Logical Problems


Direction: 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 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.









  1. View Hint View Answer Discuss in Forum

    If all drink mixes are beverages and some beverages are red, then some drink mixes are red (statement I).

    Correct Option: C

    If all drink mixes are beverages and some beverages are red, then some drink mixes are red (statement I). Since all beverages are drinkable and all drink mixes are beverages, then all red drink mixes must be drinkable (statement III). Statement II can be ruled out.


  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.









  1. View Hint View Answer Discuss in Forum

    Since Maui is an island and islands are surrounded by water, Maui must be surrounded by water.

    Correct Option: A

    Since Maui is an island and islands are surrounded by water, Maui must be surrounded by water. There is not enough information to support statements II and III.



  1. 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.









  1. View Hint View Answer Discuss in Forum

    There is not enough information to support any of the statements. Robert is known to have a minivan, but it is not known which of his vehicles is red.

    Correct Option: D

    There is not enough information to support any of the statements. Robert is known to have a minivan, but it is not known which of his vehicles is red. Robert may have a pickup or sport utility vehicle, so the second statement cannot be supported. There is no way to know if Robert’s favorite color is red (statement III).


  1. 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.









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

    Correct Option: C

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



  1. 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.









  1. View Hint View Answer Discuss in Forum

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

    Correct Option: D

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