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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1999 AMC 12/AHSME
10
10
Part of
1999 AMC 12/AHSME
Problems
(1)
Cards in an Envelope
Source:
1/19/2006
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?
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I is true.
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I is false.
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II is true.
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III is true.
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E
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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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I is true.
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I is false.
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II is true.
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III is true.
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E
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IV is false.
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