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

## Example Questions

### Example Question #91 : Determining Whether A Statement Is True, False, Or Uncertain

Alicia is older than Frank and Simon. Simon and Frank are older than Anthony. Anthony is younger than Alicia. 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 all four people on a spectrum. The youngest person should be on the right, and the oldest person is on the left. If Alicia is older than Frank and Simon, the spectrum looks like:

Alicia----Frank & Simon

If Frank and Simon are older than Anthony, the spectrum looks like:

Alicia----Frank & Simon----Anthony

The third sentence is true: Anthony is younger than Alicia.

### Example Question #782 : Hspt Verbal Skills

Corn is a more popular vegetable than broccoli. Broccoli is more popular than asparagus. Asparagus is more popular than corn. If the first two sentences are true, then the third sentence is ___________.

false

uncertain

true

false

Explanation:

Let's look at the problem visually by putting the three vegetables on a spectrum. The least popular vegetable should be on the right, and the most popular vegetable is on the left. If corn is more popular than broccoli, it goes to the left of broccoli on the spectrum:

corn----broccoli

If broccoli is more popular than asparagus, asparagus should be placed to the right of broccoli on the spectrum.

corn----broccoli----asparagus

The third sentence stating that asparagus is more popular than corn is false.

### Example Question #122 : Logic

Kennedy High School has more Russian-speaking students than Lincoln High School, but fewer Spanish-speaking students than Roosevelt High School. Roosevelt High School has more Spanish-speaking students than Lincoln High School, and more Russian-speaking students than Kennedy High School. Roosevelt High School has more Russian and Spanish-speaking students than Kennedy High School or Lincoln High School. If the first two sentences are true, than the third sentence must be __________.

true

uncertain

false

true

Explanation:

For this problem, we have to create two spectrum: one for the number of Russian-speaking students at each high school and one for the number of Spanish-speaking students at each high school. The school with the most Russian or Spanish-speaking students will be placed on the left of the spectrum, while the school with the least Russian or Spanish-speaking students will be placed on the right of the spectrum.

The first half of the first sentence tells us that Kennedy HS has more Russian-speaking students than Lincoln HS. So, our Russian spectrum looks like:

Russian-speaking students:

Kennedy----Lincoln

The second half of the first sentence tells us that Kennedy HS has fewer Spanish-speaking students than Roosevelt HS. Our Spanish spectrum looks like:

Spanish-speaking students:

Roosevelt----Kennedy

The first half of the second sentence tells us that Roosevelt HS has more Spanish-speaking students than Lincoln HS. We don't know whether Kennedy HS or Lincoln HS has more Spanish-speaking students, so we'll put them together on the spectrum for now.

Spanish-speaking students:

Roosevelt----Kennedy & Lincoln

The second half of the second sentence tells us that Roosevelt HS has more Russian-speaking students than Kennedy HS. They'll be placed to the left of Kennedy on the Russian spectrum. After the second sentence, the two spectrums look like this:

Russian-speaking students:

Roosevelt----Kennedy----Lincoln

Spanish-speaking students:

Roosevelt---Kennedy & Lincoln

Therefore, the third sentence, stating that Roosevelt HS has more Russian-speaking students AND more Spanish-speaking students than either Kennedy HS or Lincoln HS is true.

### Example Question #94 : Determining Whether A Statement Is True, False, Or Uncertain

Sandra has more shoes than Ellen and Joan. Ellen has more shoes than Kerri. Kerri has more shoes than Joan. If the first two sentences are true, than the third sentence is ___________.

false

uncertain

true

uncertain

Explanation:

We know that Sandra has more shoes than either Ellen or Joan and that Ellen has more shoes than Kerri. We do not know, however, how many shoes Ellen has compared to Joan. This is the key to determining whether Kerri has more shoes than Joan. Therefore, the third sentence is uncertain.

### Example Question #95 : Determining Whether A Statement Is True, False, Or Uncertain

Daniel is a faster swimmer than Sean. Sean is the fastest swimmer on his team. Daniel and Sean do not swim on the same team. If the first two sentences are true, then the third sentence is ___________.

True

False

Uncertain

True

Explanation:

If Daniel is faster than Sean, but Sean is the fastest swimmer on his team, Daniel cannot swim on the same team as Sean.

### Example Question #96 : Determining Whether A Statement Is True, False, Or Uncertain

Sarah gets better grades in math than Luis. Luis gets better grades in science than Sarah. Luis is a better student than Sarah. If the first two sentences are true, the third sentence must be ___________.

False

Uncertain

True

Uncertain

Explanation:

The only two facts that we know for certain are:

1) Sarah gets better grades in math than Luis; and

2) Luis gets better grades in science than Sarah.

These are both quantifiable statements. This means that we can put an absolute number to each statement. Although we don't know what the actual grades are, we know that Sarah's grades are better in math and Luis' grades are better in science.

The third sentence, "Luis is a better student than Sarah" has many unknown variables.  We don't know what grades either student receives in any other class. We don't know how much better Sarah is in math than Luis, or how much better Luis is in science than Sarah. Finally, the phrase "better student" is not defined. This could mean higher grades in classes, or it could mean higher grades on standardized tests. "Better student" could even mean the student that studies the hardest or pays the best attention in class. For these reasons, the truthfulness of the third sentence is uncertain.

### Example Question #97 : Determining Whether A Statement Is True, False, Or Uncertain

Owen and Andrea each spend exactly the same amount of money at the same restaurant. Owen purchases two hamburgers and three drinks, while Andrea purchases three hamburgers and two drinks. The hamburgers and drinks each cost the same amount. If the first two sentences are true, then the third sentence must be __________.

Uncertain

True

False

True

Explanation:

Both Owen and Andrea purchase five items at the same restaurant and spend exactly the same amount of money.  If we look at the problem mathematically, the equation would be:

h=hamburger; d=drinks (Owen is on the left-hand side of the equation and Andrea is on the right-hand side of the equation.)

For comparison, we need to isolate each variable on its own side.  First, subtract  from each side.  This results in:

Next, subtract  from each side.  This results in:

This proves, logically, that one drink costs the same amount of money as one hamburger.

### Example Question #98 : Determining Whether A Statement Is True, False, Or Uncertain

A peregrine falcon is three times faster than a cheetah. A cheetah is twice as fast as a rabbit. A rabbit is nearly three times faster than a squirrel. If the first two sentences are true, the third sentence is ____________.

False

True

Uncertain

Uncertain

Explanation:

The accuracy of the third sentence is uncertain because the speed of a squirrel is not compared to either a peregrine falcon or a cheetah in the first two sentences. Therefore, there is not enough information to form an accurate conclusion.

(In case you're wondering: all three statements are accurate.)

### Example Question #99 : Determining Whether A Statement Is True, False, Or Uncertain

Brice is older than Pat. Pat is younger than Jim. Jim is older than Brice. If the first two sentences are true, then the third sentence is ____________.

False

Uncertain

True

Uncertain

Explanation:

We know that Brice is older than Pat and that Pat is younger than Jim. We do not have any information regarding Brice and Jim's relationship. Therefore, the third sentence may be true, or it may be false.

### Example Question #100 : Determining Whether A Statement Is True, False, Or Uncertain

The zoo has more wolves than tigers. The zoo has more tigers than leopards. The zoo has more wolves than leopards. If the first two sentences are true, then the third sentence is ____________.

True

False

Uncertain

True

Explanation:

Let's put the information we have on a spectrum. The animal that the zoo has the most of will be placed on the left and the animal the zoo has the least of will be placed on the right. Sentence 1 tell us that the zoo has more wolves than tigers.

Wolves -- tigers

Sentence 2 tells us that the zoo has more tigers than leopards.

Wolves -- tigers -- leopards

Sentence 3 must be true. If the zoo has more wolves than tigers, and they have more tigers than leopards, then they must have more wolves than leopards.