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 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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(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 te 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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(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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