Logical Reasoning

Logical problem with answer: Set 4

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.

Answer:  B

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:   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.

Answer:  B

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.

 

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.

Answer:  D

 

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.

Answer:  C

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.

 

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.

Answer:  D

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.

 

6.

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.

 

A.            I only

B.            II only

C.            II and III only

D.            None of the statements is a known fact.

Answer:  D

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.

 

7.

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.

 

A.            I only

B.            II only

C.            II and III only

D.            None of the statements is a known fact.

Answer:  D

Explanation:

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

 

8.

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.

 

A.            I only

B.            II only

C.            I and II only

D.            All the statements are facts.

Answer:  D

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.

 

9.

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.

 

A.            I only

B.            II only

C.            III only

D.            None of the statements is a known fact.

Answer:  C

Explanation:

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

 

10.

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.

 

A.            I only

B.            I and II only

C.            II and III only

D.            None of the statements is a known fact.

Answer:  B

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.

 

11.

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.

 

A.            I only

B.            II only

C.            II and III only

D.            None of the statements is a known fact.

Answer:  A

Explanation:

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.

 

12.

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.

 

A.            I only

B.            II only

C.            II and III only

D.            None of the statements is a known fact.

Answer:  D

Explanation:

There is not enough information to support any of the statements. Robert is known to have a minvan, 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).

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