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Logical Reasoning :: Logical Problems

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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.

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

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  3. 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.

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

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  5. 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.

  6. 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.

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  7. 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.

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

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  9. 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.

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

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  11. 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.

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

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  13. 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.

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

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  15. 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.

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

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  17. 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.

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

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  19. 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.

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

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