During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

1999 AHSME Problems/Problem 10


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?

$\textbf{(A)}\  \text{I is true.} \qquad \textbf{(B)}\  \text{I is false.}\qquad \textbf{(C)}\ \text{II is true.} \qquad \textbf{(D)}\ \text{III is true.} \qquad \textbf{(E)}\ \text{IV is false.}$


Three of the statements are correct, and only one digit is on the card. Thus, one of I and III are false. Therefore, II and IV must both be true. The answer is therefore $\boxed{\textbf{(C)}}$.

See Also

1999 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS