Deck 1: Critical Thinking

Question 1

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: Which of the following is NOT correct?

A)The overall percentage of female applicants hired is less than that of male applicants.
B)We are observing Simpson's paradox.
C)We compare the company's overall percentage hired with the percentage hired for each division.
D)The absolute numbers involved in calculating the percentages caused a paradoxical situation.

Answer 1

C

Question 2

_____ paradox occurs when combining, or aggregating, data masks underlying patterns.

A)Taylor's
B)Samson's
C)Euler's
D)Simpson's

Answer 2

D

Question 3

The _____ type of informal fallacy simply draws a conclusion that is really a restatement of the premise.

A)false cause
B)circular reasoning
C)hasty generalization
D)straw man

Answer 3

B

Question 4

If an inductive argument claimed an invalid conclusion, what is the most likely type of fallacy?

A)false dilemma
B)false authority
C)circular reasoning
D)hasty generalization

Question 5

Choose a valid conclusion based on the premises: If you study hard, you will earn a passing grade. You have studied hard.

A)You studied hard.
B)You will earn a passing grade.
C)You studied hard and earned a passing grade.
D)If you don't study hard, you will not earn a passing grade.

Question 6

An argument is _____ if its premises justify its conclusion.

A)strong
B)weak
C)valid
D)invalid

Question 7

For an inductive argument, a conclusion can be drawn from specific examples. Therefore, we have irrefutable evidence for the conclusion.

Question 8

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: What was the overall percentage of male applicants hired?

A)10%
B)14%
C)23%
D)25%

Question 9

He shouldn't be trusted because he is a tax evader is an example of what type of informal fallacy?

A)appeal to common practice
B)hasty generalization
C)false dilemma
D)dismissal based on personal attack

Question 10

Logic is the study of methods and principles used to distinguish good from bad reasoning.

Question 11

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: For the secretarial division, what percentage of male applicants were hired?

A)22%
B)15%
C)10%
D)5%

Question 12

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: What can be observed about the percentage of males hired compared to the percentage of females hired in the engineering division?

A)A higher percentage of males were hired.
B)A higher percentage of females were hired.
C)The same percentage of males and females were hired.
D)Not enough information to make an observation.

Question 13

A study found that healthier people own more than three cars, so we need to buy more cars. What type of informal fallacy is this?

A)false authority
B)false dilemma
C)false cause
D)straw man

Question 14

An argument for a practice that is based on the popularity of that practice is an example of:

A)false authority.
B)straw man.
C)false dilemma.
D)appeal to common practice.

Question 15

We can't afford a more expensive home because it will cost more is an example of:

A)a false dilemma.
B)false authority.
C)circular reasoning.
D)a hasty generalization.

Question 16

A(n) _____ fallacy arises from the content of an argument, not its form or structure.

A)formal
B)informal
C)deductive
D)inductive

Question 17

The following is a valid argument: All dogs bark. Sparky barks. Therefore, Sparky is a dog.

Question 18

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: For the secretarial division, what percentage of female applicants were hired?

A)10%
B)13%
C)30%
D)20%

Question 19

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: For the engineering division, what percentage of male applicants were hired?

A)22%
B)25%
C)50%
D)30%

Question 20

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: For the engineering division, what percentage of female applicants were hired?

A)15%
B)13%
C)20%
D)25%

Question 21

Use inductive reasoning to make a conclusion: Every observed score of test X is above 70 and Leo took test X.

A)Leo's score is above 70.
B)Leo's score is below 100.
C)Every score is above 70.
D)There are more than 70 scores of the test.

Question 22

Two statements are logically _____ if they have the same truth tables.

A)equal
B)similar
C)associated
D)equivalent

Question 23

The logic gate XOR corresponds to the exclusive use of or, in which we ask whether one or the other, but not both, is true. If the inputs to the XOR gate are 1 and 1, what is the output?

A)0
B)1
C)2
D)3

Question 24

The inverse of the statement If , then is valid.

Question 25

Determine whether the given statement is true or false: If , then .

Question 26

Let p represent the statement I am happy and q represent the statement I enjoy my job. Express the given statement in symbolic form: I am not happy only if I enjoy my job.

A)(NOT q) $\rightarrow$ p
B)(NOT p) $\rightarrow$ q
C)p $\rightarrow$ (NOT q)
D)q $\rightarrow$ (NOT p)

Question 27

Let p represent the statement I have studied hard and q represent the statement I received a passing grade. Express the given statement in symbolic form: I studied hard but did not receive a passing grade.

A)p AND (NOT q)
B)p OR (NOT q)
C)(NOT p) OR (NOT q)
D)(NOT p) OR q

Question 28

Write the given set as a list of elements: The set of whole numbers between 4 and 8 inclusive.

A){4, 5, 6, 7}
B){5, 6, 7}
C){4, 5, 6, 7, 8}
D){5, 6, 7, 8}

Question 29

Set B is a subset of set A if every element of A is also an element of B.

Question 30

Formulate the contrapositive of the statement My friends all play video games.

A)If you are my friend, then you play video games.
B)If you are not my friend, then you do not play video games.
C)If you do not play video games, then you are not my friend.
D)If you play video games, then you are my friend.

Question 31

Formulate the converse of the statement All math classes are difficult.

A)If a class is difficult, then it is a math class.
B)If a class is a math class, then it is difficult.
C)If a class is not difficult, then it is not a math class.
D)If a class is not a math class, then it is not difficult.

Question 32

Find a logically equivalent statement of If your GPA is above 3.5, then you are eligible for membership of the honor society X.

A)If your GPA is not greater than 3.5, then you are not eligible for membership of the honor society X.
B)If you are not eligible for membership of the honor society X, then your GPA is above 3.5.
C)If you are not eligible for membership of the honor society X, then your GPA can't be greater than 3.5.
D)If you are eligible for membership of the honor society X, then your GPA is above 3.5.

Question 33

If the inputs of the OR gate are 0 and 1, what is the output?

A)0
B)1
C)2
D)-1

Question 34

Use inductive reasoning to determine the next number: 1, 2, 3, 5, 8, 13, _____.

A)18
B)19
C)20
D)21

Question 35

Formulate the inverse of the statement If you don't exercise, then you will gain weight.

A)If you gain weight, then you didn't exercise.
B)If you exercise, then you gain weight.
C)If you do not gain weight, then you exercised.
D)If you do exercise, then you will not gain weight.

Question 36

The inverse is logically equivalent to the:

A)conditional.
B)contrapositive.
C)converse.
D)conjunction.

Question 37

Consider the statement If it is Sunday, then I will go shopping. Formulate the converse.

A)If it is not Sunday, then I will not go shopping.
B)If I go shopping, then it is Sunday.
C)If I do not go shopping, then it is not Sunday.
D)If I go shopping, then it is not Sunday.

Question 38

The _____ is logically equivalent to the contrapositive.

A)converse
B)inverse
C)conjunction
D)conditional

Question 39

Two sets are called _____ if they have no elements in common.

A)subsets
B)unequal
C)disjoint
D)equivalent

Question 40

Determine whether the given statement is true or false: If Earth is flat, then donkeys are purple.

Question 41

Suppose set M is mathematics majors and set B is business majors at a certain university. The shaded region in the following Venn diagram represents students majoring in:

A)mathematics but not in business.
B)business but not in mathematics.
C)mathematics or in business.
D)mathematics and in business.

Question 42

Suppose that 100 students were given a biology exam and a chemistry exam. Assume that 36 passed the biology exam but not the chemistry exam, 25 passed the chemistry exam but not the biology exam, and 15 passed neither exam. How many passed the chemistry exam?

A)25
B)64
C)49
D)24

Question 43

If a car drives 11 kilometers per liter, how many miles does it drive per gallon?

A)11
B)15
C)21
D)26

Question 44

A dollar bill is 6.14 inches long, 2.61 inches wide, and 0.0043 inches thick. If you laid 1 million dollar bills end to end, how many miles would the trail be (to the nearest mile)?

A)1000
B)97
C)1198
D)479

Question 45

For charity, a school collects 10 million pennies. How much money has the school collected?

A)$10 million
B)$1 million
C)$100,000
D)$10,000

Question 46

The Venn diagram shows the results of a survey asking registered voters if they would vote for proposition A or proposition B: How many surveyed would vote for only proposition B?

A)12
B)58
C)52
D)46

Question 47

One kilobyte of memory can store about two-thirds of a page of typical text (excluding formatting). Suppose the typical book is 500 pages. Could a 4-gigabyte flash drive hold tens, hundreds, thousands, or millions of such books?

A)Tens
B)Hundreds
C)Thousands
D)Millions

Question 48

A group of students were surveyed to see how many used product A, product B, or product C. The following is a Venn diagram showing the results of the survey: How many students surveyed use only product C?

A)41
B)20
C)35
D)32

Question 49

A group of students were surveyed to see how many used product A, product B, or product C. The following is a Venn diagram showing the results of the survey: How many students surveyed used none of these products?

A)64
B)38
C)15
D)3

Question 50

A group of students were surveyed to see how many used product A, product B, or product C. The following is a Venn diagram showing the results of the survey: How many students surveyed did NOT use product A?

A)43
B)57
C)58
D)15

Question 51

The Venn diagram shows the results of a survey asking registered voters if they would vote for proposition A or proposition B: How many surveyed would NOT vote for proposition A?

A)46
B)52
C)98
D)58

Question 52

Suppose set M is mathematics majors and set B is business majors at a certain university. The shaded region in the following Venn diagram represents students majoring in:

A)mathematics but not in business.
B)business but not in mathematics.
C)mathematics or in business.
D)mathematics and in business.

Question 53

At a certain university, 5% and 17% of total students are mathematics majors (M) and business majors (B), respectively. If 3% of the total students are majoring in both mathematics and business, what percent of total students will be represented by the shaded region of the following Venn diagram?

A)1%
B)2%
C)3%
D)5%

Question 54

Light travels at 186,000 miles per second. How many FEET does it travel in a microsecond? (A microsecond is a millionth of a second.)

A)186.0
B)982.1
C)9821.0
D)1860.0

Question 55

Suppose set M is mathematics majors and set B is business majors at a certain university. The shaded region in the following Venn diagram represents students NOT majoring in:

A)mathematics.
B)business.
C)mathematics or in business.
D)mathematics and in business.

Question 56

A terabyte is _____ megabytes.

A)1000
B)1 million
C)1 billion
D)1 trillion

Question 57

There are 1000 billions in a trillion.

Question 58

Suppose A is the set of even numbers and B is the set of odd numbers. How are A and B related?

A)A is a subset of B.
B)B is a subset of A.
C)A and B are disjoint.
D)A and B are equivalent.

Question 59

The Venn diagram shows the results of a survey asking registered voters if they would vote for proposition A or proposition B: To get approved, a proposition must get at least 40% of the total votes. List the approved propositions.

A)None
B)A
C)B
D)A and B

Question 60

A group of students were surveyed to see how many used product A, product B, or product C. The following is a Venn diagram showing the results of the survey: How many students were surveyed?

A)38
B)53
C)64
D)79

Question 61

You are going on a 957-mile trip and your car gets 27 miles per gallon. Gas prices along your route average $3.78 per gallon. Estimate the cost of gasoline for your trip. Round your answer to the nearest dollar.

A)$120
B)$134
C)$145
D)$157

Question 62

If you had $1 million in $10 bills, how many bills would you have?

A)1 million
B)100,000
C)10 million
D)10,000

Question 63

The number of blogs has grown rapidly. Assuming that two new blogs are created each second, how many blogs will be set up in one month (30 days)?

A)
B)
C)
D)

Question 64

It has been projected that the world's population by 2050 will be 9.34 billion. If the projected U.S. population in 2050 is 438 million, what percent of the world's population will be the U.S. population? Round your answer to the nearest tenth of a percent.

A)5.1%
B)4.9%
C)4.7%
D)4.3%

Question 65

You are borrowing $8750 to buy a car. If you pay off the loan in 4 years (48 months), estimate your monthly payment (ignoring interest).

A)$165
B)$173
C)$182
D)$190

Question 66

It is estimated that in 2009 the United States consumed 18.69 million barrels of oil a day. A barrel of oil is 42 U.S. gallons. Assuming a U.S. population of 306 million, estimate per capita consumption in gallons. Round your answer to the nearest tenth.

A)2.1
B)2.5
C)2.9
D)3.5

Question 67

Suppose you wanted to line up all the people in the world. (The world's population is about 6.8 billion.) Assuming that each person takes up 12 inches of the line, how many times around Earth would they reach? (Earth has a circumference of about 25,000 miles.) Round you answer to the nearest tenth.

A)92.1
B)53.0
C)51.5
D)68.2