Difference between revisions of "1999 AHSME Problems/Problem 10"
(Added solution, formatting) |
|||
| (One intermediate revision by one other user not shown) | |||
| Line 14: | Line 14: | ||
==Solution== | ==Solution== | ||
| − | 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 <math>\boxed{\ | + | 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 <math>\boxed{\textbf{(C)}}</math>. |
==See Also== | ==See Also== | ||
{{AHSME box|year=1999|num-b=9|num-a=11}} | {{AHSME box|year=1999|num-b=9|num-a=11}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 14:34, 5 July 2013
Problem
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?
Solution
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 
.
See Also
| 1999 AHSME (Problems • Answer Key • Resources) | ||
| 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. 
