, then the sum of the interior angles is 180 degrees. D) If a geometric figure is not a triangle, then the sum of the interior angles is not 180 degrees. Determine whether the statement is true or false. 139) If Florida is in the United States, then all squares are rectangles. A) True B) False

135)

136)

137)

138)

139)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 140) -33.2 140) A) Natural numbers B) Rational numbers C) Integers D) Real numbers

State whether or is being used in the exclusive or inclusive sense in the given statement. 141) The prize is a new car or $10,000 cash. A) Inclusive B) Exclusive

141)

Decide whether the argument is inductive or deductive. 142) For any positive number p, -p = p. Therefore,|-94| = 94 A) Deductive B) Inductive

142)

Write the negation of the proposition. 143) Some athletes are musicians. A) Some athletes are not musicians. C) Not all athletes are musicians.

B) No athlete is a musician. D) All athletes are musicians.

Evaluate the validity of the chain of conditionals. 144) 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) Invalid B) Valid

143)

144)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 145) 0 145) A) Rational numbers B) Whole numbers C) Integers D) Natural numbers

Write the converse, inverse, or contrapositive off the proposition, as indicated. 146) If the sun shines, they will bask. (inverse) A) If they do not bask, then the sun does not shine. B) If they do not bask, then the sun shines. C) If the sun does not shine, then they will not bask. D) If they bask, then the sun shines.

146)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 147) (p or q) or r; p or (q or r) 147) A) No B) Yes Determine whether the statement is a proposition. 148) One inch is 2.54 meters. A) Proposition

B) Not a proposition

149) 2 + 5 = 8 A) Proposition

B) Not a proposition

148)

149)

Solve the problem. 150) The following Venn diagram describes the types of cookies in a bakery. Use it to determine how many 150) cookies have neither chocolate chips nor walnuts.

A) 17

B) 10

C) 3

D) 7

Decide whether the argument is inductive or deductive. 151) 7 + 17 = 24, 43 + 17 = 60, 41 + 13 = 54. Therefore, the sum of two prime numbers is even. A) Deductive B) Inductive Write the converse, inverse, or contrapositive off the proposition, as indicated. 152) If you received a refund of over $1000, then you cannot make a claim. (inverse) A) If you did not receive a refund of over $1000, then you can make a claim. B) If you can make a claim, then you received a refund of over $1000. C) If you cannot make a claim, then you did not receive a refund of over $1000. D) If you can make a claim, then you did not receive a refund of over $1000. State whether or is being used in the exclusive or inclusive sense in the given statement. 153) I don't know if I should wear my new skirt or my new dress tonight. A) Inclusive B) Exclusive Rephrase the statement as a conditional proposition with the form "if p, then q." 154) Having a computer is necessary for taking this class. A) If don't take this class, then you must not have a computer. B) If you take this class, then you must have a computer. C) If you have a computer, then you must take this class. D) If you take this computer, then you must have a class.

151)

152)

153)

154)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 155) 16 155) A) Real numbers B) Whole numbers C) Natural numbers D) Integers

Decide whether the argument is inductive or deductive. 156) Practice makes perfect. Therefore, if I practice, I'll be perfect. A) Deductive B) Inductive

156)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 5 157) 157) 9

A) Real numbers C) Integers

B) Natural numbers D) Rational numbers

The argument given or described involves some kind of fallacy. Identify the fallacy. 158) 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) Limited choice B) Circular reasoning C) Personal attack (ad hominem) D) Appeal to popularity Evaluate the validity of the chain of conditionals. 159) 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) Invalid B) Valid

158)

159)

Decide whether the argument is inductive or deductive. 160) Fresh fruit is expensive in winter. This is January, so these fresh strawberries will be expensive. A) Inductive B) Deductive

160)

State whether or is being used in the exclusive or inclusive sense in the given statement. 161) Shaun will win the race if he eats carbohydrates beforehand or if he has slept well. A) Exclusive B) Inclusive

161)

Decide whether the argument is inductive or deductive. 162) His last four at bats were strikeouts. Therefore, the next one will be a strikeout. A) Deductive B) Inductive

162)

Rephrase the statement as a conditional proposition with the form "if p, then q." 163) Attending practice is necessary for staying on the team. A) If you attend practice, then you must stay on the team. B) If you don't attend practice, then you must stay on the team. C) If you don't stay on the team, then you must not attend practice. D) If you stay on the team, then you must attend practice.

163)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 164) not (p and q); (not p) or q 164) A) Yes B) No Use braces to write the members of the set, or state that the set has no members. 165) The integers between 0 and 4 (not inclusive) A) {1, 2, 3, 4} B) {1, 2, 3} C) {0, 1, 2, 3, 4}

D) {0, 1, 2, 3}

165)

The argument given or described involves some kind of fallacy. Identify the fallacy. 166) Each of my brother's three dogs has fleas. Therefore, all dogs have fleas. A) Straw man B) Circular reasoning C) Hasty generalization D) False cause

166)

Rephrase the statement as a conditional proposition with the form "if p, then q." 167) Showing up at the party is sufficient to get a door prize. A) If you show up at the party, then you will get a door prize. B) If you don't show up at the party, then you will not get a door prize. C) If you get a door prize, then you don't have to show up at the party. D) If you got a door prize, then you showed up at the party.

167)

Determine whether the statement is true or false. 168) If a triangle is a parallelogram, then all rectangles are squares. A) True B) False

168)

Evaluate the validity of the chain of conditionals. 169) 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) Invalid B) Valid

169)

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 170) -3 170) A) Whole numbers B) Real numbers C) Rational numbers D) Integers

Use braces to write the members of the set, or state that the set has no members. 171) The integers from 5 to 9 (inclusive) A) {6, 7, 8} B) {5, 6, 7, 8, 9} C) {5, 6, 7, 8}

D) {6, 7, 8, 9}

171)

Solve the problem. 172) The following Venn diagram describes the optional features ordered by new telephone customers in a 172) certain region. Use it to determine how many customers did not order caller ID.

A) 76

B) 67

C) 77

D) 103

Use braces to write the members of the set, or state that the set has no members. 173) The positive-integer powers of 3 A) {3, 6, 9, 12, 15, . . .} B) {1, 8, 27, 64, 125, . . .} C) {1, 3, 9, 27, 81, 243, . . .} D) {3, 9, 27, 81, 243, . . .}

173)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 174) p or q; not [(not p) and (not q)] 174) A) No B) Yes Use braces to write the members of the set, or state that the set has no members. 175) The whole numbers greater than 3 and less than 7 A) {4, 5, 6, 7} B) {3, 4, 5, 6} C) {4, 5, 6}

D) {3, 4, 5, 6, 7}

175)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 176) not (p and q); (not p) and (not q) 176) A) No B) Yes Rephrase the statement as a conditional proposition with the form "if p, then q." 177) I will lose weight if I diet. A) If I lose weight, then I will diet. B) If I diet, then I will gain weight. C) If I diet, then I will lose weight. D) If I don't diet, then I won't lose weight. Determine whether the statement is a proposition. 178) Do you like this color? A) Proposition

B) Not a proposition

The argument given or described involves some kind of fallacy. Identify the fallacy. 179) One candidate favors eliminating affirmative action programs. The other candidate states: My opponent doesn't think there's anything wrong with discrimination." A) Limited choice B) Straw man C) Hasty generalization D) Personal attack (ad hominem) Write the negation of the proposition. 180) Not all people like football. A) All people like football. C) Some people like football.

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

177)

178)

179)

180)

Draw a Venn diagram to represent the given information. 181) Patients in a (hypothetical) hospital on a single day were taking antibiotics (A), blood pressure medication 181) (BP), and pain medication (P) in the following numbers: A only BP only P only None

11 A and BP only 8 A and P only 22 BP and P only 6 All three

14 19 21

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

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. 182) 3146 182) A) Whole numbers B) Integers C) Natural numbers D) Rational numbers

The argument given or described involves some kind of fallacy. Identify the fallacy. 183) 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) Straw man B) Diversion (red herring) C) False cause D) Appeal to force

183)

Write the converse, inverse, or contrapositive off the proposition, as indicated. 184) 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 beeps every thirty seconds. B) If you do not have to replace the battery, then the alarm does not beep 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 have to replace the battery, then the alarm does not beep every thirty seconds.

184)

Solve the problem. the 185) The following Venn diagram describes the cars on a used car lot. Use it to determine how many cars on185) lot are not red.

A) 55

B) 58

C) 38

D) 35

The argument given or described involves some kind of fallacy. Identify the fallacy. 186) You should brush your teeth every day because brushing your teeth is very important. A) Hasty generalization B) Circular reasoning C) Diversion (red herring) D) False cause Determine whether the statement is a proposition. 187) Not all flowers are roses. A) Proposition

B) Not a proposition

Evaluate the validity of the chain of conditionals. 188) 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 Determine whether the statement is a proposition. 189) Go fly a kite. A) Proposition

B) Not a proposition

186)

187)

188)

189)

Make a truth table for the given statement. The letters p, q, r, s represent propositions. 190) q and (not r) and s A) B) q r s q and (not r) and s q r s q and (not r) and s T T T T T T T F T T F F T T F F T F T F T F T T T F F F T F F F F T T F F T T F F T F F F T F F F F T F F F T F F F F F F F F F C) D) q r s q and (not r) and s q r s q and (not r) and s T T T F T T T F T T F T T T F F T F T F T F T T T F F F T F F T F T T F F T T F F T F F F T F F F F T F F F T F F F F F F F F F

190)

Solve the problem. 191) The following Venn diagram describes the types of cookies in a bakery. Use it to determine how many 191) chocolate chip cookies do not also have walnuts.

A) 25

B) 10

C) 15

D) 32

192) The following Venn diagram describes the desserts people ordered at a party. Use it to determine how 192) many people ordered ice cream but not cake.

A) 36

B) 7

C) 21

Write the negation of the proposition. 193) No fifth graders play soccer. A) At least one fifth grader plays soccer. C) No fifth grader does not play soccer.

D) 15

B) Not all fifth graders play soccer. D) All fifth graders play soccer.

193)

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? 194) not (p or q); (not p)and (not q) 194) A) Yes B) No Use braces to write the members of the set, or state that the set has no members. 195) The days of the week A) {Saturday, Sunday} B) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} C) {Monday, Tuesday, Wednesday, Thursday, Friday} D) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

195)

Answer Key Testname: CHAPTER 1 1) 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. 2) 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.) 3) 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.) 4) 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. 5) Answers may vary. Possible answer:

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.

Answer Key Testname: CHAPTER 1 7)

The X represents Pierre. The conclusion follows necessarily from the premises, and the argument is valid. 8) 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. 9) 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). 10)

11)

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.

The X represents Teri's pet. The conclusion follows necessarily from the premises, and the argument is valid.

Answer Key Testname: CHAPTER 1 12) 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.) 13) The subject set is "positive numbers" and the predicate set is "negative numbers."

14) 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.) 15) 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.) 16) True. Both individual propositions are true, so the conjunction is true. 17) 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. 18) Answers may vary. One possibility:

Answer Key Testname: CHAPTER 1 19) 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. 20) 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. 21) 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.

22)

The argument is valid.

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.

Answer Key Testname: CHAPTER 1 23) 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.) 24) 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.) 25) Answers may vary. Possible answer: The premises are true. The argument is relatively strong, and the conclusion is true. 26) 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.) 27) Answers may vary. One possibility: Cardiovascular exercise leads to a strong heart. Being healthy is important. 28) 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. 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. 30) 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.) 31) Answers may vary. Possible answer:

32) 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. 33) True. Although cats do not read books, dogs do bark. The disjunction is false only if both individual propositions are false. 34) 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.

Answer Key Testname: CHAPTER 1 35)

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

36)

This region has no members.

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.

Answer Key Testname: CHAPTER 1 37)

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. 38) 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. 39)

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 40) Answers may vary. One possibility: An unattended campfire is illegal. Getting a citation from the park ranger would be a bad thing. 41) 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. 42) 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.

Answer Key Testname: CHAPTER 1

43) 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.) 44)

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. 45) 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.) 46) 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. 47)

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. 48) Answers may vary. One possibility: A "no" vote means that you believe that the state legislature should have the authority to restrict religious expression.

Answer Key Testname: CHAPTER 1 49)

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. 50) True. Both individual propositions are true, so the conjunction is true. 51)

52)

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.

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.

Answer Key Testname: CHAPTER 1 53) 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. 54) 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. 55) 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. 56) 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. 57)

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. 58) 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.

Answer Key Testname: CHAPTER 1 59) 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.)

60) False. The proposition 7 + 8 = 15 is true, but the proposition 5 × 3 = 20 is false. Since one of the individual propositions is false, the conjunction is false. 61) 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. 62) Answers may vary. One possibility: Four consecutive terms is too many. The incumbent is running in the election. 63) 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. 64) Answers may vary. One possibility: Paying bills late will result in bad credit. It is important to be able to get a loan. 65) 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.) 66) 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. 67) 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. 68) 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.

Answer Key Testname: CHAPTER 1 69) In standard form: All movies are things that are entertaining. The subject set is "movies" and the predicate set is "things that are entertaining."

70) 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.) 71) 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.) 72) 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.) 73) 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.) 74) 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.

Answer Key Testname: CHAPTER 1 75) 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. 76) Answers may vary. Possible answer:

Answer Key Testname: CHAPTER 1 77) 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. 78) 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. 79)

The X represents Bozo. The conclusion follows necessarily from the premises, and the argument is valid. 80) 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.

Answer Key Testname: CHAPTER 1 81) 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. 82) 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! 83)

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 84) 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. 85) It is unclear whether the year in which $50,000 was collected was 1996 or 2000. 86) 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.) 87) Answers may vary. One possibility: The dictator may believe that an unarmed populace is easier to control.

Answer Key Testname: CHAPTER 1 88) The subject set is "horses" and the predicate set is "animals."

89)

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. 90) 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. 91) 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.) 92) 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?

Answer Key Testname: CHAPTER 1 93) 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. 94) 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.) 95) 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. 96)

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. 97) 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. 98) 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. 99) Answers may vary. Possible answer:

Answer Key Testname: CHAPTER 1 100) 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? 101) In standard form: No beggars are choosers. The subject set is "beggars" and the predicate set is "choosers."

102) True. Both individual propositions are true. The disjunction is true if either or both propositions are true. 103) 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. 104) 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.) 105) Answers may vary. One possibility: Healthy teeth are important. Healthy gums are important. 106) C 107) A 108) B 109) B 110) A 111) B 112) A 113) D 114) D 115) B 116) B 117) A 118) A 119) C 120) B 121) D 42

Answer Key Testname: CHAPTER 1 122) D 123) B 124) D 125) A 126) C 127) D 128) C 129) D 130) B 131) B 132) B 133) B 134) C 135) A 136) A 137) A 138) D 139) A 140) B 141) B 142) A 143) B 144) B 145) B 146) C 147) B 148) A 149) A 150) D 151) B 152) A 153) B 154) B 155) C 156) A 157) D 158) C 159) A 160) B 161) B 162) B 163) D 164) B 165) B 166) C 167) A 168) A 169) B 170) B 171) B 43

Answer Key Testname: CHAPTER 1 172) B 173) D 174) B 175) C 176) A 177) C 178) B 179) B 180) A 181) D 182) C 183) B 184) A 185) A 186) B 187) A 188) B 189) B 190) B 191) C 192) D 193) A 194) A 195) D

Chapter 2 Exam 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) The container was big enough to hold a barrel of water, but it wasn't big enough to hold a barrel of petroleum.

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

3) I figured out the distance we had traveled by dividing our speed by the amount of time we had traveled.

4) We will need 1800 cubic feet of carpeting to cover the floors in our three-story house.

5) 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 .

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

7) I can walk on my hands for 5 meters before falling down, but my goal is to walk a full decimeter without losing my balance.

Solve the problem. 8) Paul and Saul ran a 50-meter race. When Paul crossed the finish line, Saul had run only 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?

9) Suppose that you have 10 white socks and 6 black socks in a clothes dryer. How many socks must you withdraw from the dryer (without looking) to be certain of having a pair of white socks?

10) 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.

10)

Decide whether the statement makes sense. Explain your reasoning. 11) Our utility company charges 10 cents per joule for the energy we use. Solve the problem. 12) 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? 1

11)

12)

13) You are considering buying 15 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale?

13)

14) 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?

14)

Decide whether the statement makes sense. Explain your reasoning. 15) I got pulled over by a police officer for speeding. I was going 150 kiloliters per second. 16) I donated 64 fluid ounces of blood today.

15) 16)

Solve the problem. 17) 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. 18) It takes you 84 seconds to walk from the first (ground) floor of a building to the fourth 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)?

17)

18)

Decide whether the statement makes sense. Explain your reasoning.

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

Solve the problem. 20) Abe, Boris, Cal, and David all proposed to Ellie on Friday. Abe proposed at 5:00, Boris 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?

19)

20)

21) A curved bridge rises over a river, so that the two endpoints of the bridge are 140 yards apart horizontally. You walk across the bridge with a device to measure its length and discover that the walking distance is 142 yards. Approximately how high does the bridge rise above the horizontal?

21)

22) A trader bought a stock for $20 and then sold it for $30. He bought it back for $38 and then sold it again for $48. How much did he gain or lose on these transactions?

22)

Decide whether the statement makes sense. Explain your reasoning. 23) 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. 24) 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? 2

23)

24)

25) 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. 26) I drove really far, almost 200 kilometers per hour. 27) 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. 28) 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?

25)

26) 27)

28)

29) 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?

29)

30) 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 350 feet above the horizontal. Approximately what is the walking distance along the bridge, in feet?

30)

Decide whether the statement makes sense. Explain your reasoning. 31) It is not recommended that you use approximations to solve a problem, because then your solution is only an approximation.

31)

32) To convert from Kelvin to Celsius, you subtract 273.15. For example, -100 K = -373.15 °C.

32)

33) If you complete the four-step problem-solving process carefully and thoroughly, then you will have no uncertainty about your final answer.

33)

Solve the problem. 34) Suppose that China's population policy is modified so that every family could have 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? 35) 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?

34)

35)

36) 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.

36)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the units you would expect for the given quantity. 37) The density of a meteor, found by dividing its mass in kilograms by its volume in cubic meters. A) kg/m 3 B) kg/m 2 C) kg3 /m D) m 3 /kg Write as a common fraction. 38) 0.745 149 A) 2000 Evaluate. 39)

149 B) 20

149 C) 2

149 D) 200

1 1 1 × × 4 5 6

15 2

1 120

C) Larger by a factor of 109

41)

1 60

1 26

40)

D) Larger by a factor of 1015

1 1 + 5 7

38)

39)

State how much larger or smaller the first unit is than the second. 40) gigagram, microgram A) Larger by a factor of 1012 B) Larger by a factor of 1018

Evaluate.

37)

41) 24 35

6 35

12 35

35 12

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 42) 45°C, into Fahrenheit A) 57°F B) 77°F C) 49°F D) 113°F

42)

Solve the problem. 43) A 14-gram object has a volume of 35 cubic centimeters. Find its density. A) 2.5 cm3 /g B) 490 g-cm3 C) 0.4 g/cm3

43)

D) 21 cm3

Evaluate. 44)

5 3 + 7 8

44) 112 61

61 56

61 28

56 61

Solve the problem. 45) Your electrical bill states that you used 770 kilowatt-hours of energy in January. Determine your total electrical energy use, in joules. A) 277,200,000 joules B) 2,464,000,000 joules C) 246,400,000 joules D) 2,772,000,000 joules 46) 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) 6 grams B) 18 grams C) 40.5 grams D) 54 grams Carry out the indicated unit conversion. Round your answer, if appropriate. 47) Convert a distance of 48 feet into yards. A) 19 yards B) 32 yards C) 16 yards

D) 144 yards

Write as a common fraction. 48) 9.27 927 A) 100

927 D) 10

927 B) 1000

243 C) 25

Solve the problem. 49) A packing crate measures 5 feet by 11 feet by 9 feet. What is the area of its smallest side? A) 55 ft2 B) 495 ft3 C) 45 ft2 D) 99 ft2 50) 10-13 × 10-3 A) 10-10

B) 1039

51) How many cubic inches are in 17 cubic feet? A) 22,032 in.3 B) 793,152 in.3

C) 10-16

D) 1016

C) 2448 in.3

D) 29,376 in.3

Convert the measurement to the units specified. Round your answer to the nearest tenth. 52) 2900 square yards to square meters A) 3470.8 square meters B) 2651.8 square meters C) 3172.6 square meters D) 2424.8 square meters Solve the problem. 53) Your electrical bill states that you used 840 kilowatt-hours of energy in September. Determine your average power use, in watts. A) 1283.3 watts B) 1166.7 watts C) 1129 watts D) 1400 watts Answer the following question involving a conversion within the USCS system. 54) How many gallons are in 77 barrels of petroleum? A) 1.8 gal B) 3234 gal C) 2387 gal

D) 4004 gal

45)

46)

47)

48)

49)

50)

51)

52)

53)

54)

State how much larger or smaller the first unit is than the second. 55) gram, milligram A) Larger by a factor of 103 B) Smaller by a factor of 103 C) Larger by a factor of 106

Evaluate. 56)

55)

D) Smaller by a factor of 106

9 1 5 8

56) 77 40

67 40

19 10

17 10

Identify the units you would expect for the given quantity. 57) The price of pudding, found by dividing its cost in dollars by its weight in ounces. A) ounces per dollar B) ounce-dollars C) dollars per ounce D) dollar-ounces Answer the following question involving a conversion within the USCS system. 58) The container holds 3 gallons of water. How many fluid ounces is that? A) 96 fl oz B) 384 fl oz C) 768 fl oz Evaluate. 59)

57)

D) 192 fl oz

9 1 ÷ 2 5

58)

59) 45 4

9 10

9 5

45 2

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 60) -80°C, into Kelvin A) 193.15 K B) 129.15 K C) 93.15 K D) -353.15 K

60)

Solve the problem. 61) A field is 120 yards long and 90 yards wide. Find its area in square feet. A) 32,400 ft2 B) 291,600 ft2 C) 97,200 ft2

61)

Evaluate. 62)

D) 10,800 ft2

1 1 6 12

A) -

62) 1 6

1 6

1 12

D) -

1 12

Use units to help you answer the question. If necessary, round your answer to two decimal places. 63) 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 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

63)

State how much larger or smaller the first unit is than the second. 64) square decimeter, square kilometer A) Smaller by a factor of 103 B) Smaller by a factor of 104

64)

Answer the following question involving a conversion within the USCS system. 65) The baby weighs 7.4 pounds. How many ounces is that? A) 74 ounces B) 118.4 ounces C) 88.8 ounces

65)

C) Smaller by a factor of 108

D) Smaller by a factor of 106

D) 0.46 ounces

Use units to help you answer the question. If necessary, round your answer to two decimal places. 66) 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) $204.00 B) $741.82 C) $1870.00 D) $623.33 Carry out the indicated unit conversion. Round your answer, if appropriate. 67) Convert a weight of 12 pounds into ounces; there are 16 ounces in 1 pound. A) 96 ounces B) 192 ounces C) 384 ounces

D) 240 ounces

Convert the measurement to the units specified. Round your answer to the nearest tenth. 68) 37 liters to gallons A) 140 gallons B) 35 gallons C) 9.8 gallons D) 39.1 gallons Solve the problem. 69) 1010 - 104

A) 1,000,000

B) 10,000,010,000

C) 1,000,010,000

D) 9,999,990,000

70) There are 1000 meters in 1 kilometer. Find a conversion factor between cubic meters and cubic kilometers. Write it in three forms. A) 1 km3 = (1000 m)3 = 100,000 m 3 B) 1 m 3 = (1000 km)3 = 1,000,000 km3 C) 1 km3 = (1000 m)3 = 1,000,000,000 m 3

66)

67)

68)

69)

70)

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

Identify the units you would expect for the given quantity. 71) The price of gravel, found by dividing its total cost in dollars by its total weight in tons. A) cubic tons B) ton-dollars C) tons per dollar D) dollars per ton

71)

Carry out the indicated unit conversion. Round your answer, if appropriate. 72) Convert a distance of 14 miles into yards; there are 1760 yards in a mile. A) 26,320 yards B) 2464 yards C) 25,480 yards

72)

D) 24,640 yards

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 73) 370 K, into Celsius A) 296.85°C B) 196.85°C C) -67.59°C D) 96.85°C Identify the units you would expect for the given quantity. 74) The amount of electricity utilized, calculated by multiplying power in kilowatts by time in hours. A) kilowatts per hour B) hours per kilowatt C) kilowatts per second D) kilowatt-hours

73)

74)

Use units to help you answer the question. If necessary, round your answer to two decimal places. 75) Assume that you breathe once every 10 seconds. How many breaths do you take in 3 weeks? A) 181,440 B) 3024 C) 260,480 D) 25,920 Solve the problem. 76) A warehouse is 44 yards long and 25 yards wide with a height of 12 yards. What is the volume of the warehouse? A) 13,200 yd3 B) 1100 yd2 C) 13,200 ft3 D) 1100 ft2 Use units to help you answer the question. If necessary, round your answer to two decimal places. 77) Assuming that your heart beats 70 times per minute, how many times does your heart beat in 6 days? A) 201,600 B) 25,200 C) 604,800 D) 36,288,000 State how much larger or smaller the first unit is than the second. 78) centiliter, microliter A) Smaller by a factor of 1000 B) Larger by a factor of 10,000 C) Larger by a factor of 1000 D) Smaller by a factor of 10,000 Use units to help you answer the question. If necessary, round your answer to two decimal places. 79) 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) 864 acres B) 0.16 acres C) 1050 acres D) 11.14 acres

75)

76)

77)

78)

79)

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

80) How many Mexican pesos can you buy for $130? A) 1.56 pesos B) 10,832.9 pesos

C) 10.2115 pesos

D) 1654.9 pesos

Solve the problem. 81) 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) 0.05 g/100 ml B) 0.5 g/100 ml C) 0.25 g/100 ml D) 0.025 g/100 ml Carry out the indicated unit conversion. Round your answer, if appropriate. 1 82) Convert a lot size of acre to square feet (1 acre = 43,560 ft2 ). 6 A) 7260 square feet C) 737 square feet

B) 726 square feet D) 7370 square feet

80)

81)

82)

Evaluate. 83)

7 3 ÷ 3 7

84)

83) 7 3

49 9

C) 1

9 49

3 1 × 2 4

84) 1 4

3 8

1 8

3 16

Solve the problem. 85) 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 10,610 British pounds? A) $17,229.62 B) $19,981.17 C) $5495.98 D) $6533.64 Decide which of the two given prices is the better deal. 86) You can buy hair product in a 12-ounce bottle for $4.56 or in a 8-ounce bottle for $2.88. A) 12-ounce bottle for $4.56 B) 8-ounce bottle for $2.88 C) not enough information D) equal value Solve the problem. 87) You find a 2-pound nugget that is 50% gold. What is its purity in karats? A) 12 karats B) 50 karats C) 4.8 karats

D) 24 karats

Decide which of the two given prices is the better deal. 88) You can buy laundry product in a 28-ounce bottle for $6.44 or in a 24-ounce bottle for $4.80. A) not enough information B) equal value C) 24-ounce bottle for $4.80 D) 28-ounce bottle for $6.44 Solve the problem. 89) Find a conversion factor between square feet and square yards. Write it in three forms. A) 1 yd3 = (3 ft)3 = 27 ft3 B) 1 yd2 = (3 ft)2 = 9 ft2 C) 1 ft3 = (3 yd)3 = 27 yd3

State how much larger or smaller the first unit is than the second. 91) cubic micrometer, cubic meter A) Smaller by a factor of 1018 B) Smaller by a factor of 109 C) Smaller by a factor of 1012

A) 1011

86)

87)

88)

89)

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

90) A swimming pool 2 meters deep, 11 meters long, and 6 meters wide is filled with water. What volume of water does the pool contain? A) 153 m 3 B) 12 m 2 C) 132 m 3 D) 66 m 2

Solve the problem. 92) 105 × 106

85)

90)

91)

D) Smaller by a factor of 106

B) 1013

C) 1016

D) 1030

92)

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 93) 100°F, into Celsius A) 55.56°C B) 37.78°C C) 68.00°C D) 122.40°C Use units to help you answer the question. If necessary, round your answer to two decimal places. 94) Suppose you could spend $7 every hour, night and day. How much could you spend in a year? (Assume that there are 365 days in a year.) A) $3,679,200 B) $8760 C) $10,080 D) $61,320 Write as a common fraction. 95) 0.8 2 A) 25

8 11

8 9

4 5

Solve the problem. 96) How many cubic furlongs are in a cubic mile? (1 mile = 8 furlongs) A) 512 cubic furlongs B) 64 cubic furlongs C) 4096 cubic furlongs D) 8 cubic furlongs

3 B) 50

3 C) 500

3 D) 5000

Solve the problem. 106 99) 104 A) 1010

101)

B) 102

C) 10-2

2 15

97)

98)

D) 1024

2 ×5 15

95)

99)

100) A swimming pool 3 meters deep, 14 meters long, and 7 meters wide is filled with water. What is the area of the water's surface? A) 294 m 3 B) 21 m 2 C) 42 m 2 D) 98 m 2 Evaluate.

94)

96)

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 97) 70°F, into Celsius A) 56.67°C B) 21.11°C C) 38.00°C D) 38.89°C Write as a common fraction. 98) 0.0006 3 A) 50000

93)

100)

101) B)

1 3

3 2

2 3

Solve the problem. 102) An object has a total volume of 3 liters (which is 3000 cubic centimeters) and a mass of 2 kilograms. What is its density? Will it sink or float in water? A) 1.5 g/cm3 ; sink B) 0.67 g/cm3 ; sink C) 1.5 g/cm3 ; float

D) 0.67 g/cm3 ; float

102)

103) How many square inches are in 8 square yards? A) 288 in.2 B) 96 in.2

C) 10,368 in.2

D) 1152 in.2

104) Recently, one U.S. dollar was worth about 12.73 Mexican pesos. How much would 235 U.S. dollars be worth in Mexican pesos? A) $21.62 B) $18.46 C) $2568.55 D) $2991.55 Answer the following question involving a conversion within the USCS system. 105) A boat is moving at 48 miles per hour. What is its speed in knots (nautical miles per hour)? A) 57.2 knots B) 39.7 knots C) 55.2 knots D) 41.7 knots Solve the problem. 106) A supermarket in Japan sells soy milk for 379 yen per liter. If there are 83.23 yen per dollar, then what is the price in dollars per quart? A) $4.55 per quart B) $4.81 per quart C) $4.31 per quart D) $3.62 per quart 107) A column has a circular base with an area of 5 square feet and is 12 feet tall. What is its total volume? A) 300 ft3 B) 300 ft3 C) 60 ft3 D) 60 ft3 Convert the measurement to the units specified. Round your answer to the nearest tenth. 108) 11 cubic inches to milliliters A) 325.3 milliliters B) 0.4 milliliters C) 0.7 milliliters D) 180.2 milliliters Write as a common fraction. 109) 9.7 79 A) 100

79 B) 10

97 C) 10

97 D) 100

Use units to help you answer the question. If necessary, round your answer to two decimal places. 110) A paint mixture contains 16 gallons of base for every gallon of color. In 340 gallons of paint, how many gallons of color are there? A) 20 gal B) 113 gal C) 320 gal D) 170 gal Solve the problem. 111) You burn 900 Calories will exercising for 35 minutes. What is your average power while exercising, in watts? A) 1793.1 watts B) 2151.8 watts C) 1434.5 watts D) 2689.7 watts 112) 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 yd3 = (3 ft)3 = 27 ft3

104)

105)

106)

107)

108)

109)

110)

111)

112)

D) 1 yd2 = (36 in.)2 = 1296 in.2

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 6 113) 7 A) 0.854

103)

B) 1

C) 0.862

D) 0.857

113)

114) Which is worth most, 1 British pound, 1 Canadian dollar, 1 European euro, or 1 dollar? A) 1 dollar B) 1 British pound C) 1 European euro D) 1 Canadian dollar Solve the problem. 115) 104 + 108

A) 100,100,000 C) 1,000,000,000,000

B) 100,010,000 D) 10,010,000

Identify the units you would expect for the given quantity. 116) The gas mileage of a car, when you travel 4016 kilometers using 8 gallons of gas. A) $/gal B) km/gal C) 50 D) gal/km Solve the problem. 117) What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5¢ per kilowatt-hour? A) 60 cents B) 45 cents C) 30 cents D) 67 cents Carry out the indicated unit conversion. Round your answer, if appropriate. 118) Use a chain of conversions with familiar measures of time to convert 8 weeks into seconds. A) 201,600 seconds B) 4,838,400 seconds C) 691,200 seconds D) 80,640 seconds

114)

115)

116)

117)

118)

119) A fresh juice stand in Montreal sells a large glass of orange juice for 4.50 Canadian dollars. If you buy 4 glasses, how much have you spent in (U.S.) dollars? A) $23.76 B) $17.91 C) $18.09 D) $13.64 Convert the measurement to the units specified. Round your answer to the nearest tenth. 120) 39 pounds to grams A) 17,690.4 grams B) 86 grams C) 17.7 grams D) 85,995 grams

119)

120)

Decide which of the two given prices is the better deal. 121) The same kind of water is sold in two types of bottle. Which type has the lower unit price? Five 15-oz bottles for $4.13 Seven 18-oz bottles for $7.56 A) not enough information B) Five 15-oz bottles C) Seven 18-oz bottles D) equal value Convert the measurement to the units specified. Round your answer to the nearest tenth. 122) 99 kilometers per hour to miles per hour A) 71.6 miles per hour B) 61.5 miles per hour C) 138.2 miles per hour D) 159.3 miles per hour Carry out the indicated unit conversion. Round your answer, if appropriate. 123) There are 8 ounces in a cup, 4 cups in a quart, and 4 quarts in a gallon. Using a chain with these conversions, convert 7 gallons into ounces. A) 1792 ounces B) 896 ounces C) 112 ounces D) 224 ounces State how much larger or smaller the first unit is than the second. 124) nanometer, meter A) Larger by a factor of 106 B) Larger by a factor of 109 C) Smaller by a factor of 106

Write as a common fraction. 125) 0.85 29 A) 5

122)

123)

124)

D) Smaller by a factor of 109

17 B) 2

17 C) 20

29 D) 50

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 427 126) 61 A) 8

121)

B) 6.1

C) 7

Answer the following question involving a conversion within the USCS system. 127) How many quarts are in 54 barrels of water? A) 1674 qt B) 2268 qt C) 9072 qt

126)

D) 6

D) 6696 qt

Use units to help you answer the question. If necessary, round your answer to two decimal places. 128) A stockbroker sold 45 shares of stock for $35.16 each. What was the total amount of the sale? A) $1582.1 B) $1582.20 C) $1582.31 D) $1582.3

125)

127)

128)

129) You return from a trip with 3700 Japanese yen. How much are your yen worth in dollars? A) $44.40 B) $2803.12 C) $290.64 D) $308,321 Convert the measurement to the units specified. Round your answer to the nearest tenth. 130) 28 feet to meters A) 91.8 meters B) 25.6 meters C) 8.5 meters D) 10.6 meters Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 101 131) 76 A) 1.139

B) 1.439

C) 0.752

B) 0.615

C) 0.072

135)

1 1 1 + + 3 4 5

47 60

132)

133)

D) 0.727

Convert the temperature, as indicated. Round your answer to hundredths, if appropriate. 134) -25°C, into Fahrenheit A) 7°F B) -77°F C) 18.1°F D) -13°F Evaluate.

131)

D) 1562 people/mi2

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 8 133) 11 A) 0.8

130)

D) 1.329

Solve the problem. 132) A certain land area is 420,000 square miles, and it holds a population of 65.6 million people. Calculate the population density. A) 640 people/mi2 B) 64 people/mi2 C) 156 people/mi2

129)

134)

135) B)

49 60

43 60

3 4

Solve the problem. 136) A piece of land in Ottawa with an area of 0.5 square kilometers is priced at 5500 Canadian dollars. If there are 0.9976 Canadian dollars per (U.S.) dollar, then what is the price in dollars per square mile? A) $17,744.89 per square mile B) $28,556.85 per square mile C) $28,419.94 per square mile D) $4257.57 per square mile

136)

Identify the units you would expect for the given quantity. 137) A speed found by dividing a distance measured in meters by a time measured in seconds. A) meters per second B) meter-seconds C) seconds per meter D) square meters Convert the measurement to the units specified. Round your answer to the nearest tenth. 138) 8 kilometers to yards A) 22,658.9 yards B) 26,247.9 yards C) 8749.3 yards D) 67,976.8 yards Solve the problem. 105 139) 10-3 A) 108 140)

141) 102 × 10-5 A) 10-3

C) 102

B) 10-8

D) 10-15 140)

B) 10-5

C) 10-21

D) 105

B) 107

C) 10-7

D) 10-10

141)

Use units to help you answer the question. If necessary, round your answer to two decimal places. 142) Your car gets 33 miles per gallon of gasoline, and you drive at an average speed of 44 miles per hour. How much gas do you use in an hour? A) 1.45 gal B) 0.75 gal C) 1.33 gal D) 0.69 gal Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 7 143) 2 A) 14 144)

B) 3.5

C) 4.5

142)

143)

D) 2.5

16 41

A) 0.55

138)

139)

10-13 10-8

A) 10-104

137)

144) B) 2.563

C) 0.3

D) 0.39

Use units to help you answer the question. If necessary, round your answer to two decimal places. 145) A community garden contains 20 rectangular plots each measuring 4 yd by 10 yd. What is the total area available for gardening? A) 560 yd2 B) 800 yd2 C) 40 yd2 D) 820 yd2 Carry out the indicated unit conversion. Round your answer, if appropriate. 146) A car is driving at 240 miles per hour. What is its speed in miles per minute? A) 300 miles per minute B) 14,400 miles per minute C) 4 miles per minute D) 864,000 miles per minute

145)

146)

Answer the following question involving a conversion within the USCS system. 147) 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) 537.6 in.3 D) 268.8 in.3 148) If a horse ran 8 furlongs, how many yards did it run? A) 42,240 yd B) 1760 yd C) 7040 yd

D) 14,080 yd

Convert the common fraction into decimal form. If necessary, round to the nearest thousandth. 615 149) 818 A) 0.759

B) 0.862

C) 0.562

D) 0.752

147)

148)

149)

Answer Key Testname: CHAPTER 2 1) Makes sense. A barrel of liquid and a barrel of petroleum are two distinct measures of volume. A barrel of liquid, such as water, is 31 gallons, but a barrel of petroleum is 42 gallons. If the container were 31-41 gallons, it could hold a barrel of water but not a barrel of petroleum. (Explanations will vary.) 7 days 24 hr 60 min 60 sec × × × = (7 × 24 × 60 × 60) seconds, since all the other units cancel. 2) Makes sense. 1 wk × 1 wk 1 day 1 hr 1 min There are 604,800 seconds in a week. (Explanations will vary.) 3) Does not make sense. Dividing speed by time does not yield distance. Multiplying speed by time yields distance. For example, 10 mi/hr × 2 hr = 20 mi. (Explanations will vary.) 4) Does not make sense. Carpeting covers the area of the floors, not volume. (Indeed, if it covered the volume of the rooms, there wouldn't be any space left for people or furniture.) Cubic feet are a measure of volume, not area. (Explanations will vary.) 5) Does not make sense. The calculation is correct, and the units are fine, but an object with a density under 1 g/cm3

would not sink in water. (Explanations will vary.) 6) Makes sense. Gallons are a measure of volume and, depending on the size of the boat, 50 gallons could be a reasonable quantity of water. (Explanations will vary.) 7) Does not make sense. A decimeter is a tenth of a meter, and this person can already travel 50 times that. Perhaps he wants to be able to walk on his hands for a full decameter, or 10 meters. (Explanations will vary.) 8) Paul 9) 8 socks 10) 1 bag cheddar and 9 bags mozzarella; 6 bags cheddar and 7 bags mozzarella; 11 bags cheddar and 5 bags mozzarella; 16 bags cheddar and 3 bags mozzarella; 21 bags cheddar and 1 bag mozzarella. 11) Does not make sense. The units are fine, but the magnitude is ridiculous. A regular 100-watt bulb consumes energy at a rate of 100 joules per second. If the utility charged 10 cents per joule, it would cost $1 just to keep a 100-watt bulb on for a single second. That's $86,400 a day! (Explanations will vary.) 12) 45.6 mi 13) Answers may vary. One possible answer: Separate the coins into three sets of five coins. Weigh two of the sets. The lightweight coin is in the lighter of the two sets, or if the two sets balance, it is in the third set. Now weigh two pairs of coins from the lightweight set of five coins. If they balance, the fifth coin is the lightweight coin; otherwise, weigh the coins in the lightweight pair to find the lightweight coin. 14) Label the bags 1-20 and choose one coin from bag 1, two coins from bag 2, three coins from bag 3, and so on. Weigh all the coins you chose together, a total of 210 coins. If all the coins were authentic, they would would weigh 2100 oz, since 210 coins × 10 oz/coin = 2100 oz. However, 1-20 of the coins are counterfeit, and each (11-oz) counterfeit coin will add an extra ounce to the weight. If the actual weight is 2101, there must be one counterfeit coin, and since one coin was chosen from bag 1, bag 1 must have the counterfeit coins. If the actual weight is 2102, bag 2 must have the counterfeits; if the actual weight is 2103, bag 3 must have the counterfeits, etc. In general: (Actual weight, in oz) - 2100 = the number of the bag with the counterfeit coins. 15) Does not make sense. Kiloliters are a unit of volume, and speed is measured in units of distance divided by time. (Explanations will vary.) 16) Does not make sense. The units are fine, but 64 fluid ounces are equivalent to 4 pints. A typical blood donation is one pint; donating four pints would be dangerous. (Explanations will vary.)

Answer Key Testname: CHAPTER 2 17) Answers may vary. One possibility: Start both hourglasses simultaneously. When the 5-minute hourglass runs out, immediately turn it upside down and start the timing of the 6-minute interval. There will be 2 minutes of time left in the 7-minute hourglass. When it runs out, immediately turn both hourglasses upside down. There will be 2 minutes of time left in the 5-minute hourglass (the 2 minutes that ran down before it was flipped). When it runs out, immediately turn the 7-minute hourglass upside down. There will be 2 minutes of time left in it (again, the 2 minutes that ran down before it was flipped). When it runs out, the timing of the 6-minute interval is complete (2 + 2 + 2 minutes = 6 minutes). Incidentally, if you continue in this fashion, you can measure any interval of an even number of minutes using these two hourglasses. Of course, some intervals (e.g., 10 minutes, 14 minutes) can be measured much more simply using just one hourglass. 18) 252 seconds 19) Does not make sense. There are 12 inches per foot, but there are 36 inches per yard. To convert square yard to square inches, multiply by 362 or 1296. (Explanations will vary.) 20) Cal's proposal 21) 11.9 yards 22) He gained $20 on the transactions. 23) Makes sense. This is essentially step 4 in the four-step process. Although you may be tempted to think you have finished after you find a result in step 3, this final step is the most important. After all, a result is not very useful if it is wrong or misinterpreted or cannot be explained to others. (Explanations will vary.) 24) The surgeon is a woman. She is the mother of the patient. 25) Select an item from the box labeled "CDs & DVDs." Since the label is wrong, it must be either a box of CDs or a box of DVDs. First assume that the item you selected is a CD. This box is therefore a box of CDs and should be labeled "CDs." Since the box labeled "DVDs" is also labeled incorrectly, it must be either a box of CDs or a box of both CDs and DVDs. Since you have already identified the first box as a box of CDs, the second box must therefore be a box of CDs and DVDs and should be labeled "CDs & DVDs." Finally, the box incorrectly labeled "CDs" should have the remaining label, "DVDs." Now assume that the item you selected is a DVD. By similar reasoning, this box should be labeled "DVDs," the box incorrectly labeled "CDs" should be labeled "CDs & DVDs," and the box incorrectly labeled "DVDs" should be labeled "CDs." 26) Does not make sense. Kilometers per hour are a unit of speed, not distance. If you drive fast but only for a short period of time, you will not go far. (Explanations will vary.) 27) Does not make sense. 10 kilograms is about 22 pounds. If 15 pounds is too much, then certainly 22 pounds is too much. (Explanations will vary.) 28) 11 marbles 29) 68 in. 30) 5326.2 feet 31) Does not make sense. Most real problems involve approximate numbers to begin with, so an approximation is often good enough for a final answer. In other cases, an approximation will reveal the essential character of a problem, making it easer to reach an exact solution. Approximations also provide a useful check. If you come up with an "exact solution" that isn't close to the approximate one, something may have gone wrong. (Explanations will vary.) 32) Does not make sense. The general formula is correct, but the numbers don't make sense. A temperature of 0 K is the coldest possible temperature, known as absolute zero. A temperature of -100 K is theoretically impossible. (Explanations will vary.) 33) Does not make sense. The four-step process is a useful guide to problem solving, but the four steps offer only general advice. Following them will not automatically lead to a unique solution, since some questions do not lend themselves to unique solutions. This is fairly obvious when the question is one of politics or policy. For example, what is the best way to improve the economy? Different experts will recommend different-even contradictory-things (e.g., raise taxes, lower taxes), and no single best answer may be available. The same is true of mathematical problems, particularly when the information provided is incomplete or lacks context. Nonunique solutions often occur because not enough information is available to distinguish among a variety of possibilities. (Explanations will vary.) 34) 1500 35) The number of yellow marbles in the red bucket is greater. 18