1．We're trying to think of ________ way out to solve the problem, but it's quite difficult to find one.
解析：该空泛指一种解决问题的方法，用不定冠词a。
答案：a
2．As a teacher, Monica is ________ success, but as a singer, she is ________ failure.
解析：句意：作为一位老师，莫妮卡是一个成功者，而作为一名歌手，她却是一个失败者。抽象名词success和failure在此指具体的人或事物(即抽象名词具体化)，前面应加不定冠词a。
答案：a; a
