Critical Thinking Skills TEST

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Thomas Francis University • Course G120 • Segment 3 Addendum

ANALYSIS OF CRITICAL THINKING EXAMPLES

—Douglas R. Kelley, PhD, CH, CSL

Updated: September 27, 2015

STOP! You had to try it, didn’t you? 

DO NOT continue until you have

solved the problems in Segment 3!

If you don’t sincerely try to solve a few simple brainteasers,

how will you solve much bigger life problems?

If you have, in fact, solved all of the problems or at least

given it your very best try, then please proceed to the next

page. You be the judge.

Segment 3: Critical Thinking Examples

ANALYSIS OF CRITICAL THINKING EXAMPLES

When analyzing problems, it helps to use critical thinking skills to break the problem down into

“bite-size” chunks, so to speak. We can do this by identifying the premises, which will help us figure

out the solution (conclusion).

1. Johnny's mother had four children. The first was April, the second was May, and the third was

June. What was the name of her fourth child?

Your first inclination may have been to start thinking of which month of the year might provide a

suitable name for the 4th child. Perhaps you toyed around with whether next month, “July,” could be

another spelling for “Julie” as April, May, and June are successive months. Maybe you wondered if

someone would actually name her child “July” just to match the succession of the months in order. I

guess anything is possible. But there is another solution.

To aid in solving this problem, let’s determine the premises and assume they are true.

1. Johnny’s mother had four children.

2. Three of her children were named April, May, and June.

3. Johnny’s mother must also be the mother of Johnny, which would make Johnny the fourth

child.

Problem solved.

This problem is a great example to show that simply identifying the premises can lead to a con-

clusion (solution). It is also an example of deductive reasoning because if the premises are true, then

the conclusion must also be true. Everything we needed to solve this problem was contained in the

data. However, we also saw that it’s easy to miss things sometimes that are right in front of our eyes

that could solve our problems easily.

2. You are driving a bus. Four people get on, three people get off, then eight people get on and

ten people get off, then 6 people get on and 2 more people get off. What color were the bus

driver's eyes?

Perhaps your first inclination was to start counting the number of people getting on and off the

bus in anticipation of a final question such as “How many people are left on the bus?” or similar. Let’s

establish the premises in order to solve this problem and assume they are true.

1. You are driving a bus.

2. Several groups of people are getting on and off the bus at different stops (implied).

Notice that the second premise is simplified. I could have added each group of people as a separate

premise, but saw no need to do so when I got to the final question, “What color were the bus driver's

eyes?” This question obviously has nothing to do with the number of people getting on and off the

bus. By simplifying the premises, it becomes much easier to see the solution: You are the bus driver.

So, what color are your eyes? 

This problem also involves deductive reasoning because the premise is true which forces a neces-

sary conclusion that is also true. Additionally, this problem uses two related logical fallacies which

essentially accomplish the same purpose. First, it uses the Smokescreen Fallacy because it provides

too many irrelevant details that serve to block your attention from the real issue. Secondly, it uses

the Red Herring Fallacy to lead you off the track of considering only relevant information.

Segment 3: Critical Thinking Examples

3. There was an airplane crash, every single person died, but two people survived. How is this

possible?

Perhaps your first thought was, “this is impossible!” Let’s break it down into premises.

1. An airplane crashed.

2. Every person died.

3. Two people survived.

Take particular note of premise number 2. It would be very easy to do as I did and abbreviate the

stated premise (see the original wording above), but in so doing, we’ve lost our primary clue to solving

this puzzle, namely the word, “single.” This puzzle relies on the Amphiboly Fallacy, which you will

recall means “an error due to taking a grammatically ambiguous phrase in two different ways during

the reasoning.” The word “single” can have two different connotations in the context of this problem.

In the first connotation, “single” is a superfluous word that adds no further meaning to the sen-

tence. The sentence would read the same with or without it. In the second connotation, the word

“single” can mean, “not married,” which then solves the puzzle. Every “unmarried” or “single” per-

son died, but no married people died. Problem solved.

This example shows that sometimes minor wording can be the determining factor in finding a

solution. Words have meanings and shades of meanings. By substituting different words at different

times, we effectively change the lens through which we view the problem. Sometimes this can help

us with solutions.

Take a look at how I worded the premises above in the break down. By leaving out the word

“single,” I actually created an invalid deductive argument. Why? Because for an argument to be

“valid,” the conclusion must necessarily be true if the premises are true. In this case, the premises

are true (as I rewrote them) but the conclusion is false. By simply adding the word “single” or pref-

erably, “unmarried,” the argument becomes valid.

As a side point, we can also infer from this puzzle that all the people on the plane were single

(unmarried) except for two.

4. “That attorney is my brother,” testified the accountant. But the attorney testified he didn't

have a brother. Who is lying?

Perhaps your first inclination was confusion over this problem due to a perceived lack of infor-

mation. Let’s break down the premises.

1. The accountant’s brother is the attorney.

2. The attorney does not have a brother.

This puzzle relies, more or less, on the Hasty Generalization Fallacy. Let’s use deductive reasoning

to solve it. We first assume that the two premises are true. If they are true, then what factual

conclusion would solve it? What assumptions on our part are preventing us from finding the logical

conclusion (solution)? If we remove our assumption that the accountant and the attorney are both

male, what does that leave us? The attorney may not have a brother, but does he have a sister? Could

his sister be the accountant? Yes, and problem is solved.

This puzzle required that we lose our assumptions (biases) to deduce that the accountant is female

and, in fact, the sister of the attorney.

Segment 3: Critical Thinking Examples

5. A man and his son are driving in a car. The car crashes into a tree, killing the father and

seriously injuring his son. At the hospital, the boy needs to have surgery. Upon looking at the

boy, the surgeon says (telling the truth), "I cannot operate on him. He is my son." How is this

possible?

Perhaps your first thoughts were to wonder whether the boy also had a step father and whether

that step father was either the surgeon or the man who died in the crash. Let’s break down our

premises:

1. A man and his son are driving in a car.

2. They crash into a tree.

3. The father is killed.

4. The son is seriously injured.

5. The son is transported to the hospital (implied).

6. The son needs surgery.

7. The surgeon cannot operate on the boy because of him being the surgeon’s son.

We can use deductive or inductive reasoning to find the solution to this dilemma, but it’s often a

better idea to start with deductive reasoning if we have a number of presumed facts available. In

other words, before we start to speculate whether a step father could have been the surgeon or the

man who died, we should first evaluate whether we have enough information to draw a conclusion

forced by the premises, assuming they are true.

This example is similar to the previous one insofar as the Hasty Generalization Fallacy is required

to make it work. If we remove our assumption that the surgeon must be male, where does that leave

us? It leaves us with the very plausible conclusion that the surgeon was the boy’s mother. Problem

solved.

The reason that it’s preferable to go with the surgeon being the boy’s mother as opposed to being

the boy’s step-father is due to Occam’s razor which states that when there is an absence of infor-

mation, the simplest explanation is likely the correct one. It is more factually economical to conclude

that the surgeon was the boy’s mother because to conclude that the surgeon was the boy’s step

father would require that we add more data to the problem that we cannot necessarily substantiate.

6. How can you throw a ball so that it goes a short distance, comes to a total stop, reverses its

motion, and then goes the opposite way? You are not allowed to bounce it against anything, hit

it with anything, or tie it to anything.

Perhaps your first thoughts were to futilely figure out how you could throw a ball laterally and

have it come back to you. This riddle may seem quite different than the other examples we’ve dis-

cussed so far, but we can find the solution using the same methodology. Let’s break it down deduc-

tively and assume our premises are true.

1. We throw a ball a short distance.

2. The ball comes to a complete stop.

3. The ball reverses its motion and travels in the opposite direction.

4. The ball does not touch or hit anything during its travel, nor is it attached to anything.

Segment 3: Critical Thinking Examples

Assuming that all of these premises are true, what would have to happen to the ball so that we

have a conclusion (solution) that necessarily follows the premises and is also true? This is where the

analytical and evaluative aspects of critical thinking come into play. If we throw the ball straight

ahead of us, two things will happen that nullify the premises: 1) the ball will keep going because

nothing will cause it to stop in mid-air and turn around, or, 2) the ball will fall to earth because of

gravity. So, what other options are there? What if we threw the ball upwards? Problem solved.

In order to solve this problem, we had to ask open-ended questions during our analysis to develop

plausible alternatives. The next puzzle will require this same technique and more.

7. A man parks his car and gets out. He heads into the bank. While in the bank he holds up 25

people and walks out with $200. While walking back to his car a police officer stops him, but only

gives him a warning. How can this situation be explained?

Perhaps your first thought was that the police officer didn’t realize the man just robbed the bank.

This example will require more critical thinking than the other examples so far. We will start out with

deductive reasoning, but that won’t be enough. We will also have to use inductive reasoning plus a

lot of creative inference. Remember, when reasoning on problems such as this, it helps to start out

with deductive reasoning to the extent possible. In other words, what are the facts and what do the

facts tell us? When the facts do not tell us enough, we must switch to inductive reasoning and begin

creative solution-finding to discover the most likely conclusion.

So, what possible circumstances could explain this scenario? It is much the same as recreating a

crime scene. Let’s clarify what we have in a deductive manner by breaking down our premises.

1. The man parks his car.

2. He gets out.

3. He heads into the bank.

4. He holds up 25 people.

5. He walks out of the bank with $200.

6. A police officer stops him and gives him a warning.

You can see that there are gaps in our available information. So let’s reason on what we have

using inferences to help us come up with the most plausible (cogent) conclusion. We will build on the

premises stated above to do this.

1. The man parks his car and walks into the bank. Not much to infer here.

2. We are next told he holds up 25 people. This implies that he robbed either the people in

the bank and/or the bank itself.

3. He then walks out of the bank with only $200 which is our first clue in solving this problem.

This is suspicious because one would logically conclude that if someone robbed 25 people

and/or a bank, they would walk away with much more than $200.

 Conclusion 1: The man robbed the bank and/or the people in the bank.

 Pros: Perhaps something went wrong with his heist before he could get more

money thus causing him to flee the bank with only $200.

Segment 3: Critical Thinking Examples

 Cons: One would logically conclude that if something had gone wrong, there

would be commotion associated with the man’s escape such as a security

guard chasing him and people screaming out of fright. Such activity is not

reported in the original example.

4. Next, a police officer stopped the man and gave him a warning. This gives us our second

and strongest clue to solving this. We can infer from this that there was no commotion

associated with a bank robbery. We can also infer that since the police officer only gave

him a warning and one doesn’t get warnings for robbing banks, that the man did not actu-

ally rob the bank or the people inside. This rules out our Conclusion 1 above.

5. Okay, time for more questions. Since we ruled out a bank robbery, what usable information

are we left with?

1. The man parked his car.

2. The man held up 25 people.

3. The man got a warning.

6. Conclusion 2: Now we are beginning to see the solution to this issue. For what do people

often get warnings? The answer is traffic violations. Since the man “held up 25 people,”

we can infer that he got a warning for a parking violation; perhaps he double-parked thus

holding up traffic, i.e., 25 people in cars.

 Pros: It fits all the evidence we have perfectly.

 Cons: None.

7. Problem solved.

This problem relies on two logical fallacies to work, “Misrepresentation” and “False Cause.” Mis-

representation is just what the word implies; it is a form of dishonesty and lying. False Cause means

to erroneously conclude that one thing was caused by another. Both of these fallacies apply because

the problem states the man held up 25 people after stating that he headed into the bank when it

should have stated it after saying he parked his car.

8. Ted and Linda were found on the living room floor, deceased. The window is open, the curtains

are billowing and the carpet is wet. However the doors were closed and locked. This was not a

murder-suicide. What happened to Ted and Linda?

Perhaps your first thought was that the killer came in and left through the window. This example

is admittedly difficult and ambiguous because we could come up with several plausible scenarios.

However, by using critical thinking skills to analyze the problem, we can not only exercise our mental

muscles, but we can also arrive at the most likely conclusion.

As with the previous example, we will use deductive reasoning to the extent possible, then induc-

tive reasoning to reach a plausible conclusion. As always, let’s start by breaking down the problem

into its premises.

1. Ted and Linda were found dead on the living room floor.

2. The window is open.

Segment 3: Critical Thinking Examples

3. The curtains are billowing in the wind (implied).

4. The carpet is wet.

5. The doors are closed and locked.

6. This was not a murder-suicide.

Now let’s reason on the little information we have and make some inferences.

1. Ted and Linda were found dead on the living room floor.

 The implication is that Ted and Linda are the homeowners, but we do not know

this for sure. They could be guests, visiting relatives, burglars, or pets.

 We do not know who found them dead on the floor.

 We do not know how they died. The example specifically states “deceased” rather

than “murdered.” The word, “deceased,” would seem to connote something other

than murder such as natural causes. Also note that when simplifying this premise,

I used the word “dead” instead of “deceased.” This was, at first, an effort to sim-

plify and reframe the premise in an effort to reason on it. However, by doing so, I

could have potentially missed the implication of the word “deceased.” This is just

a reminder to be careful when rephrasing or reframing a premise so that you don’t

lose potential meaning.

2. The window is open.

 We don’t know when the window was opened, whether it is open all the way, or

whether there is a screen or security bars attached.

 We also don’t know whether this is a ground floor home, a 20 story high-rise, or

something in between.

3. The curtains are billowing in the wind (implied).

 The curtains are billowing most likely from the wind, but we do not know this for

sure. It could be a hot, windless day which would explain why the window was

open. There could even be an electric fan close by causing the curtains to billow.

However, Occam’s razor tells us that in the absence of data, the simplest explana-

tion is likely the correct one. So, we’ll assume the curtains are billowing in the

wind for now.

4. The carpet is wet.

 At this point, it’s anyone’s guess as to how this fits in, or if it fits in at all. We could

speculate all day long about what this means and what might account for it, which

would violate Occam’s razor. For the moment, we’ll just make a mental note of it.

5. The doors are closed and locked.

 This would imply (or, we can infer) that whoever was responsible for Ted and

Linda’s deaths either had a key to the house and locked the door as they left, or

they came in through the window instead.

Segment 3: Critical Thinking Examples

 Typically, we would probably stop here with reasoning on this specific prem-

ise, however, to do so would mean that we are assuming that Ted and Linda

are humans and that another person murdered them. We still do not know

who or what Ted and Linda are. They could be pets of some sort. So, we’ll

make a mental note of this.

6. This was not a murder-suicide.

 One thing we do know is that Ted and Linda didn’t kill themselves.

At this point, we can formulate some theories based on our reasoning as to what might have

happened.

 Conclusion 1: Ted and Linda were the homeowners. An unknown person entered through

their window, killed them, and exited through the window leaving it open in the process.

 Pros: This would explain why the door was closed and locked, why the window was

open, and why the curtains were billowing.

 Cons: It would not explain the wet carpet or why the word “deceased” was used

instead of “murder.”

 Conclusion 2: Ted and Linda were pets of the homeowners, specifically, dogs, cats, or

similar mammals. The pets were killed by someone who came in through the window or

were overcome by a natural gas leak.

 Pros: This would explain why the door was closed and locked and why the word

“deceased” was used. It would also explain why the window was open and the

curtains were billowing

 Cons: It would not explain why the carpet was wet. Additionally, one could argue

that since the window was open, a natural gas leak could not have killed the pets

especially since natural gas is lighter than air and rises thereby making the effects

of natural gas minimal near the floor where most pets are.

 Conclusion 3: Ted and Linda were pets of the homeowners, specifically, Goldfish. The

homeowners went out on errands and left the window open. The fishbowl was placed near

the window and a gust of wind came in causing the curtains to knock the fishbowl over.

 Pros: This would explain why the window was open and the curtains billowing, why

the carpet was wet, and why the door was closed and locked. We can infer that it

was a fishbowl that was knocked over because an aquarium would have been too

heavy to be knocked over by curtains.

 Cons: None.

Of course, we could have continued with possible conclusions with different scenarios, but three

were enough to make the point. Of the three possible conclusions given, it is obvious that Conclusion

3 offers the most likely explanation as to what happened. It is, in fact, the answer to this problem.

This puzzle is probably a little closer to real life when it comes to solving problems as we some-

times have very little information to use in making difficult decisions.

Segment 3: Critical Thinking Examples

LEARNING FROM THESE EXAMPLES

What did you learn from reasoning on these examples? Hopefully, you learned that by deductively

breaking down the issue into known premises and then inductively reasoning on options, you stand a

better chance of finding better solutions and making better decisions.

Did you notice how I commented on what your first impressions might have been prior to discussing

each problem? This demonstrates that we naturally bring biases and preconceived notions to problem

solving. Without thinking about it, our minds automatically start searching for possible solutions. This

is why we must deliberately strive to release any preconceived notions and beliefs before trying to

solve problems. Actually, the process that we went through to solve these problems helped us to

keep our critical thinking based on facts and not unconscious assumptions.

In the next segment, we will add to what we’ve learned in these first two segments as well as

explore specific steps in creative solution-finding.