2000 AMC 10 Problem 21

Question

If all alligators are ferocious creatures and some creepy crawlers are alligators, which statement(s) must be true?

I. All alligators are creepy crawlers.

II. Some ferocious creatures are creepy crawlers.

III. Some alligators are not creepy crawlers.

\mathrm{I}

only

\mathrm{II}

only

\mathrm{III}

only

\mathrm{II}

and

\mathrm{III}

only

None must be true

Answer: B

Concepts:logical deduction Venn Diagram

Difficulty rating: 1510

Small hint:

Some creepy crawlers are alligators, and every alligator is ferocious

Big hint:

Test statements I and III by drawing a diagram where alligators sit entirely inside the creepy crawlers

Solution:

Some creepy crawlers are alligators, and all alligators are ferocious, so those creatures are both creepy crawlers and ferocious. Hence some ferocious creatures are creepy crawlers, making II true.

Statement I fails because not every alligator need be a creepy crawler, and III fails because it is possible that all alligators are creepy crawlers. Only II must hold.

Thus, the correct answer is B.

2000 AMC 10 Problem 21

Answer: B

Difficulty rating: 1510

Small hint:

Big hint:

Solution:

Problem 21 in other years