Logical Problems Type 3 - Logical Reasoning Questions and Answers

Category: Logical Reasoning

Topic: Logical Problems

Exercise: Logical Problems - Type 3

Questions: 10 Available

Introduction & Key Concepts Concept

Logical Framework Concept

Key Techniques Concept

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Logical Problems - Type 3

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Directions to Solve

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.

Question 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.

I only

II only

II and III only

None of the statements is a known fact.

Correct Answer: 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.

Question 2

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.

I only

II only

II and III only

None of the statements is a known fact.

Correct Answer: Option D

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).

Question 3

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.

I only

II only

II and III only

None of the statements is a known fact.

Correct Answer: Option B

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.

Question 4

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.

I and II only

II only

I and III only

III only

None of the statements is a known fact.

Correct Answer: Option D

"All drink mixes are beverages" but not all beverages are drink mixes so we can conclude "some beverages are drink mixes" and "Some beverages are red".

I. Some drink mixes are red. - Only in extreme case it is true.

II. All beverages are drink mixes - Is false as per above discussion.

"All drink mixes are beverages" and "All beverages are drinkable". So we can say "All drink mixes are drinkable".

III. All red drink mixes are drinkable - true as cumulative result.

So Option D) III Only is the correct answer.

Question 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.

I only

II only

II and III only

None of the statements is a known fact.

Correct Answer: Option D

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.

Question 6

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.

I only

II only

II and III only

None of the statements is a known fact.

Correct Answer: Option C

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.

Question 7

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.

I only

II only

II and III only

None of the statements is a known fact.

Correct Answer: Option B

Since one-half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes.

Question 8

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.

I only

I and II only

II and III only

None of the statements is a known fact.

Correct Answer: Option B

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.

Question 9

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.

I only

II only

II and III only

None of the statements is a known fact.

Correct Answer: Option D

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.

Question 10

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.

I only

II only

II and III only

None of the statements is a known fact.

Correct Answer: Option D

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

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