Logical Problems

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

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.

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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

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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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

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

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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

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.

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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

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.

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Questions for: Logical Problems