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Logical Reasoning - Logical Problems

Exercise

"Forgiveness is a virtue of the brave."
- Indira Gandhi

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: 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.

2.

 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.

3.

 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.

4.

 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.

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.