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.

We know that roses smell better than geraniums and that geraniums smell worse than lilacs. That means that both roses and lilacs smell better than geraniums. There is no information, though, about whether lilacs or roses smell best. Therefore, the third sentence is uncertain.

Although Diego is the best athlete in his high school, Jocelyn is the best high school athlete in the entire city. This means both that she must go to a different high school and that she is a better athlete than Diego. Therefore, the statement that Diego is a better athlete than both Jocelyn and Allison is false.

From the information in only the first two sentences, we know that blue is the most popular color of the three; green is the next most popular; and purple is the least popular of these three colors. Orange is only introduced in the third sentence, so we have no way of knowing, looking at only the first two sentences, if purple is more popular than orange.

We know that Anika's house is less expensive than both Helena's house and Stephen's house. From the first two sentences only, however, we have nothing to compare Stephen and Helena's houses. We only know that they are both more expensive than Anika's house. Therefore, the third sentence is undetermined.

Let's look at the problem visually by putting the three dogs on a spectrum. The ugliest dog should be on the right, and the cutest dog is on the left. If Boomer is cuter than Pepper, the spectrum would look like this:

Boomer----Pepper

If Pepper is not as cute as Princess, Princess goes to the left of Pepper. We don't know where Princess is on the spectrum compared to Boomer, so we'll put them together temporarily.

Boomer & Princess ---- Pepper

Since the third sentence says that BOTH Boomer and Princess are cuter than Pepper, we don't need to know where they are on the spectrum compared to each other. The third sentence is true.

Let's look at this problem mathematically.  Where soccer players = s; basketball players = b; and football players = f, the equations would like:

It requires twice as many soccer players to equal the number of basketball players. It requires twice as many basketball players to equal the number of football players. To determine if the third sentence is true, we must multiply the first equation by 2 which gives us:

We can now determine that:

Divide each side by 4 to isolate s.

This means that  times as many athletes play high school football as soccer, so the third sentence is true.