For this problem, let us assume (as is generally safe) that bitter and sweet flavors are opposed to each other.  Now, let's use symbols from math to help us understand this. “Greater than” (>) will mean “is sweeter,” and “less than” (<) will mean “is more bitter (i.e. less sweet).”

(1) Hops are more bitter than cocoa: hops < cocoa

Note that this could be rewritten: cocoa > hops

(2) Honey is sweeter than cocoa: honey > cocoa

Now, we could combine these and get:

honey > cocoa > hops

Therefore, it is really the case that honey is sweeter than hops.

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

(1) Helga is uglier than Olga but prettier than Ilga: Ilga> Helga > Olga

(2) Olga is prettier than Gretel: Olga < Gretel or Gretel > Olga

Now, Ilga and Gretel share the distinction of being uglier than Olga; however, we cannot say which is uglier than the other.

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

(1) Crackers are drier than bread, which is drier than butter: crackers > bread > butter

(2) Butter is drier than oil but moister than potatoes: potatoes > butter > oil

Now, you can think of this as saying that certainly potatoes are drier than butter; however, this only tells us that potatoes could be (1) drier than crackers, (2) moister than crackers and drier than bread, or (3) moister than bread but drier than butter.

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

(1) Computers are more complex than typewriters, which are more complex than pencils: computers > typewriters > pencils

(2) Pencils are less complex than ink wells but more complex flint stones: ink wells > pencils > flint stones

Now, since typewriters > pencils and pencils > flint stones, we can say that typewriters > flint stones; therefore, the statement, "Typewriters are more complex than flint stones," is true.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is better at.”

(1) For Lauren: cooking > sewing

(2) For Barbara: scheduling > (Lauren sewing)

Now, let's translate (3): (Barbara scheduling) > (Lauren cooking)

Okay, now we know that Barbara is better at scheduling than Lauren was at sewing. Likewise, we know that Lauren is better at cooking than she is at sewing. Thus, Barbara's scheduling and Lauren's cooking are both better than Lauren's sewing; however, we do not know the relationship between Barbara's scheduling and Lauren's cooking; therefore, the conclusion is uncertain.

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

(1) For Nancy: vegetables > fruits

(2) For Tim: beers > (Nancy fruits)

This means that Tim's pickiness about beers is either greater than Nancy's pickiness about vegetables or is less than that but still greater than her pickiness about fruits. Thus, we cannot conclude one way or the other regarding the relationship between Nancy's pickiness regarding vegetables and Tim's pickiness concerning beers (based on our information).

Now, to be conceited is to be overly proud. Thus, humility is the opposite of such conceit. Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is more conceited than (is less humble),” and “less than” (<) will mean “is less conceited than.”

(1) John is less conceited than Jeremy but more conceited than George: George < John < Jeremy

(2) George is less humble (i.e. more conceited) than William: George > William. This could also be rewritten: William < George

Thus, we can combine 1 and 2 to get: William < George < John < Jeremy

It is false to say that that John is Less conceited than William.

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

(1) Nicholas is wealthier than Scott but poorer than Leslie: Leslie > Nicholas > Scott

(2) Leslie is poorer than Pamela and wealthier than Barbara: Pamela > Leslie > Barbara

Now, we know that Pamela is wealthier than Leslie, so we can write:

Pamela > Leslie > Nicholas > Scott

This tells us that Pamela is wealthier than Scott.

When someone is "industrious," he or she is hard working—not lazy. Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is lazier than,” and “less than” (<) will mean “is less lazy (more industrious) than.”

(1) Richard is lazier than Brandon who is more industrious than Larry. This gives us two statements:

(a) Richard > Brandon

(b) Brandon < Larry, which could also be rewritten: Larry > Brandon

(2) Larry is lazier than Paul but more industrious than Todd. This gives us two statements as well:

(a) Larry > Paul

(b) Larry < Todd, which could also be rewritten: Todd > Larry

Now, we could thus take 1.b and 2.b to get:

Todd > Larry > Brandon

Thus, it is true that Todd is lazier than Brandon

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

(1) Jonathan is more intelligent than Jeremy, who is more intelligent than Lola: Jonathan > Jeremy > Lola

(2) Regina is less intelligent than Lola, who is more intelligent than Lena.  This gives us:

(a) Regina < Lola, which could be rewritten: Lola > Regina

(b) Lola > Lena

Now, Jonathan is more intelligent than Lola, who is more intelligent than both Regina and Lena; therefore, Jonathan is more intelligent than Regina and Lena.