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- Logical Problems
- Section 4
Directions :
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.
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
- C.II and III only
- B.II only
- D.None of the statements is a known fact.
- Answer & Explanation
- Report
Answer : [B]
Explanation :
Explanation :
| Statement II is the only true statement. Since all dogs like to run, then the ones who like to swim also like to run. There is no support for statement I or statement III. |
2.
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.
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
- C.I, II, and III
- B.II only
- D.None of the statements is a known fact.
- Answer & Explanation
- Report
Answer : [D]
Explanation :
Explanation :
| All baseball caps have brims, since baseball caps are hats (Fact 3) and all hats have brims (Fact 1). This rules out statement III—but it doesn’t follow that all caps, a category that may include caps that are not baseball caps, have brims (statement I). Statement II cannot be confirmed, either, since it is possible, given the information, that all baseball caps are black. |
3.
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.
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.II only
- C.II and III only
- B.I and II only
- D.None of the statements is a known fact.
- Answer & Explanation
- Report
Answer : [B]
Explanation :
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. |
4.
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.
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.II only
- C.II and III only
- B.I and II only
- D.None of the statements is a known fact.
- Answer & Explanation
- Report
Answer : [D]
Explanation :
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. |
5.
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.
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
- C.III only
- B.II only
- D.None of the statements is a known fact.
- Answer & Explanation
- Report
Answer : [C]
Explanation :
Explanation :
| 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. |
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