Question

In a certain land, all Arogs are Brafs, all Crups are Brafs, all Dramps are Arogs, and all Crups are Dramps. Which of the following statements is implied by these facts?

All Dramps are Brafs and are Crups.

All Brafs are Crups and are Dramps.

All Arogs are Crups and are Dramps.

All Crups are Arogs and are Brafs.

All Arogs are Dramps and some Arogs may not be Crups.

Solution:

Writing the statements as implications, being a Crup implies being a Dramp, a Dramp implies being an Arog, and an Arog implies being a Braf: $C\Rightarrow D\Rightarrow A\Rightarrow B.$

So every Crup is a Dramp, an Arog, and a Braf. The only listed statement guaranteed true is that all Crups are Arogs and Brafs.

Thus, the correct answer is D.

2007 AMC 10B Problem 5

Solution:

Problem 5 in Other Years