2007 AMC 10B Problem 5

Problem 5 of 25Easier

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?

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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.

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