In a 90-question, multiple-choice test, a student gets
+4 for a correct answer
0 for a question not attempted
-1 for an incorrect attempt.
The total score is the sum of all the marks to the 90 questions. How many total scores are possible?
Between -90 (all wrong) and 360 (all ok) there are
451 possible final marks, including zero(blank form)
Missing only one correct answer results in either 356(one question not answered) or 355(one wrong answer) - no way to get 357 358 or 359.
Similar considerations exlude possibility of 353, 354 and 350.
Deducting the 6 umreachable results one gets
451-6=445 (answer)
Deducting the "no-way" numbers - solution
