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

## Example Questions

### Example Question #61 : Determining Whether A Statement Is True, False, Or Uncertain

Theobald finished the race before Leonard and Ronald. Patrick finished the race after Theobald and before Leonard. Patrick finished the race before Ronald. If the first two sentences are true, the third is __________.

uncertain

false

true

uncertain

Explanation:

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

(1) Theobald finished the race before Leonard and Ronald.

We get two statements from this:

(a) Theobald < Leonard

(b) Theobald < Ronald

(2) Patrick finished the race after Theobald and before Leonard.

We get two statements from this:

(a) Patrick > Theobald

(b) Patrick < Leonard

This can be rewritten: Leonard > Patrick

These can be combined to give us:

Leonard > Patrick > Theobald

Now, we know that Ronald is somewhere after Theobald (thus to the left of the > before Theobald); however, we cannot say anything about his relationship between Ronald and Patrick; therefore, the conclusion is uncertain.

### Example Question #62 : Determining Whether A Statement Is True, False, Or Uncertain

Monophony is plainer than homophony and polyphony. Heterophony is more complex than monophony. Heterophony is more complex than polyphony. If the first two sentences are true, the third is __________.

uncertain

false

true

uncertain

Explanation:

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

(1) Monophony is plainer than homophony and polyphony

We get two statements from this:

(a) monophony < homophony

(b) monophony < polyphony

(2) Heterophony is more complex than monophony: heterophony > monophony

Notice, this is the same thing as saying: monophony < heterophony

Thus, all we have are a set of statements that tell us that monophony is plainer than all of the others. This tells us nothing about the relationship between polyphony and heterophony.

### Example Question #63 : Determining Whether A Statement Is True, False, Or Uncertain

Regulations are more annoying than taxes and fines. Fines are less annoying than arbitrations. Regulations are more annoying than arbitrations. If the first two sentences are true, the third is __________.

false

true

uncertain

uncertain

Explanation:

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

(1) Regulations are more annoying than taxes and fines.

We get two statements from this:

(a) regulations > taxes

(b) regulations > fines

(2) Fines are less annoying than arbitrations: fines < arbitrations

This can be rewritten as arbitrations > fines

Notice that these statments tell us that arbitrations and regulations are both more annoying than fines.  However, they do not tell us the relationship between the two.

### Example Question #61 : Determining Whether A Statement Is True, False, Or Uncertain

Legalism is simpler than virtuousness. Virtuousness is more complex than pragmatism. Pragmatism is simpler than legalism. If the first two sentences are true, the third is __________.

false

true

uncertain

uncertain

Explanation:

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 simpler than (i.e. less complex than).”

(1) Legalism is simpler than virtuousness: legalism < virtuousness

This can be rewritten: virtuousness > legalism

(2) Virtuousness is more complex than pragmatism: virtuousness > pragmatism

These two statements tell us that virtuousness is more complex than the other two options; however, they do not tell us the relationship between those other two.

### Example Question #65 : Determining Whether A Statement Is True, False, Or Uncertain

Performing music is more soothing than painting and running. Running is more soothing than debating. Painting is more soothing than debating. If the first two sentences are true, the third is __________.

uncertain

false

true

uncertain

Explanation:

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

(1) Performing music is more soothing than painting and running.

We get two statements from this:

(a) Music > painting

(b) Music > running

(2) Running is more soothing than debating: running > debating

Notice that this tells us that:

Music > running > debating

However, it does not tell us the relationship between painting and debating.  We just know that debating and painting are less soothing than performing music.

### Example Question #66 : Determining Whether A Statement Is True, False, Or Uncertain

Christopher is more loving than both Richard and Timothy. Richard is less loving than Lucy but more loving than Ronald, who is less loving than Timothy. Christopher is more loving than Ronald. 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 “is more loving than,” and “less than” (<) will mean “is less loving than.”

(1) Christopher is more loving than both Richard and Timothy. This really contains two statements:

(a) Christopher > Richard

(b) Christopher > Timothy

(2) Richard is less loving than Lucy but more loving than Ronald, who is less loving than Timothy. This really contains two statements:

(a) Lucy > Richard > Ronald

(b) Ronald < Timothy

Now, notice that the link from Ronald to Christopher will have to go through Timothy. Let's rewrite 2b as:

Timothy > Ronald

This can be combined with 1.b to get:

Christopher > Timothy > Ronald

Therefore, it is true that Christopher is more loving than Ronald.

### Example Question #62 : Determining Whether A Statement Is True, False, Or Uncertain

Wheeler is a smaller town than Connellsville but larger than Chalkhill.  Chalkhill is larger than both Frogbottom and Toadhole.  Toadhole is smaller than Wheeler. If the first two statements are true, the third is __________.

false

true

uncertain

true

Explanation:

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

(1) Wheeler is a smaller town than Connellsville but larger than Chalkhill: Connellsville > Wheeler > Chalkhill

(2) Chalkhill is larger than both Frogbottom and Toadhole. This really gives us two statements:

(a) Chalkhill > Frogbottom

Now, we can relate Toadhold and Wheeler by combining 1 with 2b:

Connellsville > Wheeler > Chalkhill > Toadhole

It is therefore true to say that Toadhole is smaller than Wheeler.

### Example Question #68 : Determining Whether A Statement Is True, False, Or Uncertain

Charles is a better writer than Steven but a worse writer than Laura. Laura is a worse writer than both Nellie and John.  John is a better writer than Steven. If the first two statements are true, the third is __________.

false

true

uncertain

true

Explanation:

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

(1) Charles is a better writer than Steven but a worse writer than Laura: Laura > Charles > Steven

(2) Laura is a worse writer than both Nellie and John. This gives us two statements:

(a) Laura < Nellie

(b) Laura < John

Now, we can rewrite 2b as: John > Laura

This let's us combine 2b with 1 to get:

John > Laura > Charles > Steven

Therefore, it is true to say that John is a better writer than Steven.

### Example Question #69 : Determining Whether A Statement Is True, False, Or Uncertain

Isaac is more successful than Mallory and Peter.  Gregory is less successful than Peter and George. Isaac is less successful than Gregory. If the first two statements are true, the third is __________.

uncertain

true

false

false

Explanation:

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

(1) Isaac is more successful than Mallory and Peter. This really gives us two statements:

(a) Isaac > Mallory

(b) Isaac > Peter

(2) Gregory is less successful than Peter and George. This really gives us two statements:

(a) Gregory < Peter

(b) Gregory < George

Now, let's rewrite 2a as: Peter > Gregory. We can combine this with 1b to get:

Isaac > Peter > Gregory

Therefore, it is false to say that Isaac is less successful than Gregory.

### Example Question #70 : Determining Whether A Statement Is True, False, Or Uncertain

James is saner than Maurice but crazier than Jacques. Yves is saner than Jacques, Reginald, and Theodore. Maurice is crazier than Yves. If the first two statements are true, the third is __________.

true

uncertain

false

true

Explanation:

Since "sane" and "crazy" can be considered, opposites, we will read them as such. Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is saner than,” and “less than” (<) will mean “is less sane than (crazier than).”

(1) James is saner than Maurice but crazier than Jacques: Jacques > James > Maurice

(2) Yves is saner than Jacques, Reginald, and Theodore.  This gives us 3 separate statements:

(a) Yves > Jacques

(b) Yves > Reginald

(c) Yves > Theodore

Now, we need to relate Yves to Maurice.  We can do this by combining 2a and 1:

Yves > Jacques > James > Maurice

This means that Maurice is less sane than Yves or (in other words) he is crazier than Yves.