Critical Thinking, Reasoning/Argument, Problem Solving
For ACT Students
The ACT is a timed exam...60 questions for 60 minutes
This implies that you have to solve each question in one minute.
Some questions will typically take less than a minute a solve.
Some questions will typically take more than a minute to solve.
The goal is to maximize your time. You use the time saved on those questions you
solved in less than a minute, to solve the questions that will take more than a minute.
So, you should try to solve each question correctly and timely.
So, it is not just solving a question correctly, but solving it correctly on time.
Please ensure you attempt all ACT questions.
There is no negative penalty for a wrong answer.
For SAT Students
Any question labeled SAT-C is a question that allows a calculator.
Any question labeled SAT-NC is a question that does not allow a calculator.
For JAMB Students
Calculators are not allowed. So, the questions are solved in a way that does not require a calculator.
Unless specified otherwise, any question labeled JAMB is a question from JAMB Physics
For WASSCE Students: Unless specified otherwise:
Any question labeled WASCCE is a question from WASCCE Physics
Any question labeled WASSCE-FM is a question from the WASSCE Further Mathematics/Elective Mathematics
For NSC Students For the Questions:
Any space included in a number indicates a comma used to separate digits...separating multiples of three
digits from behind.
Any comma included in a number indicates a decimal point. For the Solutions:
Decimals are used appropriately rather than commas
Commas are used to separate digits appropriately.
Solve all questions.
Show all work.
(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.
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.
Critical thinking involves careful reading (or listening), sharp thinking, logical analysis, good visualization, and healthy skepticism, and more.
It is helpful in making informed life decisions, instead of falling into traps created by misinformation, hidden assumptions, and illogical arguments.
(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.
The correct option is C. Because problem solving is not only the most important end of mathematics, but also a means for learning mathematics.
(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.
A. If there are only two colors of socks in the drawer, then of any 3 chosen, two must be the same color.
(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
Premise: California has the largest number of foreclosures and layoffs.
Conclusion: The foreclosures must be a cause of the layoffs.
The fallacy is a Hasty Generalization because the conclusion is not logically justified by sufficient or unbiased evidence.
(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.
Part I:
A logical argument has at least one (one or more) premise and one conclusion.
It uses a set of facts or assumptions, called premises, to support a conclusion.
Part II:
A list of premises that do not lead to a conclusion is not a logical argument.
A logical argument needs to have a conclusion.
(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.
(a.) Logic is the study of the methods and principles of reasoning.
It can be useful in providing strong support for conclusions, and to help identify errors in reasoning, or fallacies.
(b.) An argument is a reasoned or thoughtful process.
An argument consists of premises that are used to support a conclusion.
(c.) A fallacy is a deceptive argument.
It is an argument in which the conclusion is not well supported by the premises.
Options A., B., and C. are fallacies 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.
This fallacy is an example of example of false cause.
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.
This fallacy is an example of circular logic.
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.
This fallacy is an example of appeal to popularity.
(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.
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.
(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
Polya's step of Problem Solving is:
(1.) Understand the problem.
(2.) Devise a plan.
(3.) Carry out the plan.
(4.) Look back and reflect on your work to see how it could be better.
The option not included is: A. Make an educated guess
(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.
The logical fallacy of appeal to ignorance uses lack of knowledge about the truth of a proposition to conclude the opposite.
The fallacy is sometimes summed up with the statement "An absence of evidence is not evidence of absence." 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.
(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."
This argument is fallacious because it doesn't challenge the provisions of the tax plan, but only questions the motives of the President.
Such an argument is called ad hominem or personal attack.
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.
(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
I
Original
New
7
14
10
20
11
22
14
28
Rule: Number on right = Double the number on the left
II
Original
New
7
49
10
100
11
121
14
196
Rule: Number on right = Square the number on the left
III
Original
New
14
12
11
9
10
8
7
5
Rule: Number on right = Subtract 2 from the number on the left
(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?
Number of guests = 48200 guests
Number of gusts to be accommodated in hotel rooms = 14700
Number of guests to be accommodated in area villages = 25000
Remaining number of guests to be accommodated on stationary cruise ships:
= 48200 − (14700 + 25000)
= 48200 − 39700
= 8500 guests
(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.
D. Looking back allows a student to check that the answer is correct. C. Looking back allows a student to check that the answer makes sense in context of the problem.
(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.
(I.) Premise: Apple's iPhone outsells all other smart phones.
(II.) Conclusion: It is the best smart phone on the market.
(III.) The fact that many people buy the iPhone does not necessarily mean it is the best smart phone on the market.
(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?
It is better to represent the information using a diagram
Distance from Planet Diner to Clark = 145 + 50 = 195 miles
(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?
If you meet four people, there is a possibility of only meeting four Americans, or only meeting four Canadians.
If you meet five people, then you must meet at most four Americans and one Canadian OR at most four Canadians and one American.
This implies that you must meet at least five (5 or more) people in order to be sure to meet one American and one Canadian.
(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?
Option A. is the answer because of the field is divided into five parts.
(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.
The fallacy of false cause occurs when the fact that one event came before another is incorrectly taken as evidence that the first event caused the second event. 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.
(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.
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.
(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.
(a.) The statement does not make sense because shouting a logical argument does not improve the argument.
Therefore, Julian does not have to shout to present his argument.
(b.) The statement makes sense.
While a conclusion may be supported by several premises, a person must believe those premises to be true to be convinced by the argument.
(c.) The statement does not make sense because unconvincing arguments do not always contain a fallacy
It is possible for a valid argument to fail to be convincing.
(d.) The statement makes sense.
An argument that contains a fallacy can be believable because logical arguments that contain fallacies can still have true conclusions.
(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?
(a.) Let the:
half-dollar = light purple disk (big)
quarter = green disk (medium)
nickel = lime disk (small)
first tower = Tower 1 = position A
second tower = Tower 2 = position B
third tower = Tower 3 = position C
Step 1: Move the nickel to Tower 3
Step 2: Move the quarter to Tower 2
Step 3: Move the nickel to stay on top of the quarter in Tower 2
Step 4: Move the half-dollar to Tower 3
Step 5: Move the nickel to Tower 1
Step 6: Move the quarter to stay on top of the half-dollar in Tower 3
Step 7: Move the nickel to stay on top of the quarter in Tower 3
It takes a minimum of 7 moves to move all coins from Tower 1 (position A) to Tower 3 (position C)
Mathematically, the formula for moving the 3 coins from position A to position C based on the condition that
a larger coin may not be placed on a smaller coin is: 2³ − 1 = 8 − 1 = 7 positions.
Therefore: For n coins of decreasing size, the number of moves is $2^n - 1$ moves.
(b.) For 64 disks of decreasing size, it will take $2^{64} - 1$ seconds to
move the disks at a rate of one move per second.
(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.
A. You should carefully evaluate the evidence and arguments invoked in debates about global warming.
Thinking critically include careful reading or listening, sharp thinking, logical analysis, good visualization, healthy skepticism and more.
These are important practices when considering controversial topics.
(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.
Things to consider
Notice that the number of squares remaining is 62, which is an even number.
The number of tiles being equal to a perfect square is not necessary in order to cover the board with dominoes.
Although the board needs to have an even number of tiles in order to be covered by the dominoes with the given restrictions, it is not the only requirement.
Let us consider the number of remaining squares of each color.
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.
(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.
This implies that: 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.
(25.) Find a 3-by-3 magic square using the numbers 2, 5, 8, 12, 15, 18, 22, 25, and 28.
For a 3-by-3 magic square:
The sum of each of the 3 rows = The sum of each of the 3 columns = The sum of each of the 2 diagonals that contains 3 numbers
Hence the sum is a multiple of 3 First: Let us determine the sum of the numbers (total sum):
2 + 5 + 8 + 12 + 15 + 18 + 22 + 25 + 28 = 135
135 is a multiple of 3...so this should work
Second: Determine the quotient of the total sum and 3
135 ÷ 3 = 45
Third: Write all the combinations of any three given numbers as a sum of 45
To save time, arrange the numbers in ascending order: already arranged
Begin with both ends and keep working towards the middle:
Keep trying until you get 8 combinations
Try:
2 + 5 + 28 = 35 ≠ 45
2 + 8 + 28 = 38 ≠ 45
2 + 12 + 28 = 42 ≠ 45
2 + 15 + 28 = 45...okay
2 + 18 + 25 = 45...okay
5 + 8 + 28 = 41 ≠ 45
5 + 12 + 28 = 45...okay
5 + 15 + 25 = 45...okay
5 + 18 + 22 = 45...okay
8 + 12 + 25 = 45...okay
8 + 15 + 22 = 45...okay
12 + 15 + 18 = 45...okay
It's now 8 combinations...cool
Fourth: List each number in each sum and the multiplicity
If the multiplicity of the number is 3, the number is positioned at the corner
If the multiplicity of the number is 4, the number is positioned at the center
The rest of the numbers are positioned accordingly
Number
Multiplicity
Position
2
2
5
3
Corner
8
2
12
3
Corner
15
4
Center
18
3
Corner
22
2
25
3
Corner
28
2
Fifth: Place the numbers accordingly in the 3-by-3 square such that:
(a.) the sum of each row is 45
(b.) the sum of each column is 45
(c.) the sum of each diagonal is 45
5 + 15 + what = 45
5 + 15 + 25
what + 8 + 25 = 45
12 + 8 + 25
5 + what + 12 = 45
5 + 28 + 12
what + 15 + 8 = 45
22 + 15 + 8
5 + 22 + what = 45
5 + 22 + 18
18 + what + 25 = 45
18 + 2 + 25
The 3-by-3 square is shown:
(26.) Shown below is a magic square (all rows, columns, and diagonals sum to the same number).
Find the value of each letter.
$
\underline{1st\;\;Row} \\[3ex]
5 + a + 17 \\[3ex]
a + 22 \\[5ex]
\underline{2nd\;\;Row} \\[3ex]
27 + 15 + b \\[3ex]
b + 42 \\[5ex]
\underline{3rd\;\;Row} \\[3ex]
c + d + 25 \\[5ex]
\underline{1st\;\;Column} \\[3ex]
5 + 27 + c \\[3ex]
c + 32 \\[5ex]
\underline{2nd\;\;Column} \\[3ex]
a + 15 + d \\[3ex]
a + d + 15 \\[5ex]
\underline{3rd\;\;Column} \\[3ex]
17 + b + 25 \\[3ex]
b + 42 \\[5ex]
\underline{Diagonal:\;TopLeftCorner\;\;to\;\;BottomRightCorner} \\[3ex]
5 + 15 + 25 \\[3ex]
45 \\[5ex]
\underline{Diagonal:\;\;BottomLeftCorner\;to\;\;TopRightCorner} \\[3ex]
c + 15 + 17 \\[3ex]
c + 32 \\[5ex]
a + 22 = 45 \\[3ex]
a = 45 - 22 \\[3ex]
a = 23 \\[5ex]
b + 42 = 45 \\[3ex]
b = 45 - 42 \\[3ex]
b = 3 \\[5ex]
c + 32 = 45 \\[3ex]
c = 45 - 32 \\[3ex]
c = 13 \\[5ex]
c + d + 25 = c + 32 \\[3ex]
d = c + 32 - c - 25 \\[3ex]
d = 7
$
(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?
There are at least two approaches to solve this question.
Quantitative Reasoning Approach: Climbing up is positive Climbing down is negative
Initial position = middle rung = 0
He climbed up 3 rungs = 3
moved down 5 rungs = −5
climbed up 7 rungs = 7
climbed up the remaining 2 rungs = 2
This implies: 0 + 3 − 5 + 7 + 2 = 7
Top = 7th rung
(a.) There are 7 rungs above the middle rung of the ladder
(b.) Similarly, there are 7 rungs below the middle rung of the ladder
(c.) The total number of rungs = 7 rungs + middle rung + 7 rungs = 7 + 1 + 7 = 15 rungs.
Diagrammatically/Graphical Approach:
We can represent the information on a diagram
(a.) There are 7 rungs above the middle rung of the ladder
(b.) Similarly, there are 7 rungs below the middle rung of the ladder
(c.) The total number of rungs = 7 rungs + middle rung + 7 rungs = 7 + 1 + 7 = 15 rungs.
(28.) In the diagram below, determine the value of the question mark.
Let:
one cheeseburger = A
one loaf of bread = B
one cup of soda = C
This means:
$
\underline{Equation\;1} \\[3ex]
A + A + A = 30 \\[3ex]
3A = 30 \\[3ex]
A = \dfrac{30}{3} = 10 \\[5ex]
\underline{Equation\;2} \\[3ex]
A + B + B + B + B = 18 \\[3ex]
10 + 4B = 18 \\[3ex]
4B = 18 - 10 \\[3ex]
4B = 8 \\[3ex]
B = \dfrac{8}{4} \\[5ex]
B = 2 \\[3ex]
\underline{Equation\;3} \\[3ex]
B + B - (C + C) = 2 \\[3ex]
2B - 2C = 2 \\[3ex]
2(2) - 2C = 2 \\[3ex]
4 - 2C = 2 \\[3ex]
4 - 2 = 2C \\[3ex]
2 = 2C \\[3ex]
2C = 2 \\[3ex]
C = \dfrac{2}{2} \\[5ex]
C = 1 \\[3ex]
\underline{Equation\;4} \\[3ex]
C + A = ? \\[3ex]
1 + 10 = 11
$
(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.
Recall that:
The premise is the set of facts or assumptions used to make an argument, and
The conclusion is the statement that is made as a result of those facts.
(I.) (a.) Premise: John started to feel sleepy after eating pizza.
(b.) Conclusion: The pizza made him sleepy.
(c.) The argument does not prove that pizza was the cause of sleepiness.
(II.) (a.) Premise: Fifty years of searching has not revealed life on other planets.
(b.) Conclusion: Life in the universe must be confined to Earth.
(c.) The premise is stated according to a lack of evidence of the opposite of the conclusion.
Opposite of the conclusion is: Life must not be confined to Earth.
Because of a lack of evidence of life outside planet Earth, the premise (Fifty years of searching has not revealed life on other planets.) was stated.
(III.) (a.) Premise: He refused to testify by invoking his Fifth Amendment rights.
(b.) Conclusion: He must be guilty.
(c.) The conclusion is stated as if it were the only possible conclusion.
(IV.) (a.) Premise: Senator Leeds accepted contributions from companies that sell genetically modified crop seeds.
(b.) Conclusion: Senator Leeds's bill on agricultural policy is a sham.
(c.) A claim about Senator Leeds's personal behavior is used to criticize his bill.
(V.) (a.) Premise: It's illegal to drive over the speed limit.
(b.) Conclusion: People who exceed the speed limit are criminals.
(c.) The argument is circular reasoning because the conclusion is a restatement of the premise.
(VI.) (a.) Premise: Good grades are needed to get into college, and a college diploma is necessary for a good career.
(b.) Conclusion: Attendance should count in high school grades.
(c.) The premise directs attention away from the conclusion.
(VII.) (a.) Premise: The mayor wants to raise taxes to fund social programs.
(b.) Conclusion: She must not believe in the value of hard work.
(c.) The mayor is characterized (perhaps wrongly) by one quality, on which the conclusion is based.
(VIII.) (a.) Premise: Liz ate fish for dinner and later that night, had a nightmare.
(b.) Conclusion: Fish caused her nightmare.
(c.) The argument does not prove that fish was the cause of the nightmare.
(IX.) (a.) Premise: Chinese restaurants in America outnumber Burger Hut's by nearly 3 to 1
(b.) Conclusion: Chinese food is preferable to hamburgers.
(c.) The fact that large numbers of people believe or act a certain way is used inappropriately as evidence.
The argument is deceptive because the fact that large numbers of people believe or act a certain way is used inappropriately as evidence.
(X.) (a.) Premise: All the mayors of my hometown have been men.
(b.) Conclusion: Men are better qualified for high office than women.
(c.) The argument is deceptive because it makes a generalization about men in office that is used to make a claim about women in office.
The premise has nothing to do with how qualified women are in office.
(XI.) (a.) Premise: Bead lives near an oil well and have never felt an earthquake.
(b.) Conclusion: Claims that fracking causes earthquakes are ridiculous.
(c.) The argument is deceptive because the lack of knowledge about the truth of a proposition is used as evidence against the proposition.
(XII.) (a.) Premise: Wider highways can relieve traffic congestion.
(b.) Conclusion: We should build wider highways to benefit the tourist industry.
(c.) The argument is deceptive because it attempts to divert attention from the real issue by focusing on another issue.
(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.
(I.) 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.
(II.) C. The money you give is spent on worthwhile causes. D. Charity A does not support unworthy causes.
(III.) B. Tax cuts are more important than other issues. C. The governer will keep his promise on tax cuts.
(IV.) C. More military spending will mean a better military. D. A stronger military means a stronger country.
(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?
Let the temperature at 5 A.M. = t
By 9 A.M.the temperature had doubled ⇒ 2 * t = 2t
By noon, it had risen another 8 degrees to 30 degrees ⇒ 2t + 8 = 30
$
2t + 8 = 30 \\[3ex]
2t = 30 - 8 \\[3ex]
2t = 22 \\[3ex]
t = \dfrac{22}{2} \\[5ex]
t = 11^\circ \\[3ex]
$
The temperature at 5 A.M. = 11°
One winter night the temperature fell 15 degrees between midnight and 5 A.M. ⇒ that the
temperature at midnight = 11 + 15 = 26°
(32.) If six people shake hands with one another exactly once:
(a.) How many handshakes take place?
(b.) Generalize the solution for n people.
(a.)
Let's start with the 1st person
1st person shakes hand with the 2nd person
1st person shakes hand with the 3rd person
1st person shakes hand with the 4th person
1st person shakes hand with the 5th person
1st person shakes hand with the 6th person
So, each person shakes hand with 5 other persons
There are 6 people
This means there are 6 * 5 = 30 handshakes
However: we counted twice... because:
1st person shakes hand with the 2nd person and 2nd person shakes hand with the 1st person should count as one (not two) handshake
This implies that the number of distinct handshakes is $\dfrac{6 * 5}{2} = \dfrac{30}{2} = 15$ handshakes
(b.) For n people:
The number of distinct handshakes = $\dfrac{n(n - 1)}{2}$
(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.
For a 3-by-3 magic square:
The sum of each of the 3 rows = The sum of each of the 3 columns = The sum of each of the 2 diagonals that contains 3 numbers
Hence the sum is a multiple of 3
We need only nine of the ten numbers.
Let us choose any nine numbers whose sum is a multiple of 3 First: Let us choose the nine numbers and determine the sum of the numbers (total sum):
21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 = 225
225 is a multiple of 3...so this should work
Second: Determine the quotient of the total sum and 3
225 ÷ 3 = 75
Third: Write all the combinations of any three given numbers as a sum of 75
Fourth: List each number in each sum and the multiplicity
If the multiplicity of the number is 3, the number is positioned at the corner
If the multiplicity of the number is 4, the number is positioned at the center
The rest of the numbers are positioned accordingly
Number
Multiplicity
Position
21
2
22
3
Corner
23
2
24
3
Corner
25
4
Center
26
3
Corner
27
2
28
3
Corner
29
2
Fifth: Place the numbers accordingly in the 3-by-3 square such that:
(a.) the sum of each row is 75
(b.) the sum of each column is 75
(c.) the sum of each diagonal is 75
Put the center: 25 in the square
27 + 25 + what = 75
27 + 25 + 23
what + 25 + 29 = 75
21 + 25 + 29
Put 26 at the top left corner
26 + 27 + what = 75
26 + 27 + 22
22 + 25 + what = 75
22 + 25 + 28
28 + 23 + what = 75
28 + 23 + 24
The 3-by-3 square is shown:
Sometimes a table can be created and used to examine a simpler case.
Identifying a subgoal is used when simpler problems can be solved and then used to solve the original question.
In the strategy of guess and check first guess at a reasonable answer and then check to see if the guess is correct.
Working backwards starts with the desired result and eliminating incorrect answers.
(b.) The strategies used are: C. Use guess and check. D. Identify a subgoal.
(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.
(I.) C. The statement makes sense.
The insurance company accepted Reed's claim, so it makes sense that Reed is relieved.
(II.) 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.
(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.
First: Check all options to make sure no number in the square is repeated.
(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?
If you meet four people, there is a possibility of only meeting four Americans, or only meeting four Canadians.
If you meet five people, then you must meet at most four Americans and one Canadian OR at most four Canadians and one American.
If you meet six people, then you must meet at most four Americans and two Canadians OR at most four Canadians and two Americans.
This implies that you must meet at least six (6 or more) people in order to be sure to meet two Americans.
(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.
(a.) Yes it would be legal.
If all you know is her name, there is no reasonable expectation that she is trying or will try to influence you.
(b.) Accepting money from a government campaign fund would conform with the law.
(c.) Accepting money from a CEO who will benefit from a bill you are sponsoring would violate the law.
(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
The finishing order of the horses (from left to right: from slowest to fastest) is:
F, H, G, E
(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.
D. If Sociology is at 10 a.m., then Art History must be at 12 noon.
(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.
(I.) probably weak
(II.) 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.
(III.) B. There is no way to tell which deal is better without knowing the amounts of the application fees.
(IV.) D. Your expense for insurance and collision repairs over a year will be less with policy B.
This is because Policy B has a high deductible ($1000) for collision repairs.
(V.) 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.
(VI.) (a.) The maximum number of consecutive years that a councilmember could serve is: three consecutive terms of four years: = 3 * 4 = 12 years
(b.) The number of years a councilmember who has served three consecutive full terms must wait before running for office again is: 8 years.
This is because: "...no sooner than for a term beginning eight years after completion of that councilmember's third consecutive full term."
(c.) No
(d.) Suppose a councilmember serves three consecutive terms and is reelected 10 years later.
According to this provision, the number of consecutive terms that she or he can serve at that time is 3 years.
(VII.) No because there is a possibility that there are no male communication majors, and half of the class would still consist of communication majors and half of the class would still be male.
(VIII.) A. Yes, because one half of one half is one quarter.
(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.
(a.) Let the number be x
Multiply by 3 → 3 * x = 3x
Subtract 20 from the product → 3x − 20
The result is 34
$
3x - 20 = 34 \\[3ex]
3x = 34 + 20 \\[3ex]
3x = 54 \\[3ex]
x = \dfrac{54}{3} \\[5ex]
x = 18 \\[3ex]
$
The number is 18
$
\underline{Check} \\[3ex]
3 * 18 = 54 \\[3ex]
54 - 20 = 34 \\[3ex]
$
(b.) A nickel is 5 cents
A dime is 10 cents
A quarter is 25 cents Given: 5 nickels, 3 dimes, and 2 quarters To Determine: the number of combinations to get 75 cents 1st Combination: 75 = 50 + 20 + 5
75 = 2 quarters + 2 dimes + 1 nickel
There are 4 combinations of getting 75 cents from 5 nickels, 3 dimes, and 2 quarters
(c.) Let the number of days worked by Paul = x
This implies that the number of days worked by Peter = x + 2 (because Peter worked 2 more days than Paul)
Paul earned $50 a day. $50 a day @ x days = 50 * x = 50x
Peter earned $40 a day. $40 a day @ x + 2 days = 40(x + 2) = 40x + 80
Peter and Paul earned the same amount of money.
This implies
$
50x = 40x + 80 \\[3ex]
50x - 40x = 80 \\[3ex]
10x = 80 \\[3ex]
x = \dfrac{80}{10} \\[5ex]
x = 8 \\[3ex]
x + 2 = 8 + 2 = 10 \\[3ex]
$
Paul worked 8 days
Peter worked 10 days
(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)?
(a.) No, because new conditions go into effect immediately, without user approval.
(b.) Not necessarily, because continued use of the service implies acceptance.
(c.) New conditions that affect the user could go into effect without user knowledge or approval.
(d.) There is no way to distinguish a typographical error from a deliberate attempt to take advantage of users.
(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?
Based on the information, the correct answer is D. Is the site visually appealing?
(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
Notice that the concerts create a parking problem, but it may not be the reason why concerts should be banned at the theater.
Another solution to the parking problem, like creating a parking lot, may seem more logical.
The weakness of the argument suggests that the writer may not really be concerned about the parking, and that there may be other issues leading the writer to oppose concerts at the theater.
So, it is important to C. Identify the real issue
(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?
Note that any of the three conditions can apply.
Let us go through each condition for each option.
But once we find out any condition that apply, then we stop.
(a.) Person A
(i) No because 750 is less than 900
(ii.) Yes because 5700 is more than 5450
Person A must file a tax return because the earned income of $5700 is more than $5450
(b.) Person B
(i) No because 200 is less than 900
(ii.) No because 3000 is less than 5450
(iii.) Gross income of $3500 is larger than $900
Earned income plus 300 is: 3000 + 300 = $3300
Gross income of $3500 is also larger than $3300
Person B must file a tax return because the gross income of $3500 is more than $3300
(c.) Person C
Earned and gross income of $5400 means that:
Earned income is $5400 (technically) but because it cannot exceed 5150 (up to $5150):
Earned income is $5150
Gross income is $5400
(i) No because 0 is less than 900
(ii.) No because 5400 is less than 5450
(iii.) Gross income of $5450 is larger than $900
Earned income plus 300 is: 5150 + 300 = $5450
But Gross income of $5450 is equal to $5450
Person C does not have to file a tax return because the gross income of $5450 is not more than $5450
(d.) Person D
(i.) No because 200 is less than 900
(ii.) No because 5200 is less than 5450
(iii.) Gross income of $5500 is larger than $900
Earned income is $5200 (technically) but because it cannot exceed 5150 (up to $5150):
Earned income is $5150
Earned income plus 300 is: 5150 + 300 = $5450
Gross income of $5500 is also larger than $5450
Person D must file a tax return because the gross income of $5500 is more than $5450
(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.
(a.)
a quarter = 25 cents
a dime = 10 cents
a penny = 1 cent
$1.07 in quarters, dimes, and pennies
Quarter
Dime
Penny
Total Number of Coins
0
10
7
17
1
8
2
11
2
5
7
14
3
3
2
8
4
0
7
11
(b.) 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.
(47.) You buy a cell phone plan that gives you up to 1000 minutes of calling for $30 per month.
During a particular month, you use only 100 minutes.
What is your per-minute cost for that month?
Per-minute cost means: what is the cost for 1 minute?
Proportional Reasoning Method
Calling Time (minutes)
Cost ($)
100
30
1
what
$
100 * what = 1 * 30 \\[3ex]
what = \dfrac{1 * 30}{100} \\[5ex]
what = \dfrac{30}{100} \\[5ex]
what = \$0.3 \\[3ex]
$
Proportional Reasoning Method
Cost (¢)
Cost ($)
100
1
what
0.3
$
what * 1 = 100 * 0.3 \\[3ex]
what = ¢30 \\[3ex]
$
(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?
Meeting two people of the same nationality implies meeting two Nigerians or two Norwegians.
If you meet 2 people, there is the possibility of meeting:
2 Nigerians (at least two people of same nationality) or
2 Norwegians (at least two people of same nationality) or
1 Nigerian and 1 Norwegian (two different nationalities).
Because of the possibility of the last option, meeting 2 people does not ensure that you will meet two people of the same nationality.
But if you meet 3 people, there is the possibility of meeting:
3 Nigerians (at least two people of same nationality) or
3 Norwegians (at least two people of same nationality) or
2 Nigerians (at least two people of same nationality) and 1 Norwegian or
2 Norwegians (at least two people of same nationality) and I Nigerian
This implies that you must meet at least 3 (3 or more) people in order to be sure to meet 2 Nigerians or 2 Norwegians.
(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?
$
(a.) \\[3ex]
\underline{Option\;A} \\[3ex]
Going:\;\; Cost = \$2200.00 \\[3ex]
Cancelling:\;\; Cost = \$0.00 \\[5ex]
\underline{Option\;B} \\[3ex]
Going:\;\; Cost = \$1200.00 \\[3ex]
Cancelling:\;\; Cost = 25\% * 1200 = 0.25(1200) = \$300.00 \\[3ex]
$
(b.) If the likelihood of cancellation is low, then Option B is better because it costs less if you do go.
If the likelihood of cancellation is high, then Option A is better because it costs less if you cancel.
(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?
Proportional Reasoning Method
Mary
Martha
16
4
80
what
$
\dfrac{what}{4} = \dfrac{80}{16} \\[5ex]
\dfrac{what}{4} = 5 \\[5ex]
what = 4 * 5 \\[3ex]
what = 20 \\[3ex]
$
If Mary is on page 80, Martha is on page 20
(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.
(I.) 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.
(II.) 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.
(III.) 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.
(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.
(I.) A. Yes, if it has not expired and has a picture.
(II.) C. No, social security cards do not have pictures or expiration dates.
(III.) B. Sign a sworn statement and cast a provisional ballot. C. Apply to the County Election Board for a voter identification card.
(IV.) D. The measure does not say what is required to obtain a voter identification card.
(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.
(I.) D. No, because you will probably have to pay for service and insurance with either plan.
(II.) The total cost of purchasing the car at the onset = $16,000
The total cost of purchasing the car at the end of the lease
= 900 + (230 * 36) + 7000
= 900 + 8280 + 7000
= $16,180 B. Yes, the total cost of the car at the end of the lease is $16,180
(III.) A. Not all of the money is needed up front and you have years to decide if you want to buy the car.
(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.
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.
(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.
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.
(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.
A. The speaker may have an ideological opposition to paying taxes.
(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?
(a.) Yes because November 28 is not more than a month after November 8.
The landlord has a month from the move out date to return the security deposit.
The landlord has complied with the lease.
(b.) Yes because December 3 is not more than a month after November 8.
The landlord has a month from the move out date to return the security deposit.
The landlord has complied with the lease.
(c.) No because December 9 is more than a month after November 8.
The landlord has a month from the move out date to return the security deposit.
The landlord has not complied with the lease.
(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.
Confirmation bias is a lapse in critical thinking in which a person tends to search only for evidence that supports some pre-existing belief or opinion, and will ignore or try to explain away any evidence that is contrary to that belief or opinion.
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.
(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.
A. Popes have never taken a position in American politics. C. Of the two major candidates in 2016, one might question why the pope would support Trump's position on a variety of issues.
(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?
(I.) Philemon ate all but 9 bagels.
So, there are 9 bagels left.
He ate (12 − 9 = 3) 3 bagels.
(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.
(I.) One-way trip = 1750 miles
Round-trip = 2(1750) = 3500 miles
Provided the mileage is under 25000 miles, Airline B is cheaper
But, at 25000 miles, Airline A is cheaper
The question then becomes: how many times would Bead fly in order to accumulate 25000 miles?
$
Number\;\;of\;\;times = \dfrac{25000}{3500} = 7.142857143 \approx 8 miles...rounded\;\;up \\[3ex]
$
This implies that every 9th flight is free for Bead to take Airline A
This implies that the cost for 9 flights for Airline A is cheaper than the cost for 9 flights for Airline B
Let us verify
$
\underline{Cost\;\;for\;\;9\;\;flights} \\[3ex]
Airline\;A:\;\;cost = 275(8) + 0 = \$2200 \\[3ex]
Airline\;B:\;\;cost = 250(9) = \$2250 \\[3ex]
\$2200 \lt \$2250 \\[3ex]
$
What about the cost for 10 flights?
$
\underline{Cost\;\;for\;\;10\;\;flights} \\[3ex]
Airline\;A:\;\;cost = 275(8) + 0 + 275 = \$2475 \\[3ex]
Airline\;B:\;\;cost = 250(10) = \$2500 \\[3ex]
\$2475 \lt \$2500 \\[3ex]
$
What about the cost for 11 flights?
$
\underline{Cost\;\;for\;\;11\;\;flights} \\[3ex]
Airline\;A:\;\;cost = 275(8) + 0 + 275 + 275 = \$2750 \\[3ex]
Airline\;B:\;\;cost = 250(11) = \$2750 \\[3ex]
\$2750 = \$2750 \\[3ex]
$
What about the cost for 18 flights?
$
\underline{Cost\;\;for\;\;18\;\;flights} \\[3ex]
Airline\;A:\;\;cost = 275(8) + 0 + 275(8) + 0 = \$4400 \\[3ex]
Airline\;B:\;\;cost = 250(18) = \$4500 \\[3ex]
\$4400 \lt \$4500 \\[3ex]
$
You may test the other values.
Based on what we have tested so far: A. Flying round-trip 9 to 11, 18 to 22, or over 26 times, Airline A is cheaper.
For any other number flights, Airline B is cheaper than or equal to the other airline.
(II.) Current Policy:
Cost for 9 months @ $113 per month = 113(9) = $1017
Cost of prenatal care and delivery = $4000
Total cost = 1017 + 4000 = $5017
Policy Upgrade:
Cost for 9 months @ $267 per month = 113(9) = $2403
Cost of prenatal care and delivery = $0 (included)
Total cost = 2403 + 0 = $2403
This implies that: A. They should upgrade to the new policy because the current policy costs $5017 for nine months, which is significantly more than the upgrade which costs
$2403 for nine months.
(62.) 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.
At least one means one or more
At least one day means one day or more than one day
At least one day per week means 1 day, 2 days, 3 days, 4 days, 5 days, 6 days, or 7 days
However:
never on two consecutive days
This means:
1 day: Sunday or Monday or Tuesday or Wednesday or Thursday or Friday or Saturday
2 days: Sunday and Tuesday, or Sunday and Wednesday, or ...
3 days:
1, 2, 3, or 4 days
For ACT Students 
