/*Add a custom field to login form with an answer: */
function custom_login_question() {
    if ( isset( $_POST['log'] ) && ! empty( $_POST['log'] ) ) {
       if ( $_POST['custom_question'] != 'Answer to Question' ) {
            wp_die( 'Incorrect answer. Please try again.' );
        }
    }
}
add_action( 'wp_authenticate', 'custom_login_question' );

/*Write your custom question here */
function custom_question_field() {
    echo '<p>Write your Question here?<br />';
    echo '<input type="text" name="custom_question" value="" /></p>';
}
add_action( 'login_form', 'custom_question_field' );