Drawing Logical Conclusions

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HSPT Language Skills › Drawing Logical Conclusions

Questions 1 - 10
1

Almost all roaches are disease-filled. The local garbage pit is overrun with millions of roaches. Which of the following is true?

The garbage pit is likely to be disease-filled.

The garbage pit is disease-filled.

There are some disease-free roaches in the garbage pit.

None of the other answers

The garbage pit is completely free of disease.

Explanation

Given that we know that almost all roaches are filled with diseases and that there are millions of them in the garbage pit, we can at least surmise that there is a great likelyhood that there will be a good deal of disease in the pit. Still, we cannot say this conclusively. There is always the (very improbable) chance that only disease-free roaches are in the pit. Likewise, we cannot guarantee that there are any disease-free roaches in the pit. It could be the case as well that all million are disease-ridden. The best that we can conclude is the modest answer, "The garbage pit is likely to be disease-filled."

2

All musicians are temperamental. Temperamental people are either angry or joyful. Peter and Ronald are friends. Ronald is joyful. Which of the following is true?

Ronald might be a musician.

Peter is also joyful.

Peter and Ronald have a tumultuous friendship.

Ronald is a musician.

Peter is not a musician.

Explanation

Do not be distracted by additional information that is included in this question. We actually are not told too terribly much, but let's note what we can. We are told nothing about Peter other than his friendship with Ronald. The best that we can say about Peter is, "Peter has a joyful friend." This is not provided among the options. Now, since Ronald is joyful, there is a chance he is temperamental. This is not guaranteed—the problem states merely that if you are temperamental, then you will be either angry or joyful. It says nothing about the "other direction" (i.e. from joy to temperamental). Someone who is joyful may just be that—joyful—without being temperamental. Still, being temperamental is not incompatible with being joyful. Thus, there is a chance that Ronald is temperamental. While not all temperamental people are musicians—given what we have said—it is not incompatible with being temperamental to be a musician. Thus, among the answers, only, "Ronald might be a musician," is correct. Note, however, that this is a very weak claim.

3

English majors read more books than anthropology majors. Computer science majors read fewer books than biology majors. Biology majors read fewer books than English majors. Which of the following is true?

None of the other answers

Biology majors read more than anthropology majors.

Anthropology majors read more than biology majors.

Anthropology majors read more than computer science majors.

Computer science majors read more than anthropology majors.

Explanation

Let's rewrite this in a semi-mathematical manner, using the following shorthand:

E: (Books read by) English Majors

A: (Books read by) Anthropology Majors

CS: (Books read by) Computer Science Majors

B: (Books read by) Biology Majors

We know the following:

(1) E > A

(2) CS < B

(3) B < E

Now, we can combine (2) and (3):

CS < B < E

Let's rewrite that:

E > B > CS

Now, while we know that E > A, we cannot say anything about the relative position of A. It could be all the way below the computer science majors, it could be between biology and computer science, etc. None of the answers are acceptable.

4

Some fanatics shout loudly. Some people who shout loudly get hoarse throats. John is fanatically devoted to video game playing. Which of the following is true?

John's throat might be hoarse.

John does not have a hoarse throat.

John likely does not have a hoarse throat.

John likely has a throat that is not hoarse.

None of the other answers

Explanation

Now, since John is fanatically devoted to video games, we can call him a fanatic in general. Based on the information provided, we cannot say what percentage of fanatics shout loudly. Likely, we do not know what percentage of those who shout loudly get hoarse throats. The safest thing to presume is merely that there is a chance that John shouts loudly and, because of that chance, there is a chance that he has a hoarse throat. Nothing more speceific can be determined.

5

Vermin infestations always bring down the price of a house. My house is filled with giant rats. Which of the following true?

The valuation of my house is lower than it could be.

My house is worthless.

My house needs fumigation.

My house is a health risk.

My house will be worth less in the future.

Explanation

Note that all we can speak about is the situation right now. (This immediately elimnates the claim about the cost of the house in the future). Now, rats (giant or not) are a type of "vermin." Thus, their presence has defintely brought down the value of my house. This is the only thing I can say with certainty among the options provided. The house is not necessarily worthless, and while I should eliminate the potentially disease-carrying animals, the information provided only allows me to say that my house has likely lost value because of their presence in the house.

6

All creeps are ring-rangs. Some ring-rangs are zip-doodles. All zip-doodles are mishmashes. Which of the following is true?

Some creeps are mishmashes.

All creeps are mishmashes.

All mishmashes are creeps.

All mishmashes are zip-doodles.

None of the other answers

Explanation

Just follow the logic of the strange expressions. Since Bob is a creep, he is also a ring-rang. Now, all zip-doodles are mishmashes. Thus, some ring-rangs are mishmashes. Thus we can say that all creeps are ring-rangs, some of which are mishmashes. Thus, some creeps are mishmashes.

7

Mildred is regularly bitter, especially when George is happy. George is always happy when it is hailing. Yesterday, there was a massive hailstorm. Which of the following is true?

None of the other answers.

Mildred is bitter.

George is happy.

George might be happy.

Mildred is not bitter.

Explanation

Among the options provided, none of them can be concluded based on the information that has been provided. While there was a hailstorm yesterday, that does not guarantee that George is happy today. Certainly, he is always happy when it is hailing. That only tells us that he was happy yesterday—when it was hailing. Now, that means that yesterday, there was a particular chance that Mildred was bitter, especially given George's joy. Indeed, we could even likely say she is bitter today—she is said to be bitter regularly (just more so when George is happy); however, that is not provided as an option. Likewise, perhaps George is only happy when it hails—we do not know one way or the other based on the information provided. Thus, the best answer among those provided is "None of the other answers."

8

All refineries are profitable businesses. All profitable businesses pay a lot of taxes. The new plant at Ralton is profitable. Which of the following is true?

The new plant pays a lot of taxes.

The new plant is a refinery.

The new plant might pay a lot of taxes.

The new plant will become a refinery.

None of the other answers

Explanation

Do not be fooled by this simple question. While all refineries are profitable, we cannot say that all profitable things are refineries. Thus, while the new plant at Ralton is profitable, we have no idea what kind of plant it is. The best we can say is that it will pay a lot of taxes (at least based on the information with which we have been provided). All of the other answers either infer too much or are indeed quite off the mark.

9

Allen spent more at the store than Sally. Sally always outspends Jim at the store. Malinda always spends twice what Sally spends. Which of the following is true?

Jim spent less than Malinda.

Malinda spent more than Allen.

Malinda spent less than Allen.

Jim spent more than Malinda.

Jim spent more than Allen.

Explanation

Let us rewrite this question in quasi-mathematical terms. The following is certain:

Allen > Sally > Jim

However, regarding Malinda, we do not know if her doubling of Sally's expenditure is necessarily more than that of Allen's or less. Perhaps Allen spent five times what Sally did. Perhaps Allen does indeed spend less than Malinda. We are not told! Thus, the most that we can say is that Jim spent less than Malinda. Perhaps this is a boring conclusion, but logic requires us to conclude in this way!

10

Chemistry is more difficult than political science. Political science is easier than Physics. Physics is more difficult than Biology. Which of the following is true?

None of the others answers

Chemistry is easier than physics.

Chemistry is more difficult than physics.

Biology is more difficult than political science.

Political science is more difficult than biology.

Explanation

Let's rewrite this in a semi-mathematical way:

C: Chemistry difficulty

PS: Political science difficulty

PH: Physics difficulty

B: Biology difficulty

We know the following from our prompt:

(1) C > PS

(2) PS < PH (or: PH > PS)

(3) PH > B

However, note that we cannot really say much else. We do not know the relative positions of biology and political science, except that they are easier than physics. Likewise, while we know that chemistry is harder than political science, we cannot say anything about its relationship to physics. (Likewise, this means that we cannot say anything about its relationship to biology). Thus, the answer is "none of the others."

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