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

## Example Questions

### Example Question #71 : Determining Whether A Statement Is True, False, Or Uncertain

Dante is more interesting than Durandus and Capreolus. Capreolus is less interesting than Avicenna and more interesting than Averroes. Averroes is less interesting than Dante. If the first two statements are true, the third is __________.

true

false

uncertain

true

Explanation:

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

(1) Dante is more interesting than Durandus and Capreolus. This really gives us two statements:

(a) Dante > Durandus

(b) Dante > Capreolus

This is the same as: Capreolus < Dante

(2) Capreolus is less interesting than Avicenna and more interesting than Averroes:

Averroes < Capreolus < Avicenna

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

Averroes < Capreolus < Dante

Therefore, it is true to say that Averroes is less interesting than Dante.

### Example Question #71 : Determining Whether A Statement Is True, False, Or Uncertain

Potato sacks are rougher than cotton, which is rougher than silk. Cotton is softer than denim and wood. Wood is rougher than silk. If the first two statements are true, the third is __________.

uncertain

false

true

true

Explanation:

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

(1) Potato sacks are rougher than cotton, which is rougher than silk:

potato sacks > cotton > silk

(2) Cotton is softer than denim and wood.  This really contains two statements:

(a) cotton < denim

(b) cotton < wood; this is the same as: wood > cotton

We can combine 1 and 2B to get:

wood > cotton > silk

Therefore, it is true to say that wood is rougher than silk.

### Example Question #72 : Determining Whether A Statement Is True, False, Or Uncertain

Sebastian reads more than Jerome, who reads less than Silvanus. Germanus, who reads less than Isidore, reads more than Silvanus. Isidore reads less than Jerome. If the first two statements are true, the third is __________.

uncertain

false

true

false

Explanation:

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

(1) Sebastian reads more than Jerome, who reads less than Silvanus. This really has two statements in it:

(a) Sebastian > Jerome

(b) Jerome < Silvanus, which can be rewritten: Silvanus > Jerome

Isidore > Germanus > Silvanus

Now, we can combine 1b and 2 to get: Isidore > Germanus > Silvanus > Jerome

This means that it is false to say that Isidore reads less than Jerome.

### Example Question #73 : Determining Whether A Statement Is True, False, Or Uncertain

Wendy is more interesting than Lilly, who is more interesting than Rachel. Rachel is less interesting than Tabitha but is more interesting than Lauren. Wendy is more interesting than Lauren. If the first two statements are true, the third is __________.

false

uncertain

true

true

Explanation:

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

(1) Wendy is more interesting than Lilly, who is more interesting than Rachel:

Wendy > Lilly > Rachel

(2) Rachel is less interesting than Tabitha but is more interesting than Lauren.  This gives us two statements:

(a) Rachel < Tabitha

(b) Rachel > Lauren

We can combine 1 and 2b to get

Wendy > Lilly > Rachel > Lauren

This means that Wendy is more interesting than Lauren.

### Example Question #75 : Determining Whether A Statement Is True, False, Or Uncertain

Gregory is smarter than Peter, who is smarter than Laurence. Harold and Theodore are less intelligent than Laurence. Theodore is more intelligent than Gregory. If the first two statements are true, the third is __________.

true

uncertain

false

false

Explanation:

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.

### Example Question #76 : Determining Whether A Statement Is True, False, Or Uncertain

Cats are sneakier than turtles, which are less sneaky than rats. Rats are sneakier than gerbils. Gerbils are less sneaky than cats. If the first two statements 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 “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.

### Example Question #77 : Determining Whether A Statement Is True, False, Or Uncertain

French is easier to learn than German but harder to learn than Esperanto. Latin is harder to learn than Esperanto. Latin is easier to learn than German. 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 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.

### Example Question #78 : Determining Whether A Statement Is True, False, Or Uncertain

Andrew is taller than Abraham. Abraham is shorter than Charles. Charles is taller than Andrew. 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 “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.

### Example Question #79 : Determining Whether A Statement Is True, False, Or Uncertain

Robert runs more quickly than Nicole. Nicole runs more quickly than Fred. Fred runs more slowly than Robert. If the first two sentences are true, the third is __________.

true

false

uncertain

true

Explanation:

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.

### Example Question #80 : Determining Whether A Statement Is True, False, Or Uncertain

Cars are more difficult to drive than tricycles, which are more difficult to drive than scooters. Farm tractors are more difficult to drive than both cars and trucks. Scooters are easier to drive than farm tractors. 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 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. 