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

(1) Gregory is smarter than Peter, who is smarter than Laurence:

Gregory > Peter > Laurence

(2) Harold and Theodore are less intelligent than Laurence. This really gives us two statements:

(a) Harold < Laurence

(b) Theodore < Laurence, which could be rewritten Laurence > Theodore

Now, combine 1 and 2b to get:

Gregory > Peter > Laurence > Theodore

This means that it is false to say that Theodore is more intelligent (smarter) than Gregory.

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

(1) Cats are sneakier than turtles, which are less sneaky than rats. Notice that this gives us two statements:

(a) cats > turtles

(b) turtles < rats, which could be rewritten: rats > turtles

(2) Rats are sneakier than gerbils: rats > gerbils

Now, we know that gerbils are less sneaky than rats. Likewise, we know that rats are sneakier than turtles (like cats); however, we do not know if rats are sneakier than cats or vice-versa.

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

(1) French is easier to learn than German but harder to learn than Esperanto.  This can be rewritten:

German > French > Esperanto

(2) Latin is harder to learn than Esperanto: Latin > Esperanto

All that we thus know is that Latin is harder than esperanto but nothing regarding its relationship to French. It could be easier than French, harder than French but easier than German, or harder than German. Thus, we cannot say one way or the other regarding the third statement.

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

(1) Andrew is taller than Abraham: Andrew > Abraham

(2) Abraham is shorter than Charles: Abraham < Charles

This could be rewritten: Charles > Abraham

Another way of looking at these two would be:

(1) Abraham < Andrew

(2) Abraham < Charles

This tells us that Abraham is shorter than Andrew and Charles.  It tells us nothing about the relationship between Charles and Andrew.

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

(1) Robert runs more quickly than Nicole: Robert > Nicole

(2) Nicole runs more quickly than Fred: Nicole > Fred

This could give us a combined statement:

Robert > Nicole > Fred

Now, (3) could be rewritten: Fred < Robert. This is the same thing as Robert > Fred, which we do see above as being true.

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

(1) Cars are more difficult to drive than tricycles, which are more difficult to drive than scooters: cars > tricycles > scooters

(2) Farm tractors are more difficult to drive than both cars and trucks. This really contains two statements:

(a) farm tractors > cars

(b) farm tractors > trucks

Now, we can combine 1 and 2a to get:

farm tractors > cars > tricycles > scooters

It is therefore true to say that scooters are easier to drive than farm tractors.

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

(1) For Peter: sweeping > cleaning kitchen

(2) For Hans: sweeping > (Peter sweeping)

This could be combined to say:

(Hans sweeping) > (Peter sweeping) > (Peter cleaning kitchen)

Therefore, the answer is true.

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

(1) Bicycling is more relaxing than running but more stressful than walking.  Be careful, this is the same as saying that bicycling is more relaxing than running but less relaxing than walking:

running < bicycling < walking

(2) Walking is less relaxing than sleeping and watching television.  This is really two statements:

(a) walking < sleeping

(b) walking < watching television

Now, we can combine 1 and 2b to get:

running < bicycling < walking < watching television

Therefore, based on this argument, it is false to say that bicycling is more relaxing than watching television.

Let's look at the problem visually by putting the three boys on a spectrum. The least funny person should be on the right, and the funniest person is on the left. If Ian is funnier than Dylan, Ian is put on the left and Dylan is on the right.

Ian----Dylan

Sam is less funny than Dylan, so he's put to the right of Dylan on the spectrum.

Ian----Dylan----Sam

Therefore, Ian is funnier than Sam.

Let's look at the problem visually by putting Sasha, Tiara, Eric and Alexis on a spectrum. The person with the least prestigious job should be on the right, and the person with the most prestigious job is on the left. 

In the first half of the first sentence, we are told that Alexis has a job more prestigious than Sasha, so Alexis should be put on the left side of the spectrum, and Sasha should be put on the right side.

Alexis----Sasha

In the second half of the first sentence, we are told that Alexis' job is less prestigious than Tiara's. Therefore, we put Tiara to the left of Alexis.

Tiara----Alexis----Sasha

In the second sentence, we discover that Tiara's job is more prestigious than Eric's. Tiara should remain on the extreme left of the spectrum, but, without further information, we can't tell where Eric should be placed on the spectrum in comparison to Alexis and Sasha. Therefore, it is uncertain whether the third sentence is true or false.