MathDB
Cards in an Envelope

Source:

January 19, 2006
percent

Problem Statement

A sealed envelope contains a card with a single digit on it. Three of the following statements are true, and the other is false. I. The digit is 1. II. The digit is not 2. III. The digit is 3. IV. The digit is not 4. Which one of the following must necessarily be correct? <spanclass=′latex−bold′>(A)</span> I is true.<spanclass=′latex−bold′>(B)</span> I is false.<spanclass=′latex−bold′>(C)</span> II is true.<spanclass=′latex−bold′>(D)</span> III is true.<spanclass=′latex−bold′>(E)</span> IV is false. <span class='latex-bold'>(A)</span>\ \text{I is true.} \qquad <span class='latex-bold'>(B)</span>\ \text{I is false.}\qquad <span class='latex-bold'>(C)</span>\ \text{II is true.} \qquad <span class='latex-bold'>(D)</span>\ \text{III is true.} \qquad <span class='latex-bold'>(E)</span>\ \text{IV is false.}
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