Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is more enjoyable than,” and “less than” (<) will mean “is less enjoyable than.”

(1) Tallis’ music is more enjoyable than Byrd’s: Tallis > Byrd

(2) Haydn’s music is less enjoyable than Byrd’s: Haydn < Byrd

This could be rewritten: Byrd > Haydn

Thus, combining everything, we would have:

Tallis > Byrd > Haydn

It is false to say that Tallis' music is less enjoyable than Haydn's.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is more enjoyable than,” and “less than” (<) will mean “is less enjoyable than.”

(1) Tallis’ music is more enjoyable than Byrd’s: Tallis > Byrd

(2) Haydn’s music is less enjoyable than Byrd’s: Haydn < Byrd

This could be rewritten: Byrd > Haydn

Thus, combining everything, we would have:

Tallis > Byrd > Haydn

It is false to say that Tallis' music is less enjoyable than Haydn's.

Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "has more fun," and "less than" (<) will mean "has less fun."

(1) Teddy has more fun than Jack: Teddy > Jack

(2) Franklin has less fun than Jack: Franklin < Jack

This could also be written: Jack > Franklin

Therefore, we could string all of these together into:

Teddy > Jack > Franklin

Therefore, (3) Teddy > Franklin does hold.

Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "has more fun," and "less than" (<) will mean "has less fun."

(1) Teddy has more fun than Jack: Teddy > Jack

(2) Franklin has less fun than Jack: Franklin < Jack

This could also be written: Jack > Franklin

Therefore, we could string all of these together into:

Teddy > Jack > Franklin

Therefore, (3) Teddy > Franklin does hold.

Note that when something is "tedious" it is boring, hence, less exciting than something else. Let’s use symbols from math to help us understand this problem. “Greater than” (>) will mean “more exciting,” and “less than” (<) will mean “more tedious (i.e. less exciting).”

(1) John is more tedious than Robert: John < Robert

Notice that this could be rewritten: Robert > John

(2) Robert is more exciting than Alan: Robert > Allen

Therefore, our information only tells us that Robert is more exciting than both John and Allen. It says nothing about the relationship between Allen and John.

Note that when something is "tedious" it is boring, hence, less exciting than something else. Let’s use symbols from math to help us understand this problem. “Greater than” (>) will mean “more exciting,” and “less than” (<) will mean “more tedious (i.e. less exciting).”

(1) John is more tedious than Robert: John < Robert

Notice that this could be rewritten: Robert > John

(2) Robert is more exciting than Alan: Robert > Allen

Therefore, our information only tells us that Robert is more exciting than both John and Allen. It says nothing about the relationship between Allen and John.

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.

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.

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."

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.