Logical Problems
- 1. The bookstore has a better selection of postcards than the newsstand does.
The selection of postcards at the drugstore is better than at the bookstore.
The drugstore has a better selection of postcards than the bookstore or the newsstand.
If the first two statements are true, the third statement is
Options- A. true
- B. false
- C. uncertain Discuss
Correct Answer: true
Explanation:
Of the three, the drugstore has the best selection of postcards.
- 2. A jar of jelly beans contains more red beans than green.
There are more yellow beans than red.
The jar contains fewer yellow jelly beans than green ones.
If the first two statements are true, the third statement is
Options- A. true
- B. false
- C. uncertain Discuss
Correct Answer: false
Explanation:
The first two statements indicate there are more yellow jelly beans than red and green.
- 3.
If the first three statements are facts, which of the following statements must also be a fact?Fact 1: All dogs like to run. Fact 2: Some dogs like to swim. Fact 3: Some dogs look like their masters. 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.
Options- A. I only
- B. II only
- C. II and III only
- D. None of the statements is a known fact. Discuss
Correct Answer: II only
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.
- 4.
If the first three statements are facts, which of the following statements must also be a fact?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. I: At least one girl has blue eyes. II: Two of the children are boys. III: The boys have brown eyes.
Options- A. I only
- B. II only
- C. II and III only
- D. None of the statements is a known fact. Discuss
Correct Answer: II only
Explanation:
Since one-half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes.
- 5.
If the first three statements are facts, which of the following statements must also be a fact?Fact 1: All drink mixes are beverages. Fact 2: All beverages are drinkable. Fact 3: Some beverages are red. I: Some drink mixes are red. II: All beverages are drink mixes. III: All red drink mixes are drinkable.
Options- 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. Discuss
Correct Answer: III only
- 6.
If the first three statements are facts, which of the following statements must also be a fact?Fact 1: All chickens are birds. Fact 2: Some chickens are hens. Fact 3: Female birds lay eggs. I: All birds lay eggs. II: Some Hens are birds. III: Some chickens are not hens.
Options- A. I only
- B. II only
- C. II and III only
- D. None of the statements is a known fact. Discuss
Correct Answer: II and III only
Explanation:
The first statement cannot be true because only female birds lay eggs. Statement II is true because some hens are chickens and all chickens are birds. Statement III is also true because if only some chickens are hens, then some must not be hens.
- 7.
If the first three statements are facts, which of the following statements must also be a fact?Fact 1: All hats have brims. Fact 2: There are black hats and blue hats. Fact 3: Baseball caps are hats. I: All caps have brims. II: Some baseball caps are blue. III: Baseball caps have no brims.
Options- A. I only
- B. II only
- C. II and III only
- D. None of the statements is a known fact. Discuss
Correct Answer: None of the statements is a known fact.
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.
- 8.
If the first three statements are facts, which of the following statements must also be a fact?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. 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.
Options- A. I only
- B. II only
- C. II and III only
- D. None of the statements is a known fact. Discuss
Correct Answer: 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.
- 9.
If the first three statements are facts, which of the following statements must also be a fact?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. 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.
Options- A. I only
- B. II only
- C. II and III only
- D. None of the statements is a known fact. Discuss
Correct Answer: None of the statements is a known fact.
Explanation:
None of the three statements is supported by the known facts.
- 10.
If the first three statements are facts, which of the following statements must also be a fact?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. I: Ann has a cat. II: Mary has a cat. III: Ann is lying.
Options- A. I only
- B. II only
- C. I and II only
- D. All the statements are facts. Discuss
Correct Answer: 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.
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