# Logical Reasoning - Logical Problems

### Exercise :: Logical Problems - Type 4

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.

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.

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.

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.

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.