1999 AMC 12 Question 10 - thichhoctoan.com

Question 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?

$\mathrm{I}$ is true.
$\mathrm{I}$ is false.
$\mathrm{II}$ is true.
$\mathrm{III}$ is true.
$\mathrm{IV}$ is false.