HSPT Verbal : Determining Whether a Statement is True, False, or Uncertain

Example Questions

Example Question #81 : Determining Whether A Statement Is True, False, Or Uncertain

Peter hated sweeping more than he hated cleaning the kitchen. Hans hated sweeping more than Peter did. Hans hated sweeping more than Peter hated cleaning the kitchen. If the first two statements are true, the third is __________.

true

uncertain

false

true

Explanation:

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)

Example Question #82 : Determining Whether A Statement Is True, False, Or Uncertain

Bicycling is more relaxing than running but more stressful than walking. Walking is less relaxing than sleeping and watching television. Bicycling is more relaxing than watching television. If the first two statements are true, the third is __________.

false

uncertain

true

false

Explanation:

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.

Example Question #83 : Determining Whether A Statement Is True, False, Or Uncertain

Ian is funnier than Dylan. Sam is less funny than Dylan. Ian is funnier than Sam. If the first two sentences are true, then the third sentence is ___________.

uncertain

false

true

true

Explanation:

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.

Example Question #781 : Hspt Verbal Skills

Alexis has a more prestigious job than Sasha, but less a prestigious one than Tiara's job. Tiara's job is more prestigious than Eric's. Eric's job is more prestigious than Sasha's. If the first two sentences are true, the third sentence is ____________.

false

true

uncertain

uncertain

Explanation:

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.

Example Question #85 : Determining Whether A Statement Is True, False, Or Uncertain

Roses smell better than geraniums. Geraniums smell worse than lilacs. Lilacs smell better than roses. If the first two sentences are true, the third sentence is ____________.

false

uncertain

true

uncertain

Explanation:

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.

Example Question #86 : Determining Whether A Statement Is True, False, Or Uncertain

Diego is the best athlete in his high school, but Jocelyn is the best high school athlete in the entire city. Allison is not an athlete, but is an outstanding concert pianist. Diego is a better athlete than both Jocelyn and Allison. If the first two sentences are true, the third sentence is ______________.

false

true

uncertain

false

Explanation:

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.

Example Question #87 : Determining Whether A Statement Is True, False, Or Uncertain

Blue is a more popular color than green. Green is a more popular color than purple. Purple is a more popular color than orange. If the first two sentences are true, than the third sentence is _____________.

true

false

uncertain

uncertain

Explanation:

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.

Example Question #88 : Determining Whether A Statement Is True, False, Or Uncertain

Helena's house cost more than Jorge's house or Anika's house. Anika's house cost less than Stephen's house. Stephen's house cost less than Helena's house. If the first two sentences are true, than the third sentence is ___________.

uncertain

false

true

uncertain

Explanation:

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.

Example Question #121 : Logic

Boomer is a cuter dog than Pepper. Pepper is not as cute as Princess. Boomer and Princess are both cuter than Pepper. If the first two sentences are true, than the third sentence is __________.

false

uncertain

true

true

Explanation:

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.

Example Question #90 : Determining Whether A Statement Is True, False, Or Uncertain

Half as many male high school athletes in the United States play soccer compared to basketball. Half as many male high school athletes in the United States play basketball as compared to the number who play football. Football is played by four times as many male high school athletes in the United States as is soccer. If the first two sentences are true, than the third sentence is __________.

uncertain

false

true

true

Explanation:

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.