Critical Thinking, Reasoning/Argument, Problem Solving

(1.) Describe critical thinking and why it is important to everyone.

A. Critical thinking involves careful reading​ (or listening), sharp​ thinking, logical​ analysis, good​ visualization, and healthy skepticism.
It is helpful in making informed life decisions.

B. Critical thinking involves working together in groups to arrive at solutions to problems.
It is helpful in promoting collaboration and sharing of opinions.

C. Critical thinking involves memorizing procedures and following them exactly.
It is helpful in being efficient when performing tasks.

D. Critical thinking involves studying and completing preparatory work.
It is helpful in ensuring that future tasks are completed correctly.

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(2.) Why do you think problem solving is important in​ mathematics?

A. Because problem solving is the most important end of mathematics.
B. Because problem solving is not only the most important end of​ mathematics, but also a means for learning mathematics.
C. Because problem solving is necessary for applying a set of procedures.
D. Because problem solving is necessary for memorizing mathematical rules and procedures.

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(3.) Explain why in a drawer containing only two different colors of socks one must draw only three socks to find a matching pair.

A. If there are only two colors of socks in the​ drawer, then of any 3​ chosen, two must be the same color.
B. Regardless of the number of different colors of socks in the​ drawer, one must only draw one more sock than the desired number of matching socks in order to get a matching set.​ Therefore, in order to get two matching​ socks, one must draw only three from the drawer.
C. If there are only two colors of socks in the​ drawer, then of any two​ chosen, both must be the same color.
D. It is not the case that one must draw only three socks to find a matching pair.

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(4.) We live in a society where we are constantly bombarded with commercials and ads that are adept at infusing fallacies in our world. Billboards on our​ roadways, commercials on​ television, advertisements in newspapers and​ magazines, as well as​ pop-up ads when surfing online are often loaded with fallacies and​ "the ability to spot fallacies is an essential​ skill" (Livio​ 2013).  
​(Source: ​Livio, M.​ "The Dangerous World of Logical​ Fallacies." Huffington Post.​ 22, Oct. 2013. Retrieved from​ http://www.huffingtonpost.com/mario-livio/logical-fallacies_b_1932906.html)
Identify the fallacy in the following statement.
California has the largest number of foreclosures and layoffs. The foreclosures must be a cause of the layoffs.

A. Appeal to Ignorance
B. Limited Choice
C. Hasty Generalization
D. Circular Reasoning

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(5.) Part I: What does a logical argument always​ include?

Part II: Which of the following could not qualify as a logical​ argument?
Explain your reasoning.

A. A list of premises that do not lead to a conclusion. A logical argument needs to have a conclusion.

B. A series of statements in which the conclusion comes before the premises. In a logical​ argument, the premises need to come before the conclusion.

C. A series of statements in which the conclusion comes before the premises. When the conclusion comes before the​ premises, the argument is actually a fallacy.

D. A series of statements that generate heated debate. If the statements lead to a heated​ debate, then the people who are debating are not thinking logically.

E. A list of premises that do not lead to a conclusion. A logical argument cannot have more than one premise.

F. A series of statements that generate heated debate. If the statements lead to a heated​ debate, then the statements are not a logical argument.

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(6.) (a.) What is​ logic?
Briefly explain how logic can be useful.

(b.) How do we define​ argument?
What is the basic structure of an​ argument? (c.) What is a​ fallacy?
Give examples of fallacies and describe how the argument is deceptive.
Which of the following are​ fallacies? Describe how each choice is deceptive. Select all that apply.

A. I placed the quartz crystal on my​ forehead, and in five minutes my headache was gone. The crystal made my headache go away. This argument is deceptive because it claims that because one thing happened before​ another, the first event caused the second​ event, but it​ doesn't prove that there is any connection between the two events.

B. Society has an obligation to provide health insurance because health care is a right of citizenship. This argument is deceptive because the premise and conclusion essentially say the same thing.

C. Company A makes the best pickup trucks in the world. More people drive Company A pickups than any other light truck. This argument is deceptive because the fact that a large number of people buy Company A pickup trucks does not necessarily mean that they are the best trucks.

D. The patient is still breathing. He must be still alive. This argument is deceptive because it makes a generalization about people who are breathing. The premise has nothing to do with being alive.

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(7.) Why is teaching problem solving an important part of​ mathematics?

A. Problem solving is important to teach in mathematics because without being able to solve math​ problems, there would be no point to any math class.

B. Problem solving is very important for mathematics because without problem​ solving, there is no way to know how advanced a​ person's mathematics knowledge is.​ Therefore, problem solving is critical in determining the depth of a​ person's understanding of mathematics.

C. ​Problem-solving skills help students meet future challenges in all aspects of life. It allows them to take on new tasks and have the confidence to do so. If a first approach to a problem​ fails, good problem solvers will be able to come up with alternative approaches. Notice that much of mathematics is taught through interesting​ problems, which a student needs good​ problem-solving skills to learn from.

D. Problem solving is not really part of mathematics.

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(8.) Which of the following options is not one of the steps Polya described for the process of problem​ solving?

A. Make an educated guess
B. Look back
C. Carry out the plan
D. Understand the problem
E. Devise a plan

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(9.) When does the fallacy of appeal to ignorance​ occur?

A. The fact that we cannot prove a statement p to be true is taken to imply that p is false. A lack of proof that a statement is true implies that the statement is false.
B. A conclusion p is disregarded because the person who stated it is ignorant. Anything stated by a person who is ignorant must be a fallacy.
C. A conclusion p is disregarded because the person who stated it is ignorant. If the person stating conclusion p is​ ignorant, then their argument cannot be logical and must be a fallacy.
D. The fact that we cannot prove a statement p to be true is taken to imply that p is false. A lack of proof that a statement is true does not mean that the statement is false.
E. The fact that a statement p is true is taken to imply that the opposite of p must be true. This fallacy comes from the assumption that the person reading the statement p is not ignorant about​ logic, and knows that the opposite of p must be false.
F. The fact that a statement p is true is taken to imply that the opposite of p must be true. This fallacy comes from the assumption that the person reading the statement p is ignorant about​ logic, and​ doesn't know that the opposite of p must be false.

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(10.) Consider the argument​ "I don't support the​ President's tax plan because I​ don't trust his​ motives."
What is this argument an example​ of? Explain your reasoning.

A. This is an argument that uses the fallacy of appeal to emotion. The premise​ "I don't trust the​ President's motives" is supposed to evoke an emotional response to persuade the listener to accept the conclusion as true.
B. This is an argument that uses the fallacy of appeal to emotion. The premise​ "I don't trust his​ motives" is supposed to evoke an emotional response to distract from the issue.
C. This is an argument that uses the fallacy of personal attack. Even if the premise​ "I don't trust the​ President's motives" is​ true, it is irrelevant to the tax plan and attacks the President personally.
D. This is a​ well-reasoned, logical argument. The premise​ "I don't support the​ President's tax​ plan" fully supports the conclusion​ "I don't trust the​ President's motives."
E. This is an argument that uses the fallacy of personal attack. Even if the premise​ "I don't support the​ President's tax​ plan" is​ true, it is irrelevant to the​ President's motives and attacks the President personally.
F. This is a​ well-reasoned, logical argument. The premise​ "I don't trust the​ President's motives" fully supports the conclusion​ "I don't support the​ President's tax​ plan."

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(11.) For​ each table, give a rule that describes the pattern for changing one number into the one beside it.

I

Original	New
7	14
10	20
11	22
14	28

II

Original	New
7	49
10	100
11	121
14	196

III

Original	New
14	12
11	9
10	8
7	5

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(12.) Hosting of the Olympic games has been a much sought after prize for many nations.
The International Olympic Committee​ (IOC) scrutinizes a wide array of factors before determining the host of any Olympic competition.
Factors such as​ venues, accommodations,​ infrastructure, and security are evaluated as well as items such as the homicide rate of a city.
While cities proudly display their best to win the opportunity to host the​ Olympics, the need for critical thinking in sorting through all the data mixed with propaganda is paramount in selecting a host city.
In​ 2007, seven cities vied for the prize of hosting the 2016 summer Olympics and Paralympics.
Despite the best​ plans, fiascos such as the 1968 slaying of hundreds of demonstrators mere days before the opening ceremonies of the Mexico City games​ can't be predicted.
For the first time since Mexico City won the​ hosting, Rio de​ Janeiro, Brazil, has been selected and will host the 2016 summer games.

Plans to house the​ 48,200 guests of the 2016 games include​ 14,700 hotel rooms and​ 25,000 rooms in the area villages.
The remaining rooms will be accommodated on stationary cruise ships.
How many guests are housed on cruise​ ships?

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(13.) Jude asks why the last step of​ Pólya's four-step problem solving​ process, looking​ back, is necessary since he has already given the answer.
What can you tell​ him?

Select all the possible reasons the last​ step, looking​ back, is necessary below.
A. Looking back allows a student to determine the best strategy to find the solution.
B. Looking back allows a student to understand the problem.
C. Looking back allows a student to check that the answer makes sense in context of the problem.
D. Looking back allows a student to check that the answer is correct.

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(14.) Consider the following example of the logical fallacy of appeal to popularity.
​Apple's iPhone outsells all other smart​ phones, so it must be the best smart phone on the market.

(I.) What is the​ premise?
(II.) What is the conclusion?
(III.) Briefly explain how appeal to popularity occurs in the argument

A. We cannot conclude that the popularity of the iPhone caused it to be the best smart phone on the market.
B. If you read​ carefully, you'll recognize that the premise and the conclusion both say essentially the same thing.
C. The fact that many people buy the iPhone does not necessarily mean it is the best smart phone on the market.
D. This conclusion was drawn from an inadequate number of cases that have not been sufficiently analyzed.

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(15.) As you leave​ Clark, the sign says Lutherville 145 ​miles, Otisburg 245 miles.
If the Planet Diner is halfway between Lutherville and ​Otisburg, how far is it from​ Clark?

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(16.) Suppose you go to a party with four Americans and four​ Canadians, none of whom you have met.
What is the minimum number of people you must meet to be sure of meeting one Canadian and one​ American?

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(17.) In a soccer​ field, four-fifths of the field is made up of soil and the remaining part is made up of grass and has 24 square meters.
Which of the given drawings is an example of math drawing that you would use when solving this given​ problem?



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(18.) Suppose that the fact that an event A occurs before event B is used to conclude that A caused B.
What is this an example​ of? Explain your reasoning.

A. A​ well-reasoned, logical argument. The premise​ "A came before​ B" fully supports the conclusion​ "A caused​ B."
B. An argument that uses the fallacy of false cause. The fact that one event came before another event is not evidence that the first event is caused by the second event.
C. A​ well-reasoned, logical argument. The premise​ "A caused​ B" fully supports the conclusion​ "A came before​ B."
D. Hasty generalization. The assumption is that because A came before B a few​ times, A must be caused by B. This is not necessarily the case.
E. Hasty generalization. The assumption is that because A came before B a few​ times, A must cause B. This is not necessarily the case.
F. An argument that uses the fallacy of false cause. The fact that one event came before another event is not evidence that the first event caused the second event.

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(19.) A student asks why he​ can't just make​ random guesses rather than​ intelligent guesses when using the​ guess-and-check problem-solving strategy.
What is the correct response to this​ question?

A. Intelligent guesses will help students systematically zero in on the exact answer because successive guesses can be based on the results given by the previous guess. This is not possible with random guessing.
B. Intelligent guesses must be used with the​ guess-and-check method because a random guess will never result in the correct answer.
C. Random guessing is actually more effective than intelligent guessing because helps students systematically zero in on the exact answer. Using intelligent​ guesses, this is not possible.
D. Random guessing is just as effective as making educated guesses when using the​ guess-and-check method of problem solving.

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(20.) Decide whether these statements makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false).
Explain your reasoning.

(a.) In order to present a logical argument to​ Andrea, Julian had to shout at her.

(b.) I​ didn't believe the premises on which he based his​ argument, so he clearly​ didn't convince me of his conclusion.

(c.) I disagree with your​ conclusion, so your argument must contain a fallacy.

(d.) Even though your argument contains a​ fallacy, your conclusion is believable.

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(21.) Place a​ half-dollar, a​ quarter, and a nickel in position A as shown in the figure below.
Try to move these​ coins, one at a time to position C.
At no time may a larger coin be placed on a smaller coin.
Coins may be placed in position B.



(a.) How many moves does it take to get them to position​ C?

(b.) Now add a penny to the pile and see how many moves are required.
This is a simple case of the famous Tower of Hanoi​ problem, in which ancient Brahman priests were required to move a pile of 64 disks of decreasing​ size, after which the world would end.
How long would it take at a rate of one move per​ second?

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(22.) What does it mean to think critically about the issue of global​ warming?
Choose the best answer.

A. You should carefully evaluate the evidence and arguments invoked in debates about global warming.
B. You should assume that global warming is a critical threat to our survival.
C. You should be critical of claims about the threat posed by global warming.

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(23.) In the​ checkerboard, two squares on opposite corners have been removed.
A domino can cover two adjacent squares on the board.
Can dominoes be arranged in such a way that all the remaining squares on the board can be covered with no dominoes overlapping or hanging off the​ board? If​ not, why​ not?
(Hint: Each domino must cover one black and one red square. Compare this with the number of each color of squares on the​ board.)



A. Each domino must cover 1 black and 1 red square.​ Hence, 31 dominoes would cover 31 red and 31 black squares. This is impossible because the board has 30 red and 32 black squares.
B. The board can still be covered by dominoes as long as there is an even number of tiles​ left, because each domino needs to cover two squares. There are 62 squares left on the board.​ Therefore, it can still be covered with dominoes.
C. There are now 62 squares on the board instead of​ 64, meaning the number of squares is no longer a perfect square.​ Therefore, the board can no longer be covered.
D. Each domino needs to cover two squares on the​ checkerboard, but the board no longer has an even number of squares.​ Therefore, the board can no longer be covered.

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(24.) ​"If you want to save the social services that would be lost with a property tax​ reduction, then vote against Proposition​ C."
Based on this​ quote, a vote for Proposition C presumably means which of the​ following?

A. You favor a decrease in property taxes over social services because if Proposition C is​ successful, then property taxes will not be reduced and no social service will be lost.
B. You favor a decrease in property taxes over social services because if Proposition C is​ successful, then property taxes will be reduced but some social services will be lost.
C. You support social services because if Proposition C is​ successful, then no social services will be lost.
D. You support social services because if Proposition C is​ successful, then some social services will be lost.
E. You favor an increase in property taxes because if Proposition C is​ successful, then property taxes will be reduced but some social services will be lost.
F. You favor an increase in property taxes because if Proposition C is​ successful, then property taxes will not be reduced and no social service will be lost.

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(25.) Find a​ 3-by-3 magic square using the numbers 2​, 5​, 8​, 12​, 15​, 18​, 22​, 25​, and 28.



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(26.) Shown below is a magic square​ (all rows,​ columns, and diagonals sum to the same​ number).
Find the value of each letter.



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(27.) Thomas stood on the middle rung of a ladder.
He climbed up 3 ​rungs, moved down 5 ​rungs, and then climbed up 7 rungs.
Then he climbed up the remaining 2 rungs to the top of the ladder.

(a.) How many rungs are above the middle rung of the ladder?
(b.) How many rungs are below the middle rung of the ladder?
(c.) How many rungs are there in the whole​ ladder?

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(28.) In the diagram below, determine the value of the question mark.



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(29.) Given the following fallacies:
(a.) Identify the premise.
(b.) Identify the conclusion.
(c.) How does the stated fallacy occur in the argument?

(I.) False Cause: John started to feel sleepy after eating pizza, so the pizza must have made him sleepy.
A false cause is the fallacy where a causal relationship is assumed between two events, but without proof.

(II.) Appeal to Ignorance: Fifty years of searching has not revealed life on other​ planets, so life in the universe must be confined to Earth.

(III.) Limited Choice: He refused to testify by invoking his Fifth Amendment​ rights, so he must be guilty.

(IV.) Personal Attack: Senator​ Leeds's bill on agricultural policy is a​ sham, because he has accepted contributions from companies that sell genetically modified crop seeds.

(V.) Circular Reasoning: It's illegal to drive over the speed limit and breaking the law makes you a​ criminal, so people who exceed the speed limit are criminals.

(VI.) Diversion: Good grades are needed to get into​ college, and a college diploma is necessary for a good career.​
Therefore, attendance should count in high school grades.

(VII.) Straw Man: The mayor wants to raise taxes to fund social​ programs, so she must not believe in the value of hard work.
A straw man is any argument based on a distortion of​ someone's words or belief.

(VIII.) False Cause: Liz ate fish for dinner and later that night, had a nightmare. Fish caused her nightmare.
Deceptive Argument: The premise tells us one thing happened before​ another, but​ doesn't prove any connection between them.
False Cause Fallacy: the fallacy where a causal relationship is assumed between two events, but without proof.

(IX.) Appeal to Popularity (Argumentum ad Populum): There are approximately​ 40,000 Chinese restaurants in America compared to about​ 14,000 Burger Huts.
Chinese food is preferable to hamburgers.
An apppeal to popularity is a logical fallacy that occurs when someone tries to argue that something is right, true, or good, based of many people who believe it.

(X.) Hasty Generalization: All the mayors in my hometown have been men, which shows that men are better qualified for high office than women.
A hasty generalization (also known as over-generalization) is a logical fallacy that occurs when someone reaches a conclusion that is not justified legally by sufficient evidence.

(XI.) Appeal to Ignorance: Claims that fracking causes earthquakes are ridiculous.
Bead lives near an oil well and have never felt an earthquake.

(XII.) Diversion: Wider highways can relieve traffic congestion, so we should build wider highways to benefit the tourist industry.




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(30.) Identify at least two hidden assumptions in these arguments.

(I.) Buying a house today makes good sense. The rent money you save can be put into a​ long-term investment.
Which of the following are hidden assumptions for this​ argument? Select all that apply.
A. People should make​ long-term investments with their money.
B. You will spend less​ out-of-pocket on your home payments than you would on rent.
C. A​ long-term investment will help pay for a house.
D. Buying a house later does not make good sense.

(II.) She recommends giving to the Charity A because it supports so many worthwhile causes.
Which of the following are hidden assumptions for this​ argument? Select all that apply.
A. Giving to Charity A is better than giving to Charity B.
B. Charity A supports worthwhile causes.
C. The money you give is spent on worthwhile causes.
D. Charity A does not support unworthy causes.

(III.) The current governer has campaigned for tax cuts. She gets my vote.
Which of the following are hidden assumptions for this​ argument? Select all that apply.
A. Voting for the current governer will put him in office.
B. Tax cuts are more important than other issues.
C. The governer will keep his promise on tax cuts.
D. Campaigning for tax cuts is important.

(IV.) He supports increased military spending because we need a strong country.
Which of the following are hidden assumptions for this​ argument? Select all that apply.
A. Military spending is important.
B. A stronger country means a stronger military.
C. More military spending will mean a better military.
D. A stronger military means a stronger country.

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(31.) One winter night the temperature fell 15 degrees between midnight and 5 A.M.
By 9 A.M.the temperature had doubled from what it was at 5 A.M.
By​ noon, it had risen another 8 degrees to 30 degrees.
What was the temperature at​ midnight?

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(32.) If six people shake hands with one another exactly​ once:
(a.) How many handshakes take​ place?
(b.) Generalize the solution for n people.

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(33.) (a.) A magic square is a square array of numbers arranged so that the numbers in all​ rows, all​ columns, and the two diagonals have the same sum.



Create a​ 3-by-3 magic square using nine of the ten​ numbers, 20,​ 21, 22,​ 23, 24,​ 25, 26,​ 27, 28, and 29.

Complete the magic square below.
While there may be multiple ways to create a magic square from the given​ values, complete the magic square using the provided starting values.



Explain your solution and reasoning.
(b.) List the strategies used.
A. Work backwards.
B. Examine a simpler case and make a table.
C. Use guess and check.
D. Identify a subgoal.

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(34.) Describe whether these statements make sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false).
Explain your reasoning.

(I.) Reade was relieved because his insurance company chose not to deny his claim.

A. The statement does not make sense.
The insurance company denied​ Reade's claim, so it does not make sense that Reade is relieved.

B. The statement makes sense.
The insurance company denied​ Reade's claim, so it makes sense that Reade is relieved.

C. The statement makes sense.
The insurance company accepted​ Reade's claim, so it makes sense that Reade is relieved.

D. The statement does not make sense.
The insurance company accepted​ Reade's claim, so it does not make sense that Reade is relieved.

(II.) Ethan decided to buy his ticket online for​ $33 plus a​ 10% surcharge rather than from the box​ office, where it costs​ $35 with no additional charges.

A. The statement does not make sense.
A​ 10% surcharge is more than no​ surcharge, so it​ doesn't make sense that Ethan would buy the ticket online.

B. The statement makes sense.
$33 is cheaper than​ $35, so it makes sense that Ethan would buy the ticket online.

C. The statement does not make sense.
$33 plus a​ 10% surcharge is more than​ $35, so it does not make sense that Ethan would buy the ticket online.

D. The statement makes sense.
$33 plus a​ 10% surcharge is less than​ $35, so it makes sense that Ethan would buy the ticket online.

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(35.) An unmagic square is one in which the​ rows, columns, and diagonals must have different sums.
Each of the digits 1 through 9 must be used.
Complete the unmagic square shown below.



Use reasoning to help you choose the square that satisfies the condition that the​ rows, the​ columns, and the two diagonals have different sums.



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(36.) Suppose you go to a party with four Americans and four​ Canadians, none of whom you have met.
What is the minimum number of people you must meet to be sure of meeting two Americans?

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(37.) In its​ "Guide to Ethics​ Laws," the Texas Ethics Commission states the following.

A state officer or employee should not accept or solicit any​ gift, favor, or service that might reasonably tend to influence the officer or employee in the discharge of official duties or that the officer or employee knows or should know is being offered with the intent to influence the​ officer's or​ employee's official conduct.

(a.) Imagine that you are a state representative. Do you believe it would be legal to accept a maximum campaign contribution from a person if you knew nothing about the person except her​ name?

(b.) Describe a situation in which you​ (as a state​ representative) would accept a contribution because it clearly conforms with this guideline.

(c.) Now describe a situation in which you would not accept a contribution because it clearly violates this guideline.

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(38.) Persons E, F, G and H are in a horse race.
Person F is the slowest.
Person G is faster than Person H but slower than Person E.
Name the finishing order of the horses. (from left to right: from slowest to fastest)

A. H, F, G, E
B. H, E, G, F
C. F, H, G, E
D. F, G, E, H

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(39.) Scheduling Classes Using an Organized List
Anthony is selecting his courses for next semester.
Because he works afternoons and also commutes, he must schedule classes that meet only on Monday, Wednesday, and Friday mornings and has decided on the following possibilities: Math at 9, 11, or 12; English at 9 or 12; Sociology at 10, 11, or 12; Art History at 9, 10, or 11.
Determine the possible ways that Anthony can schedule these classes.

9 o'clock	10 o'clock	11 o'clock	12 o'clock
Math English Art History	Art History Sociology	Math Art History Sociology	Math English Sociology

Begin by listing all the class choices that are available at each time slot.
Creating a list like this allows us to see some larger patterns in the times.
As you can see, either Art History or Sociology will have to be at 10 A.M.
Furthermore, we can see that English must be at 9 A.M. or at noon.

Possible schedules so far are:
Math; Sociology, Art History, English

9 o'clock	10 o'clock	11 o'clock	12 o'clock
Math	Sociology	Art History	English

Let's begin creating our organized lists by starting out with Math in the 9 A.M. spot.
If Math is the first class of the day, then English is either at 9 A.M. or at 12 noon (Looking at all the choices, English is either at 9 A.M or at 12 noon.)
It is then possible to have Sociology at 10 followed by Art History at 11...

Possible schedules so far are:
Math, Sociology, Art History, English
Math, Art History, Sociology, English

9 o'clock	10 o'clock	11 o'clock	12 o'clock
Math Math	Sociology Art History	Art History Sociology	English English

or to have Art History at 10 A.M. followed by Sociology at 11 A.M.

Possible schedules so far are:
Math, Sociology, Art History, English
Math, Art History, Sociology, English
English, Art History, Math, Sociology

9 o'clock	10 o'clock	11 o'clock	12 o'clock
English	Art History	Math	Sociology

If we choose to have English as the 9 A.M. class, then Art History could be at 10 A.M; Math could be at 11 A.M; and Sociology could be at noon.

Possible schedules so far are:
Math, Sociology, Art History, English
Math, Art History, Sociology, English
English, Art History, Math, Sociology
English, Art History, Sociology, Math

9 o'clock	10 o'clock	11 o'clock	12 o'clock
English English	Art History Art History	Math Sociology	Sociology Math

Or Sociology could be at 11 A.M followed by Math at noon.

Possible schedules so far are:
Math, Sociology, Art History, English
Math, Art History, Sociology, English
English, Art History, Math, Sociology
English, Art History, Sociology, Math
English, Sociology, Art History, Math

9 o'clock	10 o'clock	11 o'clock	12 o'clock
English English English	Art History Art History Sociology	Math Sociology Art History	Sociology Math Math

However, if we choose to have Sociology at 10 A.M, then class MUST be Art History (it can't be at noon), which means Math is at noon.

Possible schedules so far are:
Math, Sociology, Art History, English
Math, Art History, Sociology, English
English, Art History, Math, Sociology
English, Art History, Sociology, Math
English, Sociology, Art History, Math
Art History, Sociology, Math, English

9 o'clock	10 o'clock	11 o'clock	12 o'clock
Art History	Sociology	Math	English

If we look at the scheduling options that have Art History at 9 A.M, then Sociology MUST be at 10 A.M. (Only Art History and Sociology fit in the 10 A.M time slot) and English MUST be at noon (English can only be at 9 A.M or noon)
Therefore, Math must be at 11 A.M.

Our final list of the 6 possible course scheduling options is:

9 o'clock	10 o'clock	11 o'clock	12 o'clock
Math Math English English English Art History	Sociology Art History Art History Art History Sociology Sociology	Art History Sociology Math Sociology Art History Math	English English Sociology Math Math English

Which of the following statements is false about the possible class schedule Anthony could​ create?

A. English must be at 9 a.m. or 12 noon.
B. There are 6 possible schedules he could create.
C. If Art History is at 9​ a.m., then Sociology must be at 10 a.m.
D. If Sociology is at 10​ a.m., then Art History must be at 12 noon.

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(40.) Give the best responses to these questions.
(I.) Suppose that an argument is deductively valid only if you assume that it contains one or more unstated, hidden assumptions.
In that case, the original argument is ................

(II.) A teacher claims​ that, because spell checkers have weakened​ students' spelling​ skills, middle school students should not be allowed to use them.
What assumption is made in this​ argument?

A. The assumption is​ "Spell checkers are not​ reliable" because they often fail to point out misspelled words.

B. The assumption is​ "Traditional methods of teaching spelling are​ effective" because traditional methods are more effective than a spell checker.

C. The assumption is​ "Students should know how to spell as well as a spell​ checker" because they will not correct mistakes pointed out by the spell checker unless they understand them.

D. The assumption is​ "Spell checkers are not​ reliable" because they do not point out incorrect use of homophones.

E. The assumption is​ "Traditional methods of teaching spelling are​ effective" because using spell checkers can only weaken​ students' spelling if the alternative is superior.

F. The assumption is​ "Students should know how to spell as well as a spell​ checker" because they cannot learn from their mistakes if their spelling skills are not strong.

(III.) You need to buy a car and are considering loans from two banks.
Bank 1 offers a loan at​ 7% interest plus an application​ fee, and Bank 2 offers a loan at​ 7.5% interest plus an application fee.
The loan terms are otherwise identical.
Based on this​ information, what can you conclude about which bank offers the better​ deal?

A. Bank 2 probably offers the better​ deal, since it probably has a lower application fee.

B. There is no way to tell which deal is better without knowing the amounts of the application fees.

C. Both application fees will be small since the banks are competing for your business.

D. Bank 1 offers the better deal because it has a lower interest rate.

(IV.) Auto insurance policy A has an annual premium of​ $500 and a​ $200 deductible for collision​ (meaning you pay the first​ $200 for a collision​ claim).
Auto insurance policy B has an annual premium of​ $300 and a​ $1000 deductible for collision.
Which one of the following conclusions does not​ follow?

A. You will spend less for a​ $900 collision repair with policy A.

B. You will spend less on premiums with policy B.

C. Which policy is a better value depends on how likely you are to be in an accident.

D. Your expense for insurance and collision repairs over a year will be less with policy B.

(V.) The following is the actual wording of a ballot question posed in 1992 to Colorado voters.
Shall there be an amendment to the Colorado constitution to prohibit the state of Colorado and any of its political subdivisions from adopting or enforcing any law or policy which provides that​ homosexual, lesbian, or bisexual​ orientation, conduct, or relationships constitutes or entitles a person to claim any minority or protected​ status, quota​ preferences, or​ discrimination?
Does a​ "yes" vote support or oppose gay​ rights? Explain.

A. A​ "yes" vote opposes gay rights because the vote requires the state to treat gay people​ (and other groups identified by sexual​ orientation) as minorities who can be discriminated against.

B. A​ "yes" vote opposes gay rights because the vote is to prohibit the state from protecting gay people​ (and other groups identified by sexual​ orientation) from discrimination.

C. A​ "yes" vote supports gay rights because the vote requires the state to treat gay people​ (and other groups identified by sexual​ orientation) as minorities who can be discriminated against.

D. A​ "yes" vote supports gay rights because the vote is to prohibit the state from protecting gay people​ (and other groups identified by sexual​ orientation) from discrimination.

(VI.) A city​ charter's policy on reelection states the following.
A person who has served three consecutive terms of four years shall be eligible for​ appointment, nomination for or election to the office of councilmember no sooner than for a term beginning eight years after completion of that​ councilmember's third consecutive full term.
(a.) What is the maximum number of consecutive years that a councilmember could​ serve?
(b.) How many years must a councilmember who has served three consecutive full terms wait before running for office​ again?
(c.) Suppose a councilmember has served two consecutive full terms and is then defeated for reelection.
According to this​ provision, is she or he required to wait 8 years before running for office​ again?
(d.) Suppose a councilmember serves three consecutive terms and is reelected 10 years later.
According to this​ provision, how many consecutive terms can she or he serve at that​ time?

(VII.) Half of the class consists of communication​ majors, and half of the class consists of men.
Does it follow that one quarter of the class is male communication​ majors?

(VIII.) Half of a​ country's exports consist of​ corn, and half of the corn is from the state of Caldonia.
Does it follow that one quarter of the exports consist of corn from​ Caldonia?

A. Yes, because one half of one half is one quarter.
B.No, because it is possible that half of the exports come from Caldonia and the other half of the exports consist of corn.
C. ​Yes, because half of the exports come from Caldonia and the other half of the exports consist of corn.
D. No, because there is no link between the corn the country exports and the corn that comes from Caldonia.

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(41.) Solve these questions.
Explain your reasoning for each solution.
Check your solution as applicable.

(a.) Chloe is thinking of a number.
If you multiply it by 3 and subtract 20​, you get 34.
Find this number.

(b.) A vending machine accepts​ nickels, dimes, and quarters.
Exact change is needed to make a purchase.
How many ways can a person with five ​nickels, three​ dimes, and two quarters make a 75-cent purchase from the​ machine?
For this​ problem, treat all coins within a particular value as if they are the same. That​ is, do not count the number of ways that a single coin​ (a nickel, a​ dime, or a​ quarter) could be chosen.

(c.) Peter and Paul each worked a different number of​ days, but earned the same amount of money.
Use these clues to determine how many days each worked.
Peter earned ​$40 a day.
Paul earned ​​$50 a day.
Peter worked two more days than Paul.

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(42.) An​ end-user license agreement​ (EULA) is a contract between a software manufacturer and a user that spells out the terms of use of the software. Within the many pages of the EULA for Company​ A's online store are the following clauses.

(1.) Company A reserves the right at any time to modify this Agreement and to impose new or additional terms or conditions on your use of the online store.
Such modifications and additional terms and conditions will be effective immediately and incorporated into this Agreement.
Your continued use of the online store will be deemed acceptance thereof.

(2.) Company A is not responsible for typographic errors.

(a.) Do new conditions for the use of the online store need to be approved by the​ user?

(b.) Are users notified of changes in the​ EULA?

(c.) What potential risks for the user do you see in clause​ (1)?

(d.) What potential risks for the user do you see in clause​ (2)?

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(43.) The 2013 online library from the University of California at Los Angeles​ (UCLA) states​ "The World Wide Web has a lot to​ offer, but not all sources are equally valuable or​ reliable" (UCLA​ 2013).
The online library suggests specific points to consider including evaluating the​ audience, determining the purpose of the​ information, completeness, comparing to other​ sources, and general critical thinking skills in determining if the information is credible.
(​Source: University of California at Los Angeles. Sept 2013. Retrieved from​ http://www.library.ucla.edu/libraries/college/thinking-critically-about-world-wide-web-resources)
When evaluating a website for​ reliability, which of the following is not an item to​ consider?

A. Does the content support information shared on other similar​ websites?
B. Does the information make​ sense? Is it​ believable?
C. Who is the source or​ author?
D. Is the site visually​ appealing?

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(44.) Analyze the following segment from a local newspaper.
With last​ Saturday's sellout crowd at the​ Amphitheater, it is clear that the parking problem has become hopeless.
Concert goers parked along residential​ streets, blocking driveways and disrupting traffic. In light of this parking​ problem, future concerts should be banned.
The argument makes several claims about parking​ problems, but stripped of the details the argument boils down to the following.
​Premise: There is a parking problem for concerts at the theater.
​Conclusion: Future concerts at the theater should be banned.
What hint is this situtation an example​ of?

A. Read​ (or listen) carefully
B. Watch for fine print and missing information
C. Identify the real issue
D. Are other conclusions​ possible?
E. Understand all the options
F. Don't miss the big picture
​G. Look for hidden assumptions

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(45.) When must a single person who is claimed as a dependent by someone else file a tax​ return?
Assuming a single person is not age 65 or older and not​ blind, that person must file a return if any of the following apply.

​(i) unearned income was more than​ $900; or
​(ii) earned income was more than​ $5450; or
​(iii) gross income was more than the larger of​ $900 or your earned income​ (up to​ $5150) plus​ $300

Determine whether the following dependents​ (under age 65 and not​ blind) must file a return.

(a.) Person A had unearned income of​ $750, earned income of​ $5700, and gross income of​ $6450.
Does Person A have to file a tax​ return?

(b.) Person B had unearned income of​ $200, earned income of​ $3000, and gross income of​ $3500.
Does Person B have to file a tax​ return?

(c.) Person C had no unearned income and had earned and gross income of​ $5400.
Does Person C have to file a tax​ return?

(d.) Person D had unearned income of​ $200, earned income of​ $5200, and gross income of​ $5500.
Does Person D have to file a tax​ return?

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(46.) Suppose there is a pile of​ quarters, dimes, and pennies with a total value of ​$1.07.

​(a). How much of each coin can be present without being able to make change for a​ dollar?
If there are multiple selections of coins that will​ work, choose the selection with the largest total number of coins.

​(b). Explain why​ ​$1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar.

A. When coins are selected that total​ ​$1.19 but do not allow change for a​ dollar, adding one more of any type will then allow change to be made for a dollar.​
Therefore, it is not possible to have more than​ ​$1.19 without being able to make change for a dollar.

B. It is not possible to have more than​ ​$1.19 without being able to make change for a dollar because the problem did not allow nickels to be part of the pool of​ change, and it would require nickels to be able to have more than​ ​$1.19 without being able to make change for a dollar.

C. It is possible to have more​ $1.19 and still not be able to make change for a dollar.
The statement is incorrect.

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(47.) You buy a cell phone plan that gives you up to 1000 minutes of calling for​ $30 per month.
During a particular​ month, you use only 100 minutes.
What is your​ per-minute cost for that​ month?

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(48.) Suppose you go to a conference attended by 20 Nigerians and 20 Norwegians.
How many people must you meet to be certain that you have met two people of the same​ nationality?

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(49.) In planning a trip to New Zealand six months in​ advance, Chloe finds that an airline offer the following two options.
Option​ A: You can buy a fully refundable ticket for​ $2200.
Option​ B: You can buy a​ $1200 ticket, but you forfeit​ 25% of the price if the ticket is canceled.
(a.) Describe her options in the events that she makes and does not make the trip.
(b.) How would she decide which ticket to​ buy?

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(50.) Mary and Martha began reading a novel on the same day.
Mary reads 16 pages a day and Lauren reads 4 pages a day.
If Mary is on page 80​, on what page is​ Martha?

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(51.) Consider these fallacies​ (which was not discussed in the​ text).
Explain why each fallacy apply to the respective example.

(I.) The fallacy of division has the following form.
​Premise: X has some property.
​Conclusion: All things or people that belong to X must have the same property.
​Example: Americans use more gasoline than​ Europeans, so​ Jake, who is​ American, must use more gasoline than Europeans.

A. Jake is not​ European, so he uses a lot of gasoline.

B. X is the amount of gasoline​ used, and Jake uses a lot of gasoline because he is American.

C. Americans have some​ property, which is using more gasoline that Europeans.​
Therefore, Jake must have the same property of using more gasoline than Europeans.

D. An American uses more gasoline than​ a European, and so does every other American on Earth.

(II.) The slippery slope fallacy has the following form.
​Premise: X has occurred and is related to Y.
​Conclusion: Y will inevitably occur.
​Example: America has sent troops to three countries recently.
Before you know​ it, we will have troops everywhere.

A. America will inevitably send troops to other countries because many countries send troops to other countries.

B. Let X be America sending troops to three countries recently.
Let Y be America having troops everywhere.
The two events are​ related, and Y will inevitably occur.

C. Let Y be America sending troops to three countries recently.
This is inevitable because soon there will be troops everywhere.

D. Let X be America having troops everywhere.
Let Y be America sending troops to three countries recently.
This is inevitable because America has troops everywhere.

(III.) The slippery slope fallacy has the following form.
​Premise: X and Y are two extreme positions on a question.
​Conclusion: Z, which lies between X and Y, must be correct.
​Example: Senator Peters supports a large tax​ cut, and Senator Willis supports no tax cut.
That means a small tax cut must be best.

A. Let X be no tax cut and Y be a tax cut.
A small tax cut lies between no tax cut and a tax cut.
Let Z be a small tax cut.

B. Let X be no tax cut and Y be a small tax cut.
There​ doesn't need to be a Z because it is implied.

C. The Senate chose a middle ground position.​
Therefore, it's a middle ground fallacy.

D. Let Z be the​ Senate's decision for no tax​ cut, which is not an extreme position.

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(52.) Consider the following complex​ problem, which does not have a single straightforward solution.
Describe how you would approach the problem​ (without carrying out the​ process).
List the assumptions and information needed to carry out your solution.
Assess the uncertainty in these assumptions and data.
Determine whether you believe the problem can be solved and whether a particular solution might generate controversy.
Suppose that a city added new bus routes and handed out free bus passes.
How many people would give up driving in favor of the​ bus?
How much​ money, overall, would this cost or save the​ city?

(I.) Which of the following would be needed to carry out a solution to this​ problem?
Select all that apply.

A. The number of drivers in the city
B. The amount of money saved by the city by having more people ride buses
C. The types of cars driven in the city
D. How many traffic lights are in the city
E. The cost of buying new buses and hiring new bus drivers
F. The cost of the free passes
G. If the bus routes would be more convenient for drivers

(II.) Could any of the needed data identified above potentially have ambiguous or uncertain​ answers?

A. Yes, because convenience for drivers is more objective than subjective.
B. No, because the city could determine the new costs using current costs.
C. Yes, because there is no way to know the salary of bus drivers.
D. No, because the city will be able to determine the exact number of people who would give up driving.

(III.) If the data identified above is​ obtained, can the problem be​ solved?

A. ​No, because it is impossible to write an equation with the data to find a solution.
B. ​Yes, because an estimate is asked for in the problem.
C. ​Yes, because the city can easily determine the number of new buses and drivers it will need.
D. No, because the number of people who would give up driving will be an​ estimate, not an exact answer.

(IV.) Is a particular solution likely to generate​ controversy?

A. Yes. Any attempt to give people alternatives to driving is always met with controversy.
B. Yes. If the city does not save money and only few people give up​ driving, controversy will result.
C. No, controversy rarely occurs over buses.
D. No, the city will certainly save​ money, so no controversy will result over the new bus routes.

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(53.) You are deciding whether to buy a car for ​$16,000 or to accept a lease agreement.
The lease entails a ​$900 fee plus monthly payments of ​$230 for 36 months.
Under the lease​ agreement, you are responsible for service on the car and insurance.
At the end of the​ lease, you may purchase the car for ​$7000.

(I.) Should the cost of service and insurance determine which option you​ choose?
A. No, because it is cheaper to lease the car than to buy it.
B. Yes, because you probably​ don't have to pay for services when you buy the car.
C. Yes, because you get a discount on your insurance when you lease the car.
D. No, because you will probably have to pay for service and insurance with either plan.

(II.) Does the total cost of purchasing the car at the end of the lease agreement exceed the cost of purchasing the car at the​ outset?
A. No, the total cost of the car at the end of the lease is ​​$...
B. Yes, the total cost of the car at the end of the lease is ​$...

(III.) What are some possible advantages of leasing the​ car?
A. Not all of the money is needed up front and you have years to decide if you want to buy the car.
B. You can sell the car whenever you want and you can make money on the car when you sell it.
C. You can give the car back whenever you want and you can get a new car whenever you want.
D. The insurance costs less and you get a service discount.

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(54.) Martha says that it is possible to create a magic square with the numbers​ 1, 3,​ 4, 5,​ 6, 7,​ 8, 9, and 10.
What is the correct response to her​ statement?

A. Magic squares can only be made with numbers that are less than 10.​
Therefore, it is impossible to make a magic square from the given​ numbers, as they include 10.

B. It is possible to make a magic square from any given 9 numbers.
There is nothing special about these particular ones.

C. Some of the given numbers are even numbers.
Without the inclusion of 2 for a​ factor, it is impossible for a magic square to include even numbers.

D. Dividing the sum of the numbers by 3 does not result in a natural number.​
Therefore, there is no magic square that can be made from the​ numbers, as the fixed sum for each​ row, column, and diagonal is equal to the sum of the numbers divided by 3.

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(55.) Paul received the following​ e-mail notification.

​"Through a random selection from more than 20 million​ e-mail addresses,​ you've been selected as the winner of our grand prize: a ​two-week vacation in the Bahamas.
To claim your​ prize, please call our​ toll-free number.
Have your credit card ready for identification and a small processing​ fee."

Does this sound like a deal worth​ taking? Explain.

A. Yes, because most legitimate sweepstakes ask you to pay a processing fee in order to claim your prize.
There is no reason not to call the​ toll-free number.

B. No, because a legitimate sweepstakes would not ask you to pay a processing fee in order to claim your prize.
Note also that the notice never says that your vacation will be fully paid for.
The notification is most likely spam.

C. No, because out of 20 million​ e-mail addresses it is unlikely that yours has been chosen as the winner.
The notification is most likely spam.

D. Yes, because a​ two-week vacation in the Bahamas is something worth taking.
There is no reason not to call the​ toll-free number.

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(56.) The following argument gives several reasons for a particular political position.
Identify at least one unstated issue that may be the real issue of concern.

He opposes the​ President's spending proposal.
Taxpayer money should not be used for programs that many taxpayers do not support.
Excessive spending also risks increasing budget deficits.
Greater deficits increase the federal​ debt, which in turn increases our reliance on foreign investors.

A. The speaker may have an ideological opposition to paying taxes.
B. The speaker may want the country to depend more on foreign investors.
C. The speaker may be opposed to the government spending money.
D. The​ President's spending proposal is significantly under budget.

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(57.) Consider the following excerpt from the contract for the lease of an apartment.

"Landlord shall return the security deposit to resident within one month after termination of this lease or surrender and acceptance of the​ premises, whichever occurs first."

Suppose the lease terminates on November 30​, and the resident moves out of the apartment on November 8.

(a.) Has the landlord complied with the terms of the lease if the resident receives the security deposit back on November 28​?
(b.) Has the landlord complied with the terms of the lease if the resident receives the security deposit back on December 3?
(c.) Has the landlord complied with the terms of the lease if the resident receives the security deposit back on December 9?

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(58.) For​ centuries, enthusiasts of pyramidology have looked for hidden codes and prophecies in the structure of the Egyptian pyramids.
The measurements and orientations of the pyramids have been claimed to predict cosmic​ events, future​ events, or the end of the world.
Explain how confirmation bias might have given these claims life and made them popular.

A. Enthusiasts may have started with evidence of real design​ intentions, such as astronomical alignment of​ structures, and then been predisposed to accept unsupported assumptions of deeper knowledge not supported by evidence.
B. Even if these claims have not been conclusively​ proven, many may still be​ true, which would create a bias towards accepting them as true.
C. People who did not agree with these claims may have felt reluctant to argue for their positions.
D. Enthusiasts may have applied valid deductive reasoning to support their​ positions, but were not aware of all of the facts we know now about the Pyramids.

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(59.) The following is a fake news headline that was widely circulated prior to the 2016 presidential election.
Suggest at least one reason you should have been immediately suspicious of the headline.

​"Pope Francis Shocks​ World, Endorses Donald Trump for​ President, Releases​ Statement"

Why should you have been immediately​ suspicious? Select all that apply.
A. Popes have never taken a position in American politics.

B. The pope is not a U.S. citizen and is therefore legally barred from endorsing candidates in federal elections.

C. Of the two major candidates in​ 2016, one might question why the pope would support​ Trump's position on a variety of issues.

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(60.) Answer these questions. Provide explanations for your answers.

(I.) Philemon had 12 bagels and ate all but 9 of them.
How many bagels are left?

(II.) A​ farmer's rooster laid an egg in a​ neighbor's yard. Who owns the​ egg?

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(61.) Analyze these​ situations.
Explain what decision you would make and the reason for your decision.

(I.) Bead flies frequently between two cities 1750 miles apart.
Average​ round-trip cost on Airline A is ​$275.
Airline B offers the same trip for only ​$250.
​However, Airline A has a frequent flyer program in which you earn a free​ round-trip ticket after you fly 25000 miles.
Airline B does not have a frequent flyer program.

A. Flying​ round-trip 9 to 11, 18 to 22, or over 26 ​times, Airline ....... is cheaper.
For any other number​ flights, Airline ....... is cheaper than or equal to the other airline.

B. Flying​ round-trip under 17 ​times, Airline ....... is cheaper.
Flying round-trip 17 times or more, Airline ....... is cheaper.

C. Airline A is cheaper for any number of flights.

D. Airline B is cheaper for any number of flights.

(II.) A man and his spouse are expecting a baby.
Their current health insurance costs ​$113 per​ month, but​ doesn't cover prenatal care or delivery.
They can upgrade to a policy that will cover their prenatal care and​ delivery, but their new premium will be ​$267 per month.
The cost of prenatal care and delivery is approximately ​$4000.

A. They should upgrade to the new policy because the current policy costs ​$ ....... for nine​ months, which is significantly more than the upgrade which costs ​$ ....... for nine months.

B. They should keep their current policy because it costs ​$ ....... for nine​ months, which is significantly less than the upgrade which costs ​$ ....... for nine months.

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(62.) Determine whether these statements make sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false).
Explain your reasoning.

(I.) If you use​ logic, then your life will be organized.​
Therefore, if your life is​ organized, you must be using logic.

(II.) Through the logic of​ deduction, I will show you that if you accept the truth of my​ premises, you must also accept the truth of my conclusion.

(III.) Because my argument is​ valid, you must accept the truth of my conclusion.

(IV.) My inductive argument provides absolute proof of your​ client's guilt.

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(63.) Explain whether these arguments are deductive or inductive.

(I.) I have never found mail in my mailbox on a Saturday.
The Postal Service must not have Saturday deliveries.

(II.) I have heard every CD released by a particular singer and they have been outstanding.
Her next CD is bound to be​ good, so I will certainly buy it.

(III.) Every coach must know his sport well.
Marty Wright is a baseball​ coach, so Marty Wright knows baseball well.

(IV.) The Samuels are having their fourth child.
All of their children are musically ​gifted, so the youngest child is bound to be musically gifted as well.

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(64.) Determine if any, any counterexample that can render the following rules invalid.

(a.) For all real numbers: c and d, c + d = d + c

(b.) For all positive real numbers: c and d, $\sqrt{c + d} = \sqrt{c} + \sqrt{d}$

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(65.) Briefly describe the​ Understand-Solve-Explain approach to problem​ solving, giving examples of things that should be considered in each step.

(a.) What is the​ "Understand" step of this part of the problem solving​ approach?
(b.) What does the​ "Solve" step of this part of the problem solving​ approach?
(c.) What does the​ "Explain" step of this part of the problem solving​ approach?

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(66.) Elizabeth goes bowling at least one day per​ week, but never on two consecutive days.
List all the numbers of days per week that Elizabeth could go bowling.

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(67.) Decide whether these statements make sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false).
Explain your reasoning.

(I.) The tread on a tire can channel away 2 gallons of water per second.
That is 393 gallons per mile.

(II.) To figure out how long an airplane will take to reach​ Beijing, divide the distance to Beijing by the​ airplane's speed.

(III.) Person B drove at a speed of 35 miles for the entire trip.

(IV.) Person A has a box with a volume of 2 square feet.

(V.) One dollar is worth about 103 Japanese​ yen, so 1 yen is worth more than​ $1

(VI.) Fabric was bought at​ X-mart, because their price of $6 per square foot was better than​ Y-mart's price of $17 per square yard.

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(68.) Which of the following would not be a component the Runnells may have utilized in their letters and phone calls made for problem​ solving?

A. Make a sketch.
B. Make a list of given facts that are pertinent.
C. Determine if the information given is sufficient.
D. Work the problem backwards.

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(69.) One day in the maternity​ ward, the name tags for four girl babies become mixed up.
(a.) In how many different ways could two babies be tagged correctly and two babies be tagged​ incorrectly?
(b.) In how many different ways could three babies be tagged correctly and one baby be tagged​ incorrectly?

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(70.) Which of the following represents 9 square​ miles?

A. a square 9 miles on a side.
B. a line of small squares that is 9 miles long.
C. a line of small squares that is 3 miles long.
D. a square 3 miles on a side.

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(71.) The U.S. has competed with China in arenas from Olympic sports to economics for years.
At a time when the U.S. is struggling​ financially, China is being seen by the world as an ever emerging power.
So what is China doing to fuel their progress at a time when many world countries are​ struggling?

Five items that stand out are available as seen below.
(1.) Be ambitious​: from construction to​ investments, vision is evident in China.
(2.) Education matters​: to add to​ China's competitive​ k-12 academic​ edge, schools are expanding upon their rigid but successful curriculum to add more creativity and improved results as measured in Trends in International Mathematics and Science Study (TIMSS) reports.
(3.) Look after the elderly​: China is well known for the respect afforded to the elders of their​ society, often resulting in the care of grandparents in the homes of their adult children.
(4.) Save more​: At a time when U.S. spending is out of​ control, the Chinese appear to have a healthier balance between spending and saving.
(5.) Look over the horizon​: China has become a country of forward thinking people driven to become a country of upwardly​ mobile, responsible people.

China has consistently averaged in the top of the TIMSS educational scale for both grades 4 and 8 where the United States ranks closer to the middle.
When trying to problem solve the woes of the​ U.S., perhaps some of the answers lie in seeing what other countries are doing well.
As the U.S. continues to struggle with the aftermath of the deepest recession in 26​ years, looking at our neighbors may provide some possible answers.
Which of the following would be in line with the five ideas collected from looking at​ China?

A. Decrease​ debt, from the government levels and board rooms to the individual homes
B. Purchase a new car to eliminate the need for car pooling
C. Open more nursing homes for the elderly to alleviate the care of elderly in their​ children's homes
D. Decrease the amount of curriculum for our​ k-12 students

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(72.) Answer these critical thinking questions.
(I.) Five books of five different colors are placed on a shelf.
The brown book is placed between the gold and orange ​books, and these three books are consecutive.
The pink book is not leftmost on the shelf and the orange book is not rightmost on the shelf.
The gray book is separated from the orange book by two books.
If the pink book is not next to the gray ​book, what is the complete ordering of the​ books?

(II.) Five books of five different colors are placed on a shelf.
The pink book is placed between the gold and brown ​books, and these three books are consecutive.
The orange book is not leftmost on the shelf and the brown book is not rightmost on the shelf.
The gray book is separated from the brown book by two books.
If the orange book is not next to the gray ​book, what is the complete ordering of the​ books?

(III.) Five books of five different colors are placed on a shelf.
The gold book is placed between the pink and orange ​books, and these three books are consecutive.
The gray book is not leftmost on the shelf and the orange book is not rightmost on the shelf.
The brown book is separated from the orange book by two books.
If the gray book is not next to the brown ​book, what is the complete ordering of the​ books?

(IV.) Five books of five different colors are placed on a shelf.
The gray book is placed between the pink and brown ​books, and these three books are consecutive.
The orange book is not leftmost on the shelf and the brown book is not rightmost on the shelf.
The gold book is separated from the brown book by two books.
If the orange book is not next to the gold ​book, what is the complete ordering of the​ books?

(V.) Five books of five different colors are placed on a shelf.
The gray book is placed between the orange and brown ​books, and these three books are consecutive.
The gold book is not leftmost on the shelf and the brown book is not rightmost on the shelf.
The pink book is separated from the brown book by two books.
If the gold book is not next to the pink ​book, what is the complete ordering of the​ books?

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(73.) When confronted with a complex​ problem, why can it be useful to consider a​ simpler, similar​ problem?

A. The answer to the simpler problem will always be the same as the answer to the complex problem.
B. ​You'll be able to find the answer to the complex problem by multiplying the answer to the simpler problem by a scale factor.
C. The simpler problem may provide you with insight that will help you approach the more complex problem.

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(74.) Choose the best answer to the following questions.
Explain your reasoning with one or more complete sentences.

(I.) A person is buying apples while traveling in Europe.
How will the price be mostly likely​ quoted?

A. The price will be quoted in euros per milliliter because Europeans use the SI unit system.
B. The price will be quoted in euros per kilogram because the price is quoted in currency per weight.
C. The price will be quoted in euros per kilogram because one apple in Europe weighs one kilogram.
D. The price will be quoted in euros per kilometer because euros is the currency that is used in Europe.
E. The price will be quoted in euros per milliliter because the price has unit of euros per unit of volume.
F. The price will be quoted in euros per kilometer because because Europe is very​ large, so everything is quoted in kilometers.

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(75.) (I.) Summarize the strategic hints for problem​ solving, and give an example of the meaning of each one.
Which of the following best summarizes the strategic hint​: There may be more than one​ answer and provides an example of the​ meaning?

A. If a problem has more than one​ answer, it is not valid.
Every problem in mathematics will have one unique answer.
For​ example, $x = 2$ is the only solution to $x + 1 = 3$.

B. There may be several ways to get an answer.
For​ example, you can find a solution for $\dfrac{1}{3}x = 4$ by multiplying each side by 3 or by dividing each side by $\dfrac{1}{3}$.

C. Some problems in mathematics have more than one answer.
Without further​ information, there is no way to determine whether both solutions are valid for a particular problem.
For​ example, both $x = -2$ and $x = 2$ are solutions to $x^2 = 4$.

D. Every problem in mathematics has more than one answer.
For​ example, both $x = -2$ and $x = 2$ are solutions to $x^2 = 4$.

(II.) Which of the following best summarizes the strategic hint:​ There may be more than one​ strategy and provides an example of the​ meaning?

A. There may be several strategies to solving a problem and all of the strategies are equally efficient.
For​ example, there is more than one strategy to solve $x^2 + 3x + 2 = 0$​, all taking the same amount of time and work.

B. There may be several strategies to solving a​ problem, however only one of them will find the correct answer.
For​ example, there is more than one strategy to solve $x^2 + 3x + 2 = 0$​, ​however, only one of them will provide the correct answer.

C. There may be several strategies to solving a problem.
However, not all of the strategies are equally efficient.
For​ example, there is more than one strategy to solve $x^2 + 3x + 2 = 0$​, ​however, using the quadratic formula involves more time and work.

D. If there is more than one strategy that can be used to find an​ answer, the problem is not valid.
For​ example, since there is more than one way to solve $\dfrac{5}{4}x + 7 = \dfrac{1}{8}$, this problem is not valid.

(III.) Which of the following best summarizes the strategic hint:​ Use appropriate​ tools and provides an example of the​ meaning?

A. When given a choice of tools for a​ problem, use as many tools as possible.
This will make the​ problem-solving process much simpler.
For​ example, $\dfrac{1}{4}x = 6$ can be solved with multiplication or division.​
Thus, both methods should be used.

B. Choosing only the tools most suited to the job will make tasks much easier.
For​ example, if a problem can be solved one way with calculus and another way with​ multiplication, using multiplication will make the solving process easier.

C. For any given​ task, there will be a choice of tools to use in any problem.
Choose only the most basic tools so the problem does not get too difficult.
For​ example, $\dfrac{1}{4}x = 6$ can be solved with multiplication or division.
Use only multiplication because it is easier.

D. For any​ problem, the appropriate tools needed will always be stated in the problem statement.
For​ example, if a problem can be solved one way with calculus and another with​ multiplication, the problem statement will provide that information.

(IV.) Which of the following best summarizes the strategic hint:​ Consider simpler, similar​ problems and provides an example of the​ meaning?

A. Sometimes, it is easier to consider​ simpler, similar problems.
If there are no simpler​ problems, the question has no solution.
For​ example, if a problem involves adding​ monomials, there is no​ simpler, similar method.​
So, there is no solution to that particular question.

B. The exact strategy used to solve​ simpler, similar problems is almost never used to solve the more difficult problems.
For​ example, if a problem involves subtracting decimals to 3 places and simplier problem involves subtracting decimals to 1​ place, the exact strategy is not used to find a correct answer.

C. Sometimes, the insight gained from solving the easier problem may help to understand the original problem.
For​ example, instead of picturing molecules mixing​ together, try to picture marbles mixing together.

D. The exact strategy used to solve​ simpler, similar problems is always used to solve the more difficult problems.
For​ example, if a problem involves dividing polynomials and a simplier problem involves dividing​ integers, model that exact strategy to find a correct answer.

(V.) Which of the following best summarizes the strategic hint​: Consider equivalent problems with simpler​ solutions and provides an example of the​ meaning?

A. Consider equivalent problems with simpler solutions in any case except for when looking for numerical answers.
For​ example, instead of finding an equivalent problem to find surface area of a​ cube, look for any simpler way to solve the problem.

B. A useful approach to a difficult problem is to look for a similar​ problem, although it may have a different answer.
For​ example, suppose you cannot remember the formula for surface area of a cube.​
Instead, use dimensions of another cube with a known surface area and solve.

C. A useful approach to a difficult problem is to look for an equivalent​ problem, which does not have the same numerical answer but may be easier to solve.
For​ example, suppose you cannot remember the formula for surface area of a cube.​
Instead, compare the dimensions to another cube with a known surface area.

D. A useful approach to a difficult problem is to look for an equivalent​ problem, which has the same numerical answer but may be easier to solve.
For​ example, suppose you cannot remember the formula for surface area of a cube.​
Instead, find the surface area of each square and add them together.

(VI.) Which of the following best summarizes the strategic hint:​ Approximations can be​ useful and provides an example of the​ meaning?

A. An approximation should always be within one tenth of the exact solution.
If this is not​ true, something has gone wrong.
For​ example, if an exact solution is 7.232 and the approximation is​ 7, something is wrong in the solution process.

B. Approximations can always be used instead of an​ "exact solution", unless otherwise noted.
For​ example, if an exact solution is​ 3.1, an approximation of 3 can always be used.

C. Most​ real-world problems approximate numbers to begin​ with, so an approximation is often good enough for a final answer.
Approximations also provide a useful check.
For​ example, if a​ real-world problem involves long lengths with several​ decimals, approximating the final answer is often good enough for a final answer.

D. Approximations are only used to check solutions and are never good enough for a final answer.
For​ example, if a​ real-world problem involves long lengths with several​ decimals, approximating the final answer is never appropriate.

(VII.) Which of the following best summarizes the strategic hint​: Try alternative patterns of​ thought and provides an example of the​ meaning?

A. Avoid patterns of thought that tend to suggest the same ideas and methods.​
Instead, approach problems with an openness that allows new ideas and solving methods.
For​ example, when solving a problem that requires more​ thought, a moment of insight may be useful and make the problem easier to solve.

B. Have a list of basic solving methods to solve problems.
Keeping a narrow list of options is more efficient.
For​ example, when solving a problem that requires more​ thought, use basic solving​ methods, making the question easier to solve.

C. Avoid using any common patterns to solve problems.
Common patterns create common mistakes and may yield an incorrect answer.
For​ example, when solving a problem that requires more​ thought, avoid the most common way to solve the problem to avoid an incorrect answer.

D. Avoid patterns of thought that tend to suggest the same ideas and methods.​ Instead, create new ways to solve each​ problem, avoiding the fastest way to solve a problem.
For​ example, when solving a problem that requires more​ thought, always create your own ways to solve the problem.

(VIII.) Which of the following best summarizes the strategic hint:​ Do not spin your​ wheels and provides an example of the​ meaning?

A. Do not try problems that you have not seen before.
For​ example, if you have never seen long division with​ polynomials, do not attempt it.

B. Often the best strategy in problem solving is to put a problem aside and immediately ask for help.
For​ example, if you are struggling with a problem involving long division with​ polynomials, set it aside and go find help.

C. Often the best strategy in problem solving is to put a problem aside for a few hours or days.
For​ example, if you are struggling with a problem involving long division with​ polynomials, set it aside and come back to it in a few hours.

D. Do not use different strategies to solve problems.
The known strategy is always the most efficient.
For​ example, if you are struggling with a problem involving long division with​ polynomials, only use strategies you know to solve the problem.

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(76.) Consider the following complex​ problem, which does not have a single straightforward solution.
Describe how you would approach the problem​ (without carrying out the​ process).
List the assumptions and information needed to carry out your solution.
Assess the uncertainty in these assumptions and data.
Determine whether you believe the problem can be solved and whether a particular solution might generate controversy.
You are asked to calculate the cost of installing enough bike racks on campus to solve a bicycle parking problem.

(I.) Which of the following would be needed to carry out a solution to this​ problem?
Select all that apply.

A. How many bike racks are currently on campus
B. What time classes are held at
C. The cost of installing each new bike rack
D. How many people on campus have cars
E. How many people on campus have bicycles
F. The cost of buying a bicycle
G. How many bicycles can be parked at each bike rack

(II.) Could any of the needed data identified above potentially have ambiguous or uncertain​ answers?

A. ​No, because it is possible to find or determine each piece of data needed to solve the problem.
B. No, because the information is given.
C. ​Yes, because there is no way to calculate the number of bike racks needed.
D. ​Yes, because there is no way to determine the price of a bike rack.

(III.) If the data identified above is​ obtained, can the problem be​ solved?

A. ​​Yes, because an estimate is asked for in the problem.
B. No, because it is impossible to write an equation with the data to find a solution.
C. Yes, because it is possible to write an equation with the data to find a solution.
D. ​No, because an estimate is asked for in the problem.

(IV.) Is a particular solution likely to generate​ controversy?

A. ​​No, controversy rarely occurs on campuses.
B. No, the cost will likely be​ inexpensive, so no controversy will result over the installation.
C. Yes, it could be revealed that no new bike racks are​ needed, so controversy will result.
D. Yes. If the cost for the bike racks is determined to be too high and the problem remains unaddressed as a​ result, controversy could result.

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(77.) Karen arrives at the subway station every day at a random time and takes the first train that arrives.
If she takes the A​ train, which arrives regularly every​ hour, she goes to the museum.
If she takes the B​ train, which also arrives regularly every​ hour, she goes to the beach.
A month after starting this​ game, she has gone to the beach 25 times and to the museum 5 times.
Of the following​ options, which is the most likely​ explanation?

A. The A train arrives on the hour and the B train always arrives 30 minutes​ later, but Karen chooses wait the extra 30 minutes for train B.
B. The A train always arrives 10 minutes after the B​ train, so Karen takes train B and does not wait for train A.
C. The A train always arrives 10 minutes after the B​ train, so Karen decides to wait for train A so she does not need to rush.
D. The A train always arrives 10 minutes before the B​ train, but Karen misses train A and takes train B.
E. The A train always arrives 10 minutes before the B​ train, but Karen chooses to take train B.

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(78.) Suppose you have 40 blue socks and 40 brown socks in a drawer.
How many socks must you take from the drawer​ (without looking) to be sure of getting a pair of the same​ color?

A. 3 socks.
Suppose a brown sock is taken from the drawer.​
Then, a second sock is taken from the​ drawer, which is blue.
A third sock is​ pulled, which is either brown or blue.

B. 2 socks.
Suppose a brown sock is taken from the drawer.​
Then, a second sock is taken from the​ drawer, which is also brown.

C. 6 socks.
Suppose a brown sock is taken from the drawer.​
Then, a second sock is taken from the​ drawer, which is blue.
The​ third, fourth, and fifth socks are also​ blue, but the sixth sock is brown.

D. 4 socks.
Suppose a brown sock is taken from the drawer.​
Then, a second sock is taken from the​ drawer, which is blue.
The next sock is also​ blue, but the fourth sock is brown.

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(79.) If you add up an infinite number of​ ever-smaller fractions, what should you expect for the​ answer?

A. The answer may be finite or infinite because the fractions will either add to zero or be infinite.
B. The answer may be finite or infinite because only in some cases the fractions add up to a finite value.
C. The answer must be zero because the fractions will never be infinite.
D. The answer must be zero because all fractions add up to zero.
E. The answer must be infinity because the fractions will keep adding up to an infinitely large answer.
F. The answer must be infinity because the fractions will never add up to a finite value.

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(80.) Reuben​ says, "Two days ago I was 20 years old.
Later next​ year, I will be 23 years​ old." How is this​ possible?

A. Reuben spoke on a leap year and was born on February 28.
B. Reuben spoke on January 1 and was born on December 31.
C. Reuben spoke on February 28 and was born on a leap year.
D. Reuben spoke on December 31 and was born on January 1.

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(81.) A woman is traveling with a​ wolf, a​ goat, and a cabbage.
Altogether, there are 4 things (the woman, the wolf, the goat, and the cabbage).
They are located in the East.
The woman must use a boat to cross a river to the West.
The boat can only hold 2 things at a time.
If left to​ themselves, the goat will eat the cabbage and the wolf will eat the goat, but the wolf will not eat the cabbage.
If the woman is present, no one eats the other.

(a.) Explain how the woman can safely cross the wolf, the goat, and the cabbage across the river.
(b.) How many crossings are required to get all four things across the river​ alive?

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(82.) Consider the following ballot​ initiative, which appeared in the 2010 statewide elections in Oklahoma and was passed.

This measure ... requires that each person appearing to vote present a document proving their identity.
The document must meet the following requirements.
It must have the name and photograph of the voter.
It must have been issued by the​ federal, state, or tribal government.
It must have an expiration date that is after the date of the election.
No expiration date would be required on certain identity cards issued to person 65 years of age or older.
In lieu of such a​ document, voters could present voter identification cards issued by the County Election Board.
A person who cannot or does not present the required identification may sign a sworn statement and cast a provisional ballot.

(I.) According to the​ initiative, would a state​ driver's license allow a person to​ vote?
A. Yes, if it has not expired and has a picture.
B. ​Yes, since anybody eligible to drive is also eligible to vote.
C. ​Yes, any​ driver's license would allow a person to vote.
D. ​No, driver's licenses do not meet all of the requirements for proving​ one's identity.

(II.) According to the​ initiative, would a​ (federal) Social Security card allow a person to​ vote?
A. No, because a social security card is not issued by one of the approved levels of government.
B. Yes, because even though a social security card has no​ date, it is only issued to a person 65 years of age or older.
C. No, social security cards do not have pictures or expiration dates.
D. Yes, if it has not expired.

(III.) Without a​ "document proving their​ identity," what options for voting do citizens​ have? Select all that apply.
A. Pay a fee.
B. Sign a sworn statement and cast a provisional ballot.
C. Apply to the County Election Board for a voter identification card.
D. There are no options available.

(IV.) What documents are required to obtain a voter identification​ card? Select all that apply.
A. A driver's license.
B. A social security card.
C. A document proving identity issued by the federal or a state or tribal government.
D. The measure does not say what is required to obtain a voter identification card.

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(83.) A small grill can hold two hamburgers at a time.
If it takes minutes to cook one side of a​ hamburger, what is the shortest time needed to cook both sides of three​ hamburgers?
(Assume that once on the​ grill, a hamburger will stay on the grill until it is cooked on both​ sides.)

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(84.) Three boxes of fruit are labeled​ "Apples," "Oranges," and​ "Apples and​ Oranges."
Each label is wrong.
By selecting just one fruit from just one​ box, how can you determine the correct labeling of the​ boxes?

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(85.) A toll collector on a highway receives ​$4 for sedans and ​$7 for buses.
At the end of a 2​-hour ​period, she collected ​$148.
How many sedans and buses passed through the toll booth during that​ period?
Which of the choices below are possible solutions to the​ problem? Select all that apply.

A. 4 sedans and 19 buses B. 0 sedans and 21 buses C. 16 sedans and 12 buses D. 2 sedans and 20 buses E. 9 sedans and 16 buses

F. 32 sedans and 3 buses G. 23 sedans and 8 buses H. 18 sedans and 11 buses I. 37 sedans and 0 buses J. 30 sedans and 4 buses

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(86.) Each of ten large barrels is filled with golf balls that all look alike.
The balls in nine of the barrels weigh 1 ounce and the balls in one of the barrels weigh 2 ounces.
With only one weighing on a​ scale, how can you determine which barrel contains the heavy golf​ balls?

A. Weigh all of the balls from all ten barrels to find the average weight of the balls in all ten barrels.

B. Select one ball from the first​ barrel, two balls from the second​ barrel, and so​ on, up to ten balls from the tenth barrel to find the weight of a specific number of balls in a specific barrel.

C. Weigh all of the balls from only one barrel to narrow down the selection of barrels that may contain the heavier balls.

D. This is not possible.
There is no way to determine which barrel contains the heavy golf balls.

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(87.) If a clock takes 5 seconds to strike 5​:00 ​(chiming ​times), how long does it take to strike 6​:00 ​(chiming ​times)?
Assume each chime occurs instantaneously​ (takes no​ time).

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(88.) How many solutions does a quantitative problem from daily life​ have?

A. A quantitative problem from daily life always has exactly one​ solution, which does not always make sense.
B. A quantitative problem from daily life never has a solution.
C. A quantitative problem from daily life always has more than one algebraic​ solution, but only one of these solutions can make sense.
D. A quantitative problem from daily life may have more than one correct answer.
E. A quantitative problem from daily life always has exactly one solution.
F. A quantitative problem from daily life may have more than one algebraic​ solution, but only one of these solutions can make sense.

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(89.) In a certain​ year, economists projected that a certain government would have a surplus of ​$ trillion.
This projection never materialized.
What is the most likely reason for this incorrect​ projection?

A. The people who made this projection made basic errors in their calculations.
One of the economists was an intern who made a small mistake that affected the outcome.

B. The people who made this projection based it on assumptions about the future economy that turned out to be untrue.
These assumptions included highly uncertain predictions about the future of the​ economy, future tax​ rates, and future spending.

C. The people who made this projection did not really understand how the government budget works.
They did not realize that they were missing important variables that would affect their projection.

D. The people who made this projection based it on assumptions about the future economy that turned out to be untrue.
The media and politicians told the economists that all of the assumptions were facts

E. The people who made this projection ​didn't really understand how the government budget works.
They did not realize that most projected surpluses vanish.

F. The people who made this projection made basic errors in their calculations.
The basic errors became complex errors because of the large amounts of money being calculated.

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(90.) You are considering buying 12 gold coins that look​ alike, but you have been told that one of them is a heavy counterfeit.
How can you find the heavy coin in three weighings on a balance​ scale?

(I.) What is a possible first​ step?
A. Weigh all twelve​ coins, with eleven on one side of the balance scale and one on the other.
B. Weigh two coins at​ random, one on each side of the balance scale.
C. Weigh eight coins at​ random, four on each side of the balance scale.
D. It is not possible to find the heavy coin in only three weighings on a balance scale.

(II.) After weighing the two groups of four coins on the balance​ scale, what should be done​ next?
A. If the balance remains​ level, randomly choose one of the weighed​ groups; otherwise, choose the lighter of the weighed groups.
B. If the balance remains​ level, choose the​ un-weighed group of four​ coins; otherwise, choose the lighter of the weighed groups.
C. If the balance remains​ level, randomly choose one of the weighed​ groups; otherwise, choose the heavier of the weighed groups.
D. If the balance remains​ level, choose the​ un-weighed group of four​ coins; otherwise, choose the heavier of the weighed groups.

(III.) After determining the heaviest of the three groups of four​ coins, what should be done​ next?
A. Divide the chosen group into two groups of two coins.
Weigh the two groups and choose the lighter of the two.
Weigh the two coins in the chosen group to find the heavy counterfeit.

B. Divide the chosen group into two groups of two coins.
Weigh the two groups and choose the heavier of the two.
Weigh the two coins in the chosen group to find the heavy counterfeit.

C. Choose one of the coins in the group and weigh it against the other coins in the​ group, one at a​ time, to find the heavy counterfeit.

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(91.) A monk set out from a monastery in the valley at dawn.
He walked all day up a winding​ path, stopping for lunch and taking a nap along the way.
At dusk he arrived at a temple on the mountaintop.
The next day the monk made the return walk to the​ valley, leaving the temple at​ dawn, walking the same path for the entire​ day, and arriving at the monastery in the evening.
Must there be at least one point along the path that the monk occupied at the same time of day on both the ascent and the​ descent?

A. Yes because there is one​ path, there must be a single spot that the monk occupied at the same time of the day on both the ascent and descent.

B. Yes because it took the monk the same amount of time ascending the mountain and descending the mountain.

C. No because the monk started to ascend from the bottom and descend from the top at the same time.​
Thus, the monk did not occupy the same point at the same time at any point on the trip.

D. No because the monk stopped for lunch and to take a nap.
This causes the​ monk's path of ascension and descension to not match.

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(92.) You are asked to calculate how long a new battery will last on a flashlight when the flashlight is turned on.
How long should you expect the answer to​ be?

A. The answer should be at least several years because a flashlight battery will always recharge itself.

B. The answer should be at least several years because a new battery will last longest.

C. The answer should be a few minutes because the battery will not recharge itself.

D. The answer should be between a few hours and a few days because the battery will last more than a few minutes but less than several years.

E. The answer should be a few minutes because a new battery does not last up to a few hours.

F. The answer should be between a few hours and a few days because the battery only recharges itself up to two days.

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(93.) Jude and Jabez run a​ 200-meter race, and Jude wins by 10 meters.
They decide to run the​ 200-meter race again with Jude starting 10 meters behind the starting line.

(a.) Assuming both runners run at the same pace as they did in the first​ race, who wins the second​ race?

(b.) Suppose Jude starts 15 meters behind the starting line in the second race.
Who wins the​ race?

(c.) How far behind the starting line must Jude start so the race is a​ tie?

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(94.) Give an example of a problem that has more than one correct numerical answer.

A. Tommy bought 2 bags of chips and a box of cookies at the grocery store.
He spent​ $6 total.
How much does a bag of chips​ cost?

B. Jason bought 2 bags of chips at the grocery store.
He spent​ $6 total.
How much does a bag of chips​ cost?

C. Billy bought 2 bags of chips and a box of cookies at the grocery store.
He spent​ $6 total.
The box of cookies cost​ $3. How much does a bag of chips​ cost?

D. Zack bought 2 bags of chips and a box of cookies at the grocery store.
He spent​ $6 total.
He spent equal amounts on the cookies and the chips.
How much does a bag of chips​ cost?

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(95.) It takes someone 52 seconds to walk from the first (ground) floor of a building to the third floor.
How long will it take the person to walk from the first floor to the sixth floor (at the same pace, assuming all floors have the same height)?

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(96.) Decide whether these statements makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false).

(I.) 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.

(II.) Mathematics requires​ precision, so approximations should never be used.

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(97.) Use the graph to answer the question.




A. Taxpayers in the top​ 1% of income levels paid more money in income taxes than they would have without the tax cuts.
B. Taxpayers in the top​ 1% of income levels paid a greater percentage of total federal income tax revenue than they would have without the tax cuts.
C. Taxpayers in the top​ 1% of income levels paid ​37% of total federal income tax revenue.
D. The treasury estimate if the share of tax cuts had not been enacted is 30​%.

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(98.) During their freshman​ year, Peter's GPA was 3.5 and​ Paul's was 3.1.
During their sophomore​ year, Peter's GPA was 3.6 and​ Paul's was 3.5.
Which of the following is not necessarily​ true?

A. Peter's overall GPA for the two​ year-period was somewhere between 3.5 and 3.6.
B. Peter had a higher GPA than Paul during their freshman year and again during their sophomore year.
C. Paul had a lower GPA than Peter during their freshman year and again in their sophomore year.
D. Peter's overall GPA for the​ two-year period was higher than​ Paul's because their​ GPA's may have been weighted differently.
E. Paul's overall GPA for the two​ year-period was somewhere between 3.1 and 3.5.
F. Paul's overall GPA for the​ two-year period could be​ lower, higher or the same as​ Peter's overall GPA for the​ two-year period.

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(99.) Indicate whether this case is true positive, true negative, false positive, or false negative.
Give reasons for your answer.

Case: Court Verdict: Suspect A murdered her daughter.
The murder was ruled as death by undetermined means.
The prosecution team could not provide convincing evidence that she was guilty.
The defense team convinced the jury that she was innocent.
The jury acquitted her.

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(100.) Indicate whether this case is true positive, true negative, false positive, or false negative.
Give reasons for your answer.

Case: Secondhand Marijuana Smoke: Augustine hangs out frequently with a friend who smokes pot.
THC (Tetrahydrocannbinol) is a chemical found in pot (cannabis plants).
A urine test done immediately after he visited his friend showed traces of THC.
He vehemently denied smoking pot and requested for a second test.

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(101.) Indicate whether this case is true positive, true negative, false positive, or false negative.
Give reasons for your answer.

Case: Court Verdict: A record-breaking number of people were exonerated in 2015 — freed after serving time in American prisons for crimes they did not commit.: NBC News - February 3, 2016
One such case was that of William Vasquez who was cleared in December of an arson that killed a mother and her five children in 1981.

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(102.) Indicate whether this case is true positive, true negative, false positive, or false negative.
Give reasons for your answer.

Case: Early Menstrual Period: Menstruation usually occurs on average of 14 days after ovulation.
However, Felicity noticed an early menstrual period and decided to take a home pregnancy test.
The test was negative.
But, she was convinced that she was pregant.
So, she waited a few days and tested again in the morning.

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(103.) Show/Hide Answer

(104.) Professional athletes are routinely barred from participation for using banned substances.
Consider these scenarios and answer these questions.

(a.) For such a​ test, what is a false​ positive?
(b.) For such a​ test, what is a false​ negative?
(c.) For such a​ test, what is a true​ positive?
(d.) For such a​ test, what is a true​ negative?

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(106.) Explain how it is possible for a very accurate polygraph or drug test to result in a large proportion of false accusations.
Suppose a positive result is that the test results show not​ lying/no drug use.​
Also, assume the probability of​ lying/drug use is very low.

A. Since the probabilities of both a false negative and a true negative are very​ high, the proportion of false negatives to total negatives will be low.
B. Since the probabilities of both a false positive and a true positive are very​ low, the proportion of false positives to total positives will be large.
C. Since the probabilities of both a false negative and a true negative are very​ low, the proportion of false negatives to total negatives will be large.

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(107.) Choose the best answer to the following question.
For the average​ person, what is the single biggest category of​ expense?



A. The single biggest category is housing.
The average person uses​ 33% of his or her income on housing.

B. The single biggest category is food.
The average person uses​ 23%-43% of his or her income on food.

C. The single biggest category is food.
The average person uses​ 46%-66% of his or her income on food.

D. The single biggest category is entertainment.
The average person has not yet considered finding​ lower-cost entertainment options.

E. The single biggest category is housing.
The average person uses​ 23% of his or her income on housing.

F. The single biggest category is entertainment.
The average person spends​ 8% of his or her income on entertainment.

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(108.) Decide whether these statements make sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false).
Explain your reasoning.

(I.) Our total class score is based only on homework and​ exams, and Student A has better scores than Student B on both homework and exams.​
Therefore, Student A has a better overall score than Student B.

(II.) The Republicans claim the tax cut benefits everyone​ equally, but the Democrats say it favors the rich.
Clearly one side is lying.

(III.) Despite the fact that the new drug lowered blood pressure more than the old drug did in both the men and the women in the​ study, an overall analysis shows that the old drug was actually more effective.

(IV.) Baggage screening machines are​ 98% accurate in identifying bags that contain banned materials.​
Therefore, if the screening shows a bag that contains banned​ materials, then it almost certainly does.

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(109.) Show/Hide Answer

(110.) Choose the best answer to the following question.
What will evaluating your monthly budget help you​ learn?

A. You learn how to keep your personal spending under control.
You could be spending a lot more in certain categories than you had imagined and that the items you thought were causing the biggest difficulties are small compared to other items.

B. You learn how to earn more money.
You may figure out that you are good at managing​ finances, and then become a wealthy financial advisor.

C. You learn how to make better investments.
You may notice that you are spending a higher percentage of your money on entertainment than the average person.

D. You learn how to make better investments.
You may notice that you made a poor investment that is causing you to lose money every month.

E. You learn how to earn more money.
You may realize that you should start working more hours every week to increase your monthly cash flow.

F. You learn how to keep your personal spending under control.
Once you evaluate your current​ budget, you'll almost certainly want to make changes to improve your cash flow.

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(112.) Choose the best answer to the following question.
What does a negative monthly cash flow​ mean?

A. It means your investments are losing value.
Each month you lose a percentage of the money that you​ invested, which is the reason for the negative cash flow.

B. It means you are taking in more money than you are spending.
When you subtract your total expenses from your total​ income, the difference is negative.

C. It means you are spending more money than you are taking in.
When you subtract your total expenses from your total​ income, the difference is negative.

D. It means your investments are losing value.
When the interest rates​ decrease, your cash flow becomes negative.

E. It means you are spending more money than you are taking in.
When you subtract your total expenses from your total​ income, the difference is positive.

F. It means you are taking in more money than you are spending.
When you subtract your total expenses from your total​ income, the difference is positive.

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(113.) Show/Hide Answer

(114.) Choose the best answer to these questions.
(I.) Why is it so important to understand your personal​ finances?

A. It is important to understand your personal finances because understanding your personal finances will prevent divorce and other difficulties in personal relationships.

B. It is important to understand your personal finances because there will be an exam at the end of the term.

C. It is important to understand your personal finances because you need to know how much money you have and how much money you spend in order to find a way to live within your means.

D. It is important to understand your personal finances because you need to know what your credit card interest is so that you can pay the balance off quicker.
Once the balance is paid​ off, you can then invest in the stock market.

(II.) What types of problems are more common among people who do not have their finances under​ control?

A. People who do not have their finances under control suffer from financial​ stress, and have less friends.
They also suffer from higher interest rates.

B. People who do not have their finances under control suffer from financial stress because they usually have to pay an accountant to balance their checkbooks.

C. People who do not have their finances under control have higher marriage​ rates, and no difficulty in personal relationships.​
However, they tend to suffer from higher rates of depression among a variety of other ailments.

D. People who do not have their finances under control suffer from financial​ stress, higher divorce​ rates, and other difficulties in personal relationships.
They also suffer from higher rates of depression among a variety of other ailments.

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(115.) Give an example explaining how politicians on both sides of an issue can use numbers to support their case without lying.
Fill in the dots.

Say a candidate is running for mayor of a city.
During the incumbent​ mayor's first year in​ office, the city had a population of​ 25,000, and 50 violent crimes were committed.
During the incumbent​ mayor's most recent year in​ office, the city had a population of​ 30,000, and 55 violent crimes were committed.
The ............ might argue that the number of crimes has ............, with ............ ​crime(s) having been committed during the incumbent​ mayor's most recent year in office compared to the incumbent​ mayor's first year in office.
The ............ might argue that the crime rate has ............, with a rate of 1 violent crime for every ............ people during the incumbent​ mayor's first year in office and a rate of 1 violent crime for every ............ people during the incumbent​ mayor's most recent year in office.
​(Round to the nearest whole number as​ needed.)

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(116.) The impact of the recession of 2009 was widely felt across America.
One response that continues well into 2013 is an effort to build local economies by thinking and spending locally.
This decry has been heard in both large cities and small towns and has colored the shopping habits of a growing number of individuals even as some relief from the recession is felt.
The results can be noteworthy.
A national newspaper reported that if residents of New Orleans were to reallocate​ 10% of their spending to locally owned businesses and​ services, more than​ $200 million would be remain in the local economy.
To meaningfully build local economies for the long​ haul, consumers as well as business owners must take the next step and produce more of what the community has imported over the years. (​Source: Christian Science​ Monitor, volume 101)

Which of the following would not be an example of thinking and spending​ locally?
A. Holiday shopping at a craft fair featuring community vendors.
B. Using locally grown ingredients in country restaurants.
C. Selling jams made from area berry farms to surrounding communities.
D. Contracting with a nationally known music group to provide entertainment for a​ town's centennial celebration.

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(117.) Show/Hide Answer

(118.) Choose the best answer to these questions.
(I.) What terms should you include when calculating how much it costs you to attend​ college?

A. Extracurricular​ fees, auto​ insurance, size of​ classes, and majors offered
B. Insurance, deductibles,​ premiums, and​ co-payments
C. Dining hall​ food, size of dorm​ room, parking, and activities
D. Tuition, student​ fees, cost of​ textbooks, rent, and scholarships

(II.) How can you decide whether this is a worthwhile​ expense?

A. Whether this expense is worthwhile is subjective.​
However, the average high school graduate will earn more over a career than the average college graduate.

B. Whether this expense is worthwhile is subjective.​
However, the average college graduate does not earn more over a career than the average high school graduate.

C. Whether this expense is worthwhile is subjective.​
However, the average college graduate earns about​ $1.2 million more over a career than the average high school graduate.

D. This expense is not worthwhile.

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(126.) Choose the best answer to these questions.
(I.) Summarize how average spending patterns change with age.

A. As people get​ older, they tend to spend more on transportation and housing than younger people.
They also tend to spend less on health care.

B. As people get​ older, they tend to spend more on health care and donations to charity than younger people.
They also tend to spend less on personal​ insurance, pensions,​ clothing, and services than younger people.

C. As people get​ older, they tend to spend more on food and entertainment than younger people.
They also tend to spend less on housing than younger people.

D. As people get​ older, they tend to spend more on clothing and services than younger people.
They also tend to spend less on food and housing than younger people.

(II.) How can comparing your own spending to average spending patterns help you evaluate your​ budget?

A. If you are spending a higher percentage of your money on entertainment than the average​ person, you might be able to find cheaper ticket prices if you ask around.

B. If you are spending a higher percentage of your money on an item in your budget than the average​ person, you might want to consider finding​ lower-cost options or adjusting your budget.

C. It is a good idea to check how you compare to the rest of the population.
If you find that people spend more than you on​ gas, you can give others advice on how to spend less.

D. It can be useful to check how you compare to the rest of the population.
If you notice that most people donate less than you do to​ charity, it might be time to stop giving away so much.

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