4. ( 1 mark) A multiple choice test consists of 100 questions. If a student answers a question correctly, he will get 4 marks; if he answers a question wrongly, he will get -1 mark. He will get 0 marks for an unanswered question. Determine the number of different total marks of the test. (A total mark can be negative.)
(1 分) A multiple choice test consists of 100 questions. If a student answers a question correctly, he will get 4 marks; if he answers a question wrongly, he will get -1 mark. He will get 0 marks for an unanswered question. Determine the number of different total marks of the test. (A total mark can be negative.)
4. If a student answers 100 questions correctly, he gets 400 marks. If he answers 99 questions correctly, depending on whether he answers or does not answer the remaining question, he gets 396 or 395 marks. If a student answers 98 questions correctly, depending on whether he answers or does not answer the remaining 2 questions, he gets 390, 391, or 392 marks. Hence the total marks cannot be 389, 393, $394, 397, 398, 399$. If a student answers 97 (or fewer) questions correctly, he gets at most 388 marks, by adjusting the questions he answers wrongly, he gets everything possible "in between". Thus the number of different "total marks" $=100+401-6=\underline{\underline{495}}$.