Marks on Marks off
In a 90-question, multiple-choice test, a student gets
- for a correct answer
- for a question not attempted
- for an incorrect attempt.
The total score is the sum of all the marks to the 90 questions. How many total scores are possible?
For example, if a student attempts 70 questions, of which 60 are correct and 10 are incorrect, then the total score is
The answer is 445.
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Firstly, we look that every number from − 9 0 to 0 is possible. Next, Let m>0 be a natural number which we've to check weather could be possible total or not and 4 y is the smallest possible number greater than m such that y is also a natural number. For m to be a possible total, 4 y − m < = m − y Hence, every number from 1 to 8 7 × 4 = 3 4 8 is a possible total. For rest numbers left, check that the possible numbers reduce arithmetically 3+2+1.
Total Numbers possible= 9 1 + 3 4 8 + 6 = 445 Basically, it could be proved just as above that if + 4 , − 1 is marking scheme, total number of possible scores are 5(n-1)