Logical Reasoning - Logical Problems

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.
6. 

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.

Answer: Option D

Explanation:

There is no information in the facts to support statements I or II. Statement III is clearly wrong because, according to Fact 1, no frames cost less than $35.

7. 

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.

Answer: Option D

Explanation:

None of the three statements is supported by the known facts.

8. 

Fact 1: Mary said, "Ann and I both have cats."
Fact 2: Ann said, "I don't have a cat."
Fact 3: Mary always tells the truth, but Ann sometimes lies.
If the first three statements are facts, which of the following statements must also be a fact?
I: Ann has a cat.
II: Mary has a cat.
III: Ann is lying.

A. I only
B. II only
C. I and II only
D. All the statements are facts.

Answer: Option D

Explanation:

If Mary always tells the truth, then both Ann and Mary have cats (statements I and II), and Ann is lying (statement III). So all the statements are facts.

9. 

Fact 1: Pictures can tell a story.
Fact 2: All storybooks have pictures.
Fact 3: Some storybooks have words.
If the first three statements are facts, which of the following statements must also be a fact?
I: Pictures can tell a story better than words can.
II: The stories in storybooks are very simple.
III: Some storybooks have both words and pictures.

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

Answer: Option C

Explanation:

Statements I and II are not supported by the facts. Statement III is true because if all story-books have pictures and only some have words, then some storybooks have both words and pictures.

10. 

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.

Answer: Option B

Explanation:

Since some pens don't write, some writing utensils don't write (statement I). Since there are blue pens and since pens are writing utensils, some writing utensils are blue (statement II). There is not enough information to support statement III.