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Logical Reasoning

Logical Problems - Type 3

Directions to Solve

The logic problems in this set present you with three true statements: Fact 1, Fact 2, and Fact 3. Then, you are given three more statements (labeled I, II, and III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; all of the statements could be true; or none of the statements could be true. Choose your answer based solely on the information given in the first three facts.

1. 
Fact 1: Islands are surrounded by water.
Fact 2: Maui is an island.
Fact 3: Maui was formed by a volcano.
If the first three statements are facts, which of the following statements must also be a fact?
I: Maui is surrounded by water.
II: All islands are formed by volcanoes.
III: All volcanoes are on islands.

A. I only
B. II only
C. II and III only
D. None of the statements is a known fact.
2. 
Fact 1: Robert has four vehicles.
Fact 2: Two of the vehicles are red.
Fact 3: One of the vehicles is a minivan.
If the first three statements are facts, which of the following statements must also be a fact?
I: Robert has a red minivan.
II: Robert has three cars.
III: Robert's favorite color is red.

A. I only
B. II only
C. II and III only
D. None of the statements is a known fact.
3. 
Fact 1: All dogs like to run.
Fact 2: Some dogs like to swim.
Fact 3: Some dogs look like their masters.
If the first three statements are facts, which of the following statements must also be a fact?
I: All dogs who like to swim look like their masters.
II: Dogs who like to swim also like to run.
III: Dogs who like to run do not look like their masters.

A. I only
B. II only
C. II and III only
D. None of the statements is a known fact.
4. 
Fact 1: All drink mixes are beverages.
Fact 2: All beverages are drinkable.
Fact 3: Some beverages are red.
If the first three statements are facts, which of the following statements must also be a fact?
I: Some drink mixes are red.
II: All beverages are drink mixes.
III: All red drink mixes are drinkable.

A. I and II only
B. II only
C. I and III only
D. III only
E. None of the statements is a known fact.
5. 
Fact 1: All hats have brims.
Fact 2: There are black hats and blue hats.
Fact 3: Baseball caps are hats.
If the first three statements are facts, which of the following statements must also be a fact?
I: All caps have brims.
II: Some baseball caps are blue.
III: Baseball caps have no brims.

A. I only
B. II only
C. II and III only
D. None of the statements is a known fact.
6. 
Fact 1: All chickens are birds.
Fact 2: Some chickens are hens.
Fact 3: Female birds lay eggs.
If the first three statements are facts, which of the following statements must also be a fact?
I: All birds lay eggs.
II: Some Hens are birds.
III: Some chickens are not hens.

A. I only
B. II only
C. II and III only
D. None of the statements is a known fact.
7. 
Fact 1: Jessica has four children
Fact 2: Two of the children have blue eyes and two of the children have brown eyes.
Fact 3: Half of the children are girls.
If the first three statements are facts, which of the following statements must also be a fact?
I: At least one girl has blue eyes.
II: Two of the children are boys.
III: The boys have brown eyes.

A. I only
B. II only
C. II and III only
D. None of the statements is a known fact.
8. 
Fact 1: Some pens don't write.
Fact 2: All blue pens write.
Fact 3: Some writing utensils are pens.
If the first three statements are facts, which of the following statements must also be a fact?
I: Some writing utensils don't write.
II: Some writing utensils are blue.
III: Some blue writing utensils don't write.

A. I only
B. I and II only
C. II and III only
D. None of the statements is a known fact.
9. 
Fact 1: Eyeglass frames cost between $35 and $350.
Fact 2: Some eyeglass frames are made of titanium.
Fact 3: Some eyeglass frames are made of plastic.
If the first three statements are facts, which of the following statements must also be a fact?
I: Titanium eyeglass frames cost more than plastic frames.
II: Expensive eyeglass frames last longer than cheap frames.
III: Only a few eyeglass frames cost less than $35.

A. I only
B. II only
C. II and III only
D. None of the statements is a known fact.
10. 
Fact 1: Most stuffed toys are stuffed with beans.
Fact 2: There are stuffed bears and stuffed tigers.
Fact 3: Some chairs are stuffed with beans.
If the first three statements are facts, which of the following statements must also be a fact?
I: Only children's chairs are stuffed with beans.
II: All stuffed tigers are stuffed with beans.
III: Stuffed monkeys are not stuffed with beans.

A. I only
B. II only
C. II and III only
D. None of the statements is a known fact.

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Exercise